Member, IEEE Marco Di Renzo
email: marco.direnzo@lss.supelec.fr

Member, IEEE Harald Haas

Fellow, IEEE Peter M Grant
email: peter.grant@ed.ac.uk

S Aissa

M Di

Renzo Is With L2s

Spatial Modulation for Multiple-Antenna Wireless Systems : A Survey

Keywords:

Multiple-antenna techniques constitute a key technology for modern wireless communications, which trade-off superior error performance and higher data rates for increased system complexity and cost. Among the many transmission principles that exploit multiple-antenna at either the transmitter, the receiver, or both, Spatial Modulation (SM) is a novel and recently proposed multipleantenna transmission technique which can offer, with a very low system complexity, improved data rates compared to Single-Input-Single-Output (SISO) systems, and robust error performance even in correlated channel environments. SM is an entirely new modulation concept that exploits the uniqueness and randomness properties of the wireless channel for communication. This is achieved by adopting a simple but effective coding mechanism that establishes a one-to-one mapping between blocks of information bits to be transmitted and the spatial positions of the transmit-antenna in the antenna-array. In this article, we summarize the latest research achievements and outline some relevant open research issues of this recently proposed transmission technique.

INTRODUCTION

The use of multiple-antenna for wireless communication systems has received an upsurge of research interest during the last decade, both in academia and industry [START_REF] Mietzner | Multiple-antenna techniques for wireless communications -A comprehensive literature survey[END_REF]. The multiple-antenna in Multiple-Input-Multiple-Output (MIMO) systems can be exploited in different ways to get multiplexing, diversity, or antenna gains. However, regardless of the use as spatial multiplexing, diversity, or smart antenna system, the main drawback of any MIMO scheme is an increase in complexity and cost. This is primarily due to three main reasons [START_REF] Mesleh | Spatial modulation[END_REF], [START_REF] Jeganathan | Space shift keying modulation for MIMO channels[END_REF]: i) Inter-Channel Interference (ICI), which is introduced by superimposing independent information sequences to be transmitted by multiple transmit-antenna; ii) Inter-Antenna Synchronization (IAS), which represents the baseline assumption for space-time and delay-diversity encoded methods; and iii) multiple Radio Frequency (RF) chains, which are needed to transmit all the signals simultaneously and are, in general, expensive and do not follow Moore's law. Furthermore, several transceiver designs require a number of receiveantenna greater than the number of transmit-antenna, which may limit, due to economical reasons on mobile handsets, their application to downlink settings. These issues make the practical implementation of MIMO schemes difficult, especially in mobile stations, as the necessary hardware and digital signal processing require significant energy. However, due to the important advantages of MIMO techniques it must be a clear research goal to develop new approaches for multiple-antenna transmission in order to mitigate the practical limitations while retaining the key advantages.

Following this ambitious research objective, Spatial Modulation (SM) [START_REF] Chau | Space modulation on wireless fading channels[END_REF]- [START_REF] Song | A channel hopping technique I: Theoretical studies on band efficiency and capacity[END_REF] has been recently proposed as a new modulation concept for MIMO systems, which aims at reducing the complexity and cost of multiple-antenna schemes without deteriorating the end-to-end system performance and still guaranteeing good data rates. More specifically, the lowcomplexity transceiver design and high spectral efficiency are simultaneously achieved by adopting the simple modulation and coding mechanisms in what follows:

1) Just one transmit-antenna is activated for data transmission at any signaling time instance. This allows SM to entirely avoid the ICI, to require no synchronization among the transmit-antenna, and to need only one RF chain for data transmission. This is in net contrast with respect to conventional MIMO schemes where the multiple-antenna are used to simultaneously transmit multiple data streams [START_REF] Mietzner | Multiple-antenna techniques for wireless communications -A comprehensive literature survey[END_REF]. Furthermore, this allows SM to exploit a low-complexity single-stream receiver design for optimal Maximum-Likelihood (ML) decoding.

2) The spatial position of each transmit-antenna in the antenna-array is used as a source of information. This is obtained by establishing a one-to-one mapping between each antenna index and a block of information bits to be transmitted, which results in a coding mechanism that can be called transmit-antenna index coded modulation. This allows SM to achieve a spatial multiplexing gain with respect to conventional single-antenna systems since part of the information is implicitly conveyed by the position of the transmit-antenna [START_REF] Mesleh | Spatial modulation[END_REF], [START_REF] Song | A channel hopping technique I: Theoretical studies on band efficiency and capacity[END_REF]. Accordingly, even though just one antenna is active, SM can also achieve high data throughput.

The two distinguishable features above make SM a fundamentally new physical layer transmission technique which combines, in a unique fashion, digital modulation, coding, and multiple-antenna to achieve high data rates and low-complexity implementations. In particular, the coding mechanism in 2) makes SM very different from, apparently similar, Transmit-Antenna Selection (TAS) or Spatial Division Multiplexing (SDM) schemes [START_REF] Mietzner | Multiple-antenna techniques for wireless communications -A comprehensive literature survey[END_REF]- [START_REF] Jeganathan | Space shift keying modulation for MIMO channels[END_REF].

Motivated by the appealing characteristics of SM for various practical applications, in this article we offer a careful overview of the most recent results related to this novel transmission technology and outline some important research issues and challenges that appear relevant to better aid the understanding and evaluation of its advantages and disadvantages with respect to other popular MIMO schemes.

Notation: In this article, N t and N r denote the number of transmit-and receive-antenna, respectively, M is the size of the complex signal-constellation diagram, and Rx denotes the received signal corrupted by additive noise. Furthermore, E m and N 0 denote the energy radiated by each transmit-antenna and the noise power at the receiver input, respectively.

For illustrative purposes, a Nakagami-m fading channel is considered [7, Ref. [START_REF] Di Renzo | Improving the performance of space shift keying (SSK) modulation via opportunistic power allocation[END_REF]], with Ω i and m i denoting the average power gain and the fading parameter of the i-th transmit-toreceive wireless link, and ρ i,j being the correlation coefficient between the i-th and j-th transmit-to-receive wireless links, respectively.

HOW IT WORKS

The basic idea of SM is to map a block of information bits into two information carrying units: 1) a symbol that is chosen from a complex signal-constellation diagram, and 2) a unique transmit-antenna index that is chosen from the set of transmit-antenna in the antenna-array (i.e., the so-called spatial-constellation diagram). The net result of embedding part of the information to be transmitted into the position of the transmit-antenna is a hybrid modulation and MIMO technique in which the modulated signals belong to a tridimensional constellation diagram, which jointly combines signal and spatial information. A simple example is shown in Fig. 1 [Callout to Fig. 1] for a linear antenna-array with N t = 4 and a QPSK (Quadrature Phase Shift Keying) modulation. When the information carrying unit is only the transmitantenna index, SM reduces to the so-called Space Shift Keying (SSK) modulation, which avoids any form of conventional modulation and trades-off receiver complexity for achievable data rates [START_REF] Jeganathan | Space shift keying modulation for MIMO channels[END_REF]. A simple example of the encoding and decoding processes are shown in Fig. 2 [Callout to Fig. 2] when N t = 4, N r = 1, and M = 2. If multiple-antenna are available at the receiver, they are exploited, under the assumption of ML-optimum detection, to get receive diversity gains via Maximal Ratio Combining (MRC).

The Transmitter

At the transmitter, the bitstream emitted by a binary source is divided into blocks containing log 2 (N t ) + log 2 (M ) bits each, with log 2 (N t ) and log 2 (M ) being the number of bits needed to identify a transmit-antenna in the antenna-array and a symbol in the signal-constellation diagram, respectively. Each block is then processed by a SM mapper, which splits each of them into two sub-blocks of log 2 (N t ) and log 2 (M ) bits each. The bits in the first subblock are used to select the antenna that is switched on for data transmission, while all other transmit-antenna are kept silent in the current signaling time interval. The bits in the second sub-block are used to choose a symbol in the signal-constellation diagram. In the example shown in Fig. 2 [Callout to Fig. 2], Tx2 will be activated for data transmission by the first two bits ("10") and a -1 binary signal will be sent from it out corresponding to the third bit ("1"). If SSK modulation instead of SM is considered, each transmit-antenna, when switched on, will send exactly the same signal out: the information is, thus, encoded only in the position within the antenna-array.

The Wireless Channel as a Modulation Unit

The signal emitted by the active antenna then goes through a generic wireless channel.

Owing to the different spatial positions occupied by the transmit-antenna in the antennaarray, the signal transmitted by each antenna will experience different propagation conditions due to the different interacting environmental objects along any transmit-to-receive wireless link. This represents the fundamental working principle of SM as is shown in Fig. 2 [Callout to Fig. 2], which depicts the signals impinging upon the single receive-antenna and corresponding to each of the four transmit-antenna. Let us emphasize that only one transmitantenna is active at any time instance, so only one signal will be actually received. The other antennas will radiate no power. It is apparent from this working mechanism that, especially for SSK modulation, the wireless channel plays the role of a "modulation unit", by introducing a distinct fingerprint that makes the signal emitted by distinct transmit-antenna distinguishable at the receiver. If the transmit-to-receive wireless links are not sufficiently different, data communication might be impossible since the signals emitted by the transmit-antenna will look approximately the same.

The Receiver

The receiver exploits the random modulation introduced by the wireless channel for signal detection. In particular, Fig. 2 [Callout to Fig. 2] shows a ML detector with perfect Channel State Information (CSI) at the receiver [START_REF] Jeganathan | Spatial modulation: Optimal detection and performance analysis[END_REF]. In order to detect the transmitted signal from the noisy received signal Rx, the receiver must know a priori (in practice this is obtained via channel estimation) the channel impulse response of all the transmit-to-receive wireless links.

In Fig. 2 [Callout to Fig. 2], the receiver must estimate four channel impulse responses (including the effects of the transmit-and receive-filters) since N t = 4 and N r = 1.

In general, N t N r channel impulse responses need to be estimated. According to the ML principle, the receiver computes the Euclidean distance between the received signal and the set of possible signals modulated by the wireless channel (including signal modulation if SM is used) and chooses the closest one. In general, M N t N r Euclidean distances need to be computed. This way, all the bits in the transmitted block can be decoded and the original bitstream recovered [START_REF] Jeganathan | Spatial modulation: Optimal detection and performance analysis[END_REF].

In summary, the working principle of SM is based on the following facts: i) the wireless environment naturally modulates the transmitted signal, ii) each transmit-to-receive wireless link has a different channel, and iii) the receiver employs the a priori channel knowledge to detect the transmitted signal. In other words, SM exploits the location-specific property of the wireless channel, i.e., the uniqueness of each transmit-to-receive wireless link, for communication. Accordingly, SM differs from Space Division Multiple Access (SDMA) [START_REF] Mietzner | Multiple-antenna techniques for wireless communications -A comprehensive literature survey[END_REF] as well, as in SDMA the differences in the channel impulse responses are exploited for multiple-access and are not used for data modulation.

ADVANTAGES AND DISADVANTAGES

In this section, we summarize the main advantages and disadvantages of SM with respect to other MIMO schemes.

Advantages 1) With respect to conventional MIMO solutions, such as V-BLAST (Vertical-Bell Laboratories Layered-Space-Time) and Alamouti space-time schemes [START_REF] Mietzner | Multiple-antenna techniques for wireless communications -A comprehensive literature survey[END_REF], SM entirely avoids ICI and IAS, and only requires a single RF chain at the transmitter. This is due to the working mechanism of SM: a single transmit-antenna is switched on for data transmission while all the other antennas are kept silent.

2) With respect to conventional single-antenna systems, the tridimensional constellation diagram inherent in SM introduces a multiplexing gain in the spatial domain that increases logarithmically with the number of transmit-antenna. This yields a net increase, by a factor of log 2 (N t ) and without any bandwidth expansion, of the spectral efficiency [START_REF] Mesleh | Spatial modulation[END_REF]. When regarded as a coding technique, SM provides a high spectrally-efficient code with an equivalent code rate greater than one [START_REF] Song | A channel hopping technique I: Theoretical studies on band efficiency and capacity[END_REF].

3) The receiver design is inherently simpler than the V-BLAST scheme since complicated interference cancelation algorithms are not required to cope with the ICI: unlike conventional spatial-multiplexing methods for MIMO systems, SM can attain ML decoding via a simple single-stream receiver. 4) SM can efficiently work if N r < N t since the receive-antenna are used to get only a diversity gain. In principle, a single receive-antenna is needed to exploit the SM paradigm: this makes SM suitable for downlink settings with low-complexity mobile units. 5) SM is inherently able to work in multiple-access scenarios: since different pairs of transmitters and receivers usually occupy different spatial positions, the channel impulse response of each pair of users will likely be statistically different from the others. If each intended receiver uses, for data detection, the set of channel impulse responses of all the transmitters (i.e., multi-user detection), several users might share the same wireless resources for communication. In other words, the wireless channel acts not just as a modulation unit, but also as a natural source of purely random signatures (i.e., the channel impulse responses) for multiple-access. An example of the suitability of the SM concept to a multi-user scenario is shown in Fig. 3 [Callout to Fig. 3] for a setup with 2 transmitters and 1 receiver. It can be noticed that, by using a multi-user detector with perfect CSI at the receiver, both users can attain almost the same performance as in a single-user scenario (i.e., the so-called single-user lower-bound). Let us emphasize here that the performance assessment of SM in an interference channel is an open research problem. 6) Thanks to the multiplexing gain achieved by exploiting the spatial domain to convey part of the information bits, SM provides a larger capacity than conventional lowcomplexity coding methods for MIMO systems, such as Space-Time-Block-Codes (STBCs) [START_REF] Yang | Information-guided channel-hopping for high data rate wireless communication[END_REF]. 7) SSK modulation can reduce further the receiver complexity since conventional modulation schemes are avoided. The price to be paid is a loss in the achievable data rate [START_REF] Mesleh | Spatial modulation[END_REF]. Disadvantages 1) At least two transmit-antenna are required to exploit the SM concept.

2) If the transmit-to-receive wireless links are not sufficiently different, the SM paradigm might not be used or might not yield adequate performance. This limitation is somehow similar to conventional spatial multiplexing techniques, which require a rich-scattering environment to guaranteeing a significant boost in the achievable data rate [START_REF] Mietzner | Multiple-antenna techniques for wireless communications -A comprehensive literature survey[END_REF].

3) The receiver requires perfect channel knowledge for data detection: this may pose complexity constraints on the channel estimation unit, as well as some overhead for channel estimation (N t N r channel impulse responses need to be estimated). In the spacetime coding literature, advanced techniques to avoid the knowledge of the wireless channel at the transmitter and at the receiver have been proposed, which represent an advanced extension of well-known differential encoding/decoding modulation schemes for single-antenna systems [1, Sec. III-H]. Since the wireless channel is the actual modulation unit in SM, the development of such receiver structures poses some design challenges.

4) When compared to, e.g., V-BLAST, SM can offer only a logarithmic (instead of linear) increase of the data rate with the number of transmit-antenna. This might limit SM to achieve very high spectral efficiencies for practical numbers of antennas at the transmitter.

The above list of advantages and disadvantages clearly indicates that SM appears to be a promising candidate for low-complexity MIMO implementations in asynchronous multipleaccess scenarios and for wireless applications that require moderately high data rates.

STATE-OF-THE-ART

In this section, we provide an up-to-date overview of the most important results available in the literature for SM.

Historical Perspective

Along the history, the "space modulation" concept has been introduced for different application scenarios and termed in different ways. The first published contribution is [START_REF] Chau | Space modulation on wireless fading channels[END_REF], where the approach was called SSK modulation and the idea of exploiting the differences in the signals received from different antennas to discriminate the transmitted information messages was described for the first time. However, in [START_REF] Chau | Space modulation on wireless fading channels[END_REF] more than one antenna could be switched on at any time instance, thus requiring IAS and multiple RF chains. It is worth mentioning that in [START_REF] Chau | Space modulation on wireless fading channels[END_REF] the term SSK modulation was adopted even though, similar to Fig. 2 [Callout to Fig. 2], two information carrying units were used. One year later, in [START_REF] Haas | Increasing spectral efficiency by data multiplexing using antennas arrays[END_REF] the principle of using the positions of the transmit-antenna as a source of information was exploited, for the first time, to accomplish a form of multiplexing in the spatial domain rather than, as usually done in Orthogonal Frequency-Division Multiplexing (OFDM) systems, in the frequency domain. For this reason, the spatial multiplexing method was called Orthogonal Spatial-Division Multiplexing (OSDM). Independently, in [START_REF] Song | A channel hopping technique I: Theoretical studies on band efficiency and capacity[END_REF] other authors proposed a modulation technique based on the same principle as in [START_REF] Chau | Space modulation on wireless fading channels[END_REF]. The method was called Channel-Hopping modulation (later re-named by the same authors as Information-Guided Channel-Hopping (IGCH) modulation [START_REF] Yang | Information-guided channel-hopping for high data rate wireless communication[END_REF]), and, unlike [START_REF] Chau | Space modulation on wireless fading channels[END_REF], it was applicable to any number of transmit-antenna and foresaw the activation of a single antenna for each transmission time-slot. The term SM has been coined only recently in [START_REF] Mesleh | Spatial modulation -A new low complexity spectral efficiency enhancing technique[END_REF].

Overview of Recent Results

In the recent period, the main research interest has been focused on the application of the SM concept to MIMO wireless systems, in order to quantify the performance difference with other popular MIMO schemes. The main aim of this section is to summarize the most significant results available to date. The overview follows a chronological order according to the publication date.

In [START_REF] Yang | Information-guided channel-hopping for high data rate wireless communication[END_REF], the authors have developed an information-theoretic framework to compute the outage and ergodic capacity of SM (therein called IGCH) over Rayleigh fading channels, and have shown that SM offers a capacity gain with respect to STBCs when the number of transmit-antenna in greater than two. Furthermore, a low-complexity decoding algorithm has been proposed.

In [START_REF] Mesleh | Spatial modulation[END_REF], the authors have proposed a simple MRC-based receiver design for SM, which independently detects the bits conveyed by the two information carrying units. The performance of this receiver has been analyzed over independent and identically distributed (i.i.d.) Rayleigh fading channels and compared to V-BLAST and Alamouti space-time schemes. Furthermore, simulation results have been obtained over more realistic propagation environments that take into account Rician fading, channel correlation, and antenna coupling. All the results have been obtained for an OFDM-based implementation of the SM concept. The results in [START_REF] Mesleh | Spatial modulation[END_REF] have clearly showcased that SM can offer better error performance than V-BLAST and Alamouti space-time schemes with a lower receiver complexity (in terms of complex operations), while still guaranteeing the same spectral efficiency (simulation results for 6 bits/s/Hz and 8 bits/s/Hz are shown in [START_REF] Mesleh | Spatial modulation[END_REF]). In particular, [START_REF] Mesleh | Spatial modulation[END_REF] has pointed out that the superiority of SM with respect to V-BLAST is due to the avoidance of the ICI at the receiver and the simplified design of the detector, while the main advantage of SM with respect to the Alamouti code stems from the possibility of reducing the modulation order by increasing the number of antennas at the transmitter, which allows SM to exploit the multiplexing gain inherent in the transmit-antenna index coded modulation concept. More specifically, for high bits/s/Hz reducing the modulation order allows SM to overcoming the higher transmit-diversity gain achieved by the Alamouti code. Depending on the requested bits/s/Hz, a crossing point might be expected between the error probability curves of SM and Alamouti code for high values of the received SNR (Signal-to-Noise-Ratio).

In [START_REF] Jeganathan | Spatial modulation: Optimal detection and performance analysis[END_REF], the authors have moved from [START_REF] Mesleh | Spatial modulation[END_REF] and have developed the ML-optimum receiver for SM. The comparison with the heuristic detector in [START_REF] Mesleh | Spatial modulation[END_REF] has revealed a performance gain of approximately 4 dB with a slight increase in the receiver complexity. Performance comparisons with V-BLAST and MRC schemes have revealed that SM can offer performance gains between 1.5 dB and 3 dB over i.i.d. Rayleigh fading channels.

In [START_REF] Jeganathan | Space shift keying modulation for MIMO channels[END_REF], the authors have comprehensively analyzed the performance of SSK modulation for uncoded and bit interleaved coded systems. It has been shown that the performance of SSK modulation degrades when increasing the number of transmit-antenna, while it gets better when increasing the number of receive-antenna. In particular, it has been analytically proved that, over i.i.d. Rayleigh fading channels, the diversity order of the system is equal to the number of receive-antenna. Performance comparisons with conventional multi-level modulation schemes have shown that, under uncorrelated channel conditions, SSK modulation can yield a better error probability than conventional modulation schemes with a high modulation order.

In [START_REF] Jeganathan | Generalized space shift keying modulation for MIMO channels[END_REF], the authors have proposed an improved version of the SSK modulation concept, by allowing, similar to [START_REF] Chau | Space modulation on wireless fading channels[END_REF], a sub-set of transmit-antenna (not just one) to be switched on for data transmission at any time instance. The main contribution of this paper is the optimization criterion to design the spatial-constellation diagram, i.e., the set of antennas to be switched on and kept silent, by minimizing the error probability. The proposed method offers performance similar to SM but with lower complexity. However, the price to be paid to implement this scheme is the need of IAS and multiple RF chains.

In [START_REF] Alshamali | Performance of spatial modulation in correlated and uncorrelated Nakagami fading channel[END_REF], the authors have extended to correlated Nakagami-m fading channels the analytical framework to compute the Average Bit Error Probability (ABEP) of the heuristic detector in [START_REF] Mesleh | Spatial modulation[END_REF]. Furthermore, in [START_REF] Hwang | Soft-output ML detector for spatial modulation OFDM systems[END_REF] the ML-optimum receiver based on hard-decision decoding [START_REF] Jeganathan | Spatial modulation: Optimal detection and performance analysis[END_REF] has been generalized by using a ML-optimum soft-decision decoding algorithm. It has been shown that soft-decision decoding can improve the performance of approximately 3 dB if compared to hard-decision decoding.

Finally, in [START_REF] Mesleh | Trellis coded spatial modulation[END_REF] the authors have proposed a new modulation concept that aims at reducing the effect of channel correlation on the performance of SM. As a matter of fact, if, e.g., due to closely-spaced radiating elements, the transmit-to-receive wireless links experience channel correlation, the detector might be unable to distinguish the different transmit-antenna since they will appear almost the same at the receiver. The proposed scheme is called Trellis Coded Spatial Modulation (TCSM). It exploits convolutional encoding and Maximum-Likelihood Sequence Estimation (MLSE) decoding to increase the free distance between sequences of spatial-constellation points. Simulation results in [START_REF] Mesleh | Trellis coded spatial modulation[END_REF] have indicated that TCSM can provide better performance than SM and V-BLAST schemes over correlated Rician fading channels, while still guaranteeing the same spectral efficiency.

THE CHALLENGES AHEAD

Owing to its peculiar working principle, SM turns out to be a very new transmission technique for data communication over wireless channels. Research in this field is still at its infancy, and fundamental issues need to be still addressed to assess the possibilities of exploitation of this technology over realistic propagation environments and for practical operating conditions. This section aims at summarizing some research problems that seem of paramount importance in this area.

Key Role Played by the Wireless Channel

The statistical properties of the wireless channel play a fundamental role to enable the application of SM to MIMO wireless systems: SM might offer different error probabilities and spectral efficiencies depending on the capability of the wireless channel to make the signals emitted by a transmit-antenna distinguishable from the others. The results available in the literature so far have mainly analyzed the system performance in simplified fading conditions, which can capture only in part the unique characteristics of SM. The basic understanding of the performance and achievable rates offered by SM over more realistic fading scenarios appears instrumental to assess its potential, possibility of exploitation, and adaptive optimization.

In order to substantiate the importance of the wireless channel, which is the actual modulation unit in SM, we have investigated in Fig. 4 [Callout to Fig. 4] and Fig. 5 [Callout to Fig. 5] the ABEP of a simple SSK modulation scheme with N t = 2 and N r = 1. A Nakagami-m fading channel [7, Ref. [START_REF] Di Renzo | Improving the performance of space shift keying (SSK) modulation via opportunistic power allocation[END_REF]] with ML-optimum detection has been considered. The following important trends can be observed: i) the performance of SM is significantly affected by different fading conditions; ii) SM offers better performance in the presence of power imbalance (i.e., the channel power gains Ω 1 , Ω 2 are different) between the wireless links: in this scenario the links are inherently more distinguishable from one another, and, since the effective SNR at the receiver is given by the difference of the instantaneous channel gains [START_REF] Jeganathan | Spatial modulation: Optimal detection and performance analysis[END_REF], the ABEP gets better; iii) by comparing the curves in Fig. 4 [Callout to Fig. 4] (independent fading) and Fig. 5 [Callout to Fig. 5] (correlated fading) we note that channel correlation can improve the ABEP when the wireless links are unbalanced: in this scenario, the average power gap between the wireless links (i.e., Ω 1 -Ω 2 ) can unlikely be offset by channel fading because the wireless links are subject to correlated fluctuations. On the contrary, if the wireless links are balanced, the ABEP degrades for increasing values of the correlation coefficient, as expected; iv) different values of the fading parameter m, which gives the amount of fading (AF = 1/m ) of each wireless link [7, Ref. [START_REF] Di Renzo | Improving the performance of space shift keying (SSK) modulation via opportunistic power allocation[END_REF]], can yield a substantially different ABEP in the presence of power imbalance; and v) by looking into all the results in Fig. 4 [Callout to Fig. 4] and Fig. 5 [Callout to Fig. 5] we can argue that the best propagation scenario for SM is given by correlated and non-identically distributed wireless links, while the worst one arises when the wireless links are correlated but identically distributed. All these results point out a fundamentally different behavior with respect to conventional MIMO schemes [START_REF] Mietzner | Multiple-antenna techniques for wireless communications -A comprehensive literature survey[END_REF]: i) channel correlation can improve the ABEP by keeping the average power gap almost constant regardless of the fading fluctuations, and ii) power imbalance can assist in making the wireless links more distinguishable from one another. These intriguing results clearly highlight that more emphasis should be given to understanding the performance of SM over realistic fading conditions. Further results, supported by analytical derivation, about the performance of SM in fading channels are in available in [START_REF] Di Renzo | Improving the performance of space shift keying (SSK) modulation via opportunistic power allocation[END_REF]Ref. [7]].

Opportunistic Power Allocation Methods

The results in Fig. 4 [Callout to Fig. 4] and Fig. 5 [Callout to Fig. 5] clearly establish that the ABEP of SM can substantially change for different fading conditions. All these results are obtained by assuming that each transmit-antenna, when switched on, radiates the same power. However, it can be easily shown that power imbalance between the wireless links can be artificially created by allowing the transmit-antenna to emit a different power while still transmitting the same signal according to the SM principle. This way, a wireless environment with identically distributed fading could be made equivalent, at the receiver, to a nonidentically distributed fading scenario, thus yielding better performance. This consideration allows for opportunistic power allocation mechanisms that could be used to allocate the available power at the transmitter by either emphasizing or de-emphasizing, according to the actual fading conditions, the propagation modes corresponding to the transmit-to-receive wireless links. This approach requires a feedback channel to make available the required CSI at the transmitter. However, this method may yield a substantial reduction in terms of minimum SNR required at the receiver to satisfy some quality of service requirements. This could potentially offer important possibilities for green radio applications. Initial results confirming the potential benefits of opportunistic power allocation methods for improving the performance of SM can be found in [START_REF] Di Renzo | Improving the performance of space shift keying (SSK) modulation via opportunistic power allocation[END_REF].

Receiver Complexity vs. Achievable Performance

The possibility to exploit the paradigm of SM is conditioned upon making available at the receiver the channel impulse response of all the transmit-to-receive wireless links (see Fig. 2 [Callout to Fig. 2]). All the performance studies and receiver designs available for SM have implicitly retained this assumption so far. However, the perfect estimation of such CSI might be impractical due to the complexity of the channel estimator and the required overhead for channel estimation. It is widely accepted that in some mobile scenarios the channel fading might be sufficiently rapid to preclude the availability of the perfect knowledge of the channel phase. In Fig. 6 [Callout to Fig. 6], we have compared the performance of SSK modulation by considering two ML-optimum receivers with Full CSI (F-CSI) and Partial CSI (P-CSI) [7, Ref. [START_REF] Di Renzo | Improving the performance of space shift keying (SSK) modulation via opportunistic power allocation[END_REF]]. In particular, in the latter case the receiver is blind to the channel phase. The results in Fig. 6 [Callout to Fig. 6] show, for various system setups, an unexpected high performance loss when the receiver has only P-CSI. This result showcases the important trade-off between receiver performance and complexity of the channel estimator. Accordingly, the development of optimal and sub-optimal receiver schemes with good performance, moderate complexity, and low a priori channel knowledge is expected to play an important role for the successful exploitation of the SM concept in a wireless context, especially in high dynamic environments.

Channel-Aware Coding Methods

With respect to conventional modulation schemes in which the set of signals to be transmitted belong to a fixed and known signal space, in SM the effective constellation space is purely random and highly dependent on the channel characteristics. Over time, several techniques have been proposed to design optimal coding mechanisms for conventional modulation schemes with the aim of improving the end-to-end performance for channels impaired by additive white Gaussian noise and fading. Owing to the implicit role as a modulation unit played by the wireless channel, in SM the development of channel-aware coding methods that aim either at the maximization of the channel capacity or at the minimization of the error probability appears an open and challenging research issue. Solutions with either full or partial channel knowledge are of interest to trade-off complexity for performance.

Development of Novel Communication-and Information-Theoretic Tools for Performance Analysis and Optimization

By carefully looking at all the performance results available in the literature so far, it follows that frameworks for the analysis and design of SM exist mainly for the simple and not very realistic propagation scenario with i.i.d. Rayleigh fading. However, the results in Fig. 4 [Callout to Fig. 4] and Fig. 5 [Callout to Fig. 5] clearly show that slightly different channel conditions can yield substantially different performance. Owing to the particular characteristics of both the transmitter and the receiver along with the role as a modulation unit played by the wireless channel, novel specific communication-and information-theoretic frameworks seem to be required to understand and analyze the performance of this new technology over fading channels. These new tools appear important for a systematic system optimization based on either capacity or error probability requirements. An interesting information-theoretic framework for computing the capacity of SM over Rayleigh fading channels has been recently proposed in [START_REF] Yang | Information-guided channel-hopping for high data rate wireless communication[END_REF].

Design of SM-based Schemes with Transmit-Diversity Gains

Looking into the various forms of SM proposed so far, it can be readily argued that all of them provide only receive diversity gains, while the transmit-antenna are used only for enabling data transmission. However, it is well-known that various MIMO schemes that can guarantee transmit diversity gains exist in the literature [START_REF] Mietzner | Multiple-antenna techniques for wireless communications -A comprehensive literature survey[END_REF]. It is believed that the development of novel MIMO schemes based on the SM principle and offering diversity gains by exploiting the antennas at the transmitter may find remarkable applications in downlink settings with low-complexity and compact mobile units.

Design of SM-based Schemes for an Arbitrary Number of Transmit-Antenna

Unlike conventional MIMO schemes, SM requires that the number of transmit-antenna is a power of two. Thus, only 2, 4, 8, 16, etc. antennas at the transmitter can be used. Since in SM the spatial multiplexing gain increases logarithmically with the transmit-antenna, this fact might pose practical limits on the bit rates achievable by small-size portable devices. In fact, especially for these systems, there is a limit, in cost and physical space, on the maximum number of antennas (and so on the achievable multiplexing gain) that can be installed on them. For example, it might not be possible to install 8 antennas in such devices, while 5 or 6 antennas might still be a cost-effective option. However, SM will allow us to use, in practice, only 4 antennas. The development of flexible SM schemes accommodating an arbitrary number of antennas at the transmitter seem of practical relevance to offer the desired degrees of freedom for trading-off achievable performance and rates for system complexity and cost. Initial results about this research challenge have been reported in [START_REF] Serafimovski | Fractional bit encoded spatial modulation (FBE-SM)[END_REF].

Ultra Wide Band (UWB-) Assisted Design of SM

In [START_REF] Jeganathan | Space shift keying modulation for MIMO channels[END_REF], it has been recently argued that UWB technology could be an important enabler for SM. We believe that the integration of SM and UWB technologies in a common framework might be a very interesting research area, and pulse-based transmission methods could significantly improve the performance and offer further degrees of freedom for system optimization.

Application of SM to Multi-Hop and Cooperative Networks: Can SM go Distributed?

It is well-known that the benefits of multiple-antenna systems can be applied to distributed settings, where multiple transmitting or receiving nodes cooperate in terms of a joint transmission/reception strategy. These systems are known as virtual MIMO or cooperative networks.

To date, the paradigm of SM has been applied to MIMO schemes where the antennas are electrically connected, while the application of this principle to distributed settings has not yet received sufficient attention. We believe that the implicit role as a "compressing unit" (i.e., a block of bits is compressed into a single antenna index) realized by the SM mapper in Fig. 2 [Callout to Fig. 2] may be exploited in distributed MIMO settings to overcome the wellknown spectral efficiency loss of some conventional cooperative protocols. The application of SM to virtual MIMO systems and the understanding of its potential in distributed networks seem a very intriguing area of research. A first step towards the application of SM to relay networks has been achieved in [START_REF] Yang | Information-guided relay selection for high throughput in half-duplex relay channels[END_REF], where the author has introduced a new Information-Guided Relay-Selection (IGRS) scheme and has shown, via a capacity analysis, its improved performance with respect to state-of-the-art solutions.

Experimental Assessment: From Theory to Practice

Although numerical simulations and theoretical analysis can give an important and often reliable taste of the performance offered by novel transmission technologies, it is believed that only practical experiences and testbed validations can yield definitive answers about the achievable performance in real-world devices. In order to fully capture the benefits of SM in real-world settings, we are firmly persuaded that research on SM should evolve from pure theoretical studies to more practical experimental assessments.

CONCLUSION This article has summarized recent research achievements and open research issues of a novel transmission technology named SM. SM is an entirely new physical layer transmission

technique, which combines digital modulation, coding, and multiple-antenna transmission in a unique fashion, and exploits the location-specific property of the wireless channel for communication. This enables the position of each transmit-antenna in the antenna-array to be used as an additional dimension for conveying information. Recent results have indicated that SM can be a promising candidate for low-complexity MIMO implementations. However, SM is still a young-born research field and several issues need to be addressed to fully understand its potential and limitations in practical and realistic propagation environments.

Fig. 1 .

 1 Fig. 1. Tridimensional constellation diagram of SM: each spatial-constellation point (i.e., the antenna index) defines an independent complex plane of signal-constellation points. For illustration purposes, only two of such planes are shown in the figure for: i) N t = 4, and ii) M = 4. Legend: i) Re = real axis of the signal-constellation diagram, and ii) Im = imaginary axis of the signal-constellation diagram.

Fig. 2 .

 2 Fig. 2. SM: How it works. Setup: i) Nt = 4, ii) Nr = 1, and ii) M = 2. Legend: i) BPSK = Binary Phase Shift Keying, ii) CSI = Channel State Information, and iii) distance (x, y) = Euclidean distance between signals x and y [7, Ref. [7]].

Fig. 3 .Ω 1

 31 Fig.3. Average Bit Error Probability (ABEP) against E m /N 0 for a scenario with 2 transmitters and 1 receiver (i.e., multi-user setup): i) each transmitter has N t = 2, ii) the receiver has N r = 1, iii) the channel of both users is uncorrelated and identically distributed according to a Nakagami-m distribution with parameters (Ω 1 , m 1 ), (Ω 2 , m 2 ) with m 1 = m 2 = 1 and Ω1 = Ω2 = 1 [7, Ref.[START_REF] Di Renzo | Improving the performance of space shift keying (SSK) modulation via opportunistic power allocation[END_REF]]. A multi-user ML-optimum receiver is considered[START_REF] Mietzner | Multiple-antenna techniques for wireless communications -A comprehensive literature survey[END_REF].

Fig. 4 .

 4 Fig. 4. Average Bit Error Probability (ABEP) againstE m /N 0 for: i) N t = 2, ii) N r = 1, iii) uncorrelated Nakagami-m fading with parameters (Ω 1 , m 1 ), (Ω 2 , m 2 ) [7, Ref. [7]], and iv) m = m 1 = m 2 . The ML-optimum receiver in [7, Ref.[START_REF] Di Renzo | Improving the performance of space shift keying (SSK) modulation via opportunistic power allocation[END_REF]],[START_REF] Jeganathan | Spatial modulation: Optimal detection and performance analysis[END_REF] is considered.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Average Bit Error Probability (ABEP) againstE m /N 0 for: i) N t = 2, ii) N r = 1, iii) correlated Nakagami-m fading with parameters (Ω 1 , m 1 ), (Ω 2 , m 2 ) and correlation coefficient ρ = ρ 1,2 = ρ 2,1 = 0.75 [7, Ref. [7]], and iv) m = m1 = m2. The ML-optimum receiver in [7, Ref.[START_REF] Di Renzo | Improving the performance of space shift keying (SSK) modulation via opportunistic power allocation[END_REF]],[START_REF] Jeganathan | Spatial modulation: Optimal detection and performance analysis[END_REF] is considered.

ACKNOWLEDGMENT This work is supported by the research grant EP/G011788/1 "Spatial Modulation" awarded by the Engineering and Physical Sciences Research Council (EPSRC) in the United Kingdom. Marco Di Renzo acknowledges support of the Laboratory of Signals and Systems (L2S) under the research project "Jeunes Chercheurs". Harald Haas acknowledges the Funding Council support of his position within the Edinburgh Research Partnership in Engineering and Mathematics between the University of Edinburgh and Heriot Watt University.

Furthermore, the authors wish to thank an anonymous reviewer for pointing out the IGCH concept for MIMO systems (references [6], [9], [16]) and its similarity to SM.


Nikola Serafimovski
email: n.serafimovski@ed.ac.uk

Sinan Sinanović
email: s.sinanovic@ed.ac.uk

Abdelhamid Younis
email: a.younis@ed.ac.uk

Marco Di Renzo
email: marco.direnzo@lss.supelec.fr

Harald Haas
email: h.haas@ed.ac.uk

2-User Multiple Access Spatial Modulation

Spatial modulation (SM) is a recently proposed approach to multiple-input-multiple-output (MIMO) systems which entirely avoids inter-channel interference (ICI) and requires no synchronisation between the transmit antennas, while achieving a spatial multiplexing gain. SM allows the system designer to freely trade off the number of transmit antennas with the signal constellation. Additionally, the number of transmit antennas is independent from the number of receive antennas which is an advantage over other multiplexing MIMO schemes. Most contributions thus far, however, have only addressed SM aspects for a point-to-point communication systems, i.e. the single-user scenario. In this work we seek to characterise the behaviour of SM in the interference limited scenario. The proposed maximumlikelihood (ML) detector can successfully decode incoming data from multiple sources in an interference limited scenario and does not suffer from the near-far problem.

I. INTRODUCTION

Multiple-antenna systems are fast becoming a key technology for modern wireless systems. They offer improved error performance and higher data rates, at the expense of increased complexity and power consumption [START_REF] Mietzner | Multiple-antenna techniques for wireless communicationsa comprehensive literature survey[END_REF]. Spatial modulation (SM) is a recently proposed approach to multiple-inputmultiple-output (MIMO) systems which entirely avoids interchannel interference (ICI) and requires no synchronisation between the transmit antennas, while achieving a spatial multiplexing gain [START_REF] Mesleh | Interchannel Interference Avoidance in MIMO Transmission by Exploiting Spatial Information[END_REF]. A spatial multiplexing gain is achieved by mapping a block of information bits into a constellation point in the signal and spatial domains [START_REF] Mesleh | Spatial Modulation[END_REF]. In SM, the number of information bits, ℓ, encoded in the spatial domain can be related to the number of transmit antennas N t as N t = 2 ℓ . This means that the number of transmit antennas must be a power of two unless fractional bit encoding is used [START_REF] Serafimovski | Fractional Bit Encoded Spatial Modulation (FBE-SM)[END_REF]. Additionally, compared to other MIMO schemes, the spatial multiplexing gain i.e. the number of transmit antennas, is independent of the number of receive antennas. This offers the flexibility to trade off the number of transmit antennas with the modulation order in the signal domain to meet the desired data rate without regard for the number of receive antennas. It should also be noted that SM is shown to outperform other MIMO schemes in terms of bit-error-ratio (BER) [START_REF] Mesleh | Spatial Modulation[END_REF].

A number of papers are available in the literature which are aimed at understanding and improving the performance of SM in various scenarios. Trellis coding on the transmit antenna is proposed in [START_REF] Mesleh | Trellis Coded Spatial Modulation[END_REF], a reduced complexity decoder is given in [START_REF] Younis | Reduced Complexity Sphere Decoder for Spatial Modulation Detection Receivers[END_REF] and the performance of SM over a wide range of channels is presented in [START_REF] Di Renzo | Performance analysis of spatial modulation[END_REF]. The optimal detector is known with and without channel state information at the receiver in [START_REF] Jeganathan | Spatial Modulation: Optimal Detection and Performance Analysis[END_REF][START_REF] Hwang | Soft-Output ML Detector for Spatial Modulation OFDM Systems[END_REF][START_REF] Di Renzo | Spatial modulation with partial-csi at the receiver: optimal detector and performance evaluation[END_REF]. The optimal power allocation problem for a 2 transmit with 1 receive antenna system is solved in closed form in [START_REF]Improving the performance of space shift keying (SSK) modulation via opportunistic power allocation[END_REF] and the performance of SM in correlated fading channels is considered in [START_REF] Handte | BER analysis and optimization of generalized spatial modulation in correlated fading channels[END_REF]. Recent work has also shown that SM can be combined with space-time block codes to attain spectral efficiency gains [START_REF] Basar | Space-time block coded spatial modulation[END_REF]. SM has also been applied to relaying systems in [START_REF] Serafimovski | Dualhop Spatial Modulation (Dh-SM)[END_REF] where it exhibits significant signal-to-noise-ratio (SNR) gains when compared to non-cooperative decode and forward.

Most contributions thus far, however, have only addressed SM aspects for a point-to-point communication systems, i.e. the single-user scenario. These scenarios include the application of SM in traditional orthogonal access systems such as frequency division multiple access (FDMA), time division multiple access (TDMA) or orthogonal frequency division multiple access (OFDMA) where co-channel interference is managed by ensuring orthogonal transmissions by all nodes in the system. A notable exception is given in [START_REF] Di Renzo | On the performance of ssk modulation over multiple-access rayleigh fading channels[END_REF], where the authors focus their analysis on a limited two user scenario employing only space-shift-keying (SSK). It should be noted, that SSK is similar to SM in that the antenna index is used for data transmission, but instead of a full signal-symbol only a reference signal is sent to enable channel estimation at the receiver.

In this work we seek to characterise the behaviour of SM in the interference limited scenario. In particular, we propose a maximum-likelihood (ML) detector which can successfully decode incoming data in the case of simultaneous transmission and does not suffer from the near-far problem, i.e. the detector can successfully decode data from a user with a lower signalto-noise-ratio (SNR). The proposed jointly optimum multi-user detector minimises the BER for all users and does not suffer from the near-far problem.

The remainder of this work is organized as follows. In Section II, the system and channel models are introduced. In Section III, the performance of SM in the multiple access scenario is characterised and the analytical modelling for the multi-user detector is proposed. Section IV provides numerical and simulation results to substantiate the accuracy of the analytical framework developed. In Section V, we summarise and conclude the work.

II. SYSTEM MODEL

The basic idea of SM is to map blocks of information bits into two information carrying units [START_REF] Mesleh | Spatial Modulation[END_REF]: i) a symbol, chosen from a complex signal-constellation diagram, and ii) a unique transmit-antenna, chosen from the set of transmit-antennas in the antenna-array, i.e. the spatial-constellation. The general SM constellation point is thus a combination of a signalconstellation point and a spatial-constellation point. The SM constellation diagram is presented in Fig. 1. Fig. 1. A transmission of four bits is assumed. The first two bits from right to left define the spatial-constellation point identifying the active antenna, while the remaining two bits determine the signal-constellation point that will be transmitted. This scenario means that a single SM constellation point carries four information bits.

In the following work we assume a three node scenario as shown in Fig. 2 where we seek to characterise the behaviour of SM during simultaneous transmission i.e. in the presence of co-channel interference. We assume that the two transmit nodes, denoted as User1, node (U 1 ), and User2, node (U 2 ), in Fig. 2, transmit simultaneously to the receiver on the same time-frequency slot. Each node broadcasts a signal constellation symbol, x, from one of its available antennas.

The received signal is given by:

y j = E m σ 2 (U1) h i (U 1 ) j x (U1) + E m σ 2 (U2) h k (U 2 ) j x (U2) + η (1) where:
• E m is the average energy per symbol for both nodes,

• i and k are the indices of the transmit antennas from nodes 1 and 2 respectively, • j is the index of the receive antenna from a total of N r available,

Receiver User1 User2

Fig. 2. Spatial modulation with simultaneous transmission. The receive cannot distinguish which is the desired and which is the interferencing user. Therefore, it must treat each users as its intended user.

• σ 2 (U1) and σ 2 (U2) are the channel attenuation coefficients on the U 1 to receiver and U 2 to receiver links in Fig. 2 respectively,

• h i (U 1 ) j and h k (U 2 ) j are the fast fading channel coefficients of the link between the active antennas (i, k) and the receiving antenna j, and • η, is a complex normal random variable with zero mean and variance N o , CN (0, N o ), and represents the additive white Gaussian noise (AWGN) at the receiver. We note that all bold notations indicate vector notations. We now look at the analytical formulation of the system.

III. ANALYTICAL MODELLING

In this section, we develop a ML detector for use in the presence of co-channel interference. The detector computes the Euclidean distance between the received vector signal ȳ and the set of all possible received signals, selecting the closest one. The mathematical formulation of the ML detector used in the system is given in [START_REF] Mesleh | Interchannel Interference Avoidance in MIMO Transmission by Exploiting Spatial Information[END_REF]. We note that this formulation is valid for any channel vectors and any transmitted symbols. In particular, if the channels are correlated i.e. non-orthogonal, then it will be more difficult for the receiver to distinguish the individual antennas used in the transmission, which will result in an increase of the BER.

Starting from the system model presented in Section II, the decoded pair (x est , n t ) (ξ) , formed from the estimated symbol x est emitted from antenna n t on node ξ, where ξ ∈ {(U 1 ), (U 2 )}, is given by:

(x est , n t ) (U1) , (x est , n t ) (U2) = argmin      ȳ - u∈{(U1), (U2)} x (u) h n (u) t 2 F      (2) x (u) ∈ X (u) n (u) t ∈ {1 . . . N (u)
t } X (u) is the set of all possible signal constellation points for node u with M (u) number of elements, N (u) t is the number of available transmit antennas on node u and || • || F is the Frobenius norm.

From here we can use techniques base on the union bound to describe the behaviour of the interference aware SM detector in the high SNR regions. The union bound for the interference aware SM detector, which estimates the average bit-errorratio (ABER) for node ξ, can be expressed as given in [START_REF] Mesleh | Spatial Modulation[END_REF] where N ξ (b, b) = N ξ (n t , nt ) + N ξ (x, x). N ξ (n t , nt ) denotes the Hamming distance between the binary representations of the antenna indices n t and nt on node ξ. Similarly, N ξ (x, x) denotes the Hamming distance between the binary representations of the symbols x and x on node ξ.

We define PEP x (U1),(U2) , n (U1),(U2) t

, x(U1),(U2) , n(U1),(U2) t to be the pairwise error probability between the symbol x (U1),(U2) emitted from antennas n (U1),(U2) t being detected as symbol x(U1),(U2) emitted by antenna n(U1),(U2) t . It should be noted that the pairs, x (U1),(U2) , n (U1),(U2) t and

x(U1),(U2) , n(U1),(U2) t , come from the set of

ABER ξ ≤ M (U 1 ) N (U 1 ) t x (U1),(U2) , n (U1),(U2) t M (U 2 ) N (U 2 ) t x(U1),(U2) , n(U1),(U2) t N ξ (b, b) log 2 M (ξ) N (ξ) t E H PEP x (U1),(U2) , n (U1),(U2) t , x(U1),(U2) , n(U1),(U2) t M (U1) N (U1) t M (U2) N (U2) t . (3) PEP (•) = Q E m 2N o σ (U1) h n (U 1 ) t x (U1) -h n(U 1 ) t x(U1) + σ (U2) h n (U 2 ) t x (U2) -h n(U 2 ) t x (U2) 2 (4)
all possible symbol-antenna pairs for both nodes, i.e.

x (U1),(U2) , n

(U1),(U2) t = h n (U 1 ) t x (U1) + h n (U 2 ) t
x (U2) and

x(U1),(U2) , n(U1),(U2)

t = h n(U 1 ) t x(U1) + h n(U 2 ) t x(U2) . E H [•]
represents the expectation of the system with respect to the channel and

Q(ω) = 1 √ 2π ∞ ω exp -t 2 dt.
The ABER for node ξ is shown in [START_REF] Mesleh | Spatial Modulation[END_REF], where the pairwise error probability is given in [START_REF] Serafimovski | Fractional Bit Encoded Spatial Modulation (FBE-SM)[END_REF]. Due to space constraints, we omit the derivation of (4). We note that thus far no assumptions have been made as to the distribution of the channel.

If we consider a Rayleigh fading channel, then we can derive the closed form solution for E H [PEP (•)] in (3) by employing the solution to [16, eq. 62]. We note that by assuming a Rayleigh fading channel, the argument within (4) can be represented as the summation of 2N r squared Gaussian random variables, with zero mean and variance equal to 1, which means that they can be described by a central Chi-squared distribution with 2N r degrees of freedom and a probability density function of:

p K (κ) = 1 2 Nr (N r -1)! κ Nr-1 exp (-κ/2).
The result for E H [PEP (•)] is given as:

E H [PEP (•)] = f (c) Nr Nr-1 r=0 N r -1 + r r (1 -f (c)) r (5) such that f (c) = 1 2 1 - c 1 + c where c = E m 4N o u∈{U1,U2} σ 2 (u) λ (u) (6)
which is a quarter of the received SNR at the receiver, and

λ (u) =      |x (u) | 2 + |x (u) | 2 n (u) t = n(u) t , |x (u) -x(u) | 2 n (u) t = n(u) t , 0 n (u) t = n(u) t and x (u) = x(u) .

IV. SIMULATION RESULTS AND DISCUSSION

In this section we aim to show that the interference aware detector proposed in (2) can successfully decode the incoming streams for the two users. Numerical results are shown which demonstrate that (3) provides a tight upper bound for the BER of the interference aware detector at high SNR. The aim of this work is to develop and test a viable multi-user detector for SM.

A. Simulation Setup

A frequency-flat Rayleigh fading channel with no correlation between the transmitting antennas and AWGN is assumed. Perfect channel state information (CSI) is assumed at the receiving node, with no CSI at the transmitter. Only one of the available transmit antennas for each node is active at any transmitting instance. In theory each user independently decides the number of transmit antennas and the symbol modulation it uses. For use in the simulation we assume each node has the same number of transmit antennas as well as the same spectral efficiency target. In each figure, for each user, there are three presented results: i) the simulation results for the interference aware detector, denoted by Sim(Userξ), ii) the theoretical results from (3) using ( 5), denoted by Analytical(Userξ), and iii) the single-user-lower-bound (SULB), denoted by SULB(Userξ). We define SULB as the system performance in a single-user-single-receiver scenario where the system performance is determined purely by its SNR, defined as Em 2No . The theory behind SULB is well developed in [START_REF] Di Renzo | Performance analysis of spatial modulation[END_REF].

B. Results

Fig. 3 and Fig. 4 clearly demonstrate that the analytical model presented in (3) represents a tight upper bound for the system in the high SNR region. Additionally, we can see that the system with the lowest SNR has similar performance to that predicted by its SULB. It should be noted that this is not the case for the node with the better SNR. This difference in performance of the two systems can be explained by looking at the error contribution of each element from each node in the analytical prediction.

We define two sets, one for every pairwise possibility within a particular user, given by Ω (U1) in ( 7) for User1. We can similarly define the set Ω (U2) for User2. If we now consider ( 3) and ( 4) we see that the overall error for each user is inevitably influenced by the errors from the other user. However, since each element from Ω (U1) is associated with the full set of possible errors from Ω (U2) , then all erroneous terms from Ω (U1) will 'carry' the full error from the terms in Ω (U2) and vice versa. This means that besides the pairwise error associated with the mis-detection of the antenna-symbol combination of User1 alone, the error term for User1 is increased by the pairwise error of User2 and vice versa, i.e. the overall error for node 1 has card Ω (U1) -M (U1) N (U1) t

card Ω (U2) number of error terms where card{•} denotes the cardinality of a given set.

We further note that each pairwise error from the user with the worse SNR makes a bigger contribution to the overall BER than the pairwise error from the node with the better SNR. This can be shown if we look at the Euclidean distance between the different pairwise errors. We classify a pairwise error if the Euclidean distance between the symbol-antenna pairs being tested is greater than zero. In particular, the greater the Euclidean distance becomes, the smaller the error from that term. From (4) it is clear that the pairwise error depends on the SNR as well as the Euclidean distance. It thus follows that given pairwise error terms with the same Euclidean distance, the worse the SNR is for each term, the greater the absolute pairwise error. Considering the above, it is clear that the node with the better channel gain never performs close to its SULB, while the node with the worse channel gain does perform near its SULB. Fig. 3 and Fig. 4 demonstrate this behaviour. The gap in performance with respect to the SULB for the main contributor to the overall user error, i.e. the node with the lower SNR, effectively increases the BER of the node with the higher SNR.

To further elaborate, we note that the difference between the simulation BER curves of the two nodes when N r = 2 and N r = 3 increases as more receive antennas are added. This can be explained if we consider that by increasing the number of receive antennas, the diversity of the system increases and the pairwise error terms for each node approach zero more rapidly. This mean that the absolute pairwise error contributed to the overall BER is less for each node. As a consequence, the node with the better channel gain i.e. the node with higher SNR, will perform closer to its SULB.

On the one hand, moving from Fig. 3 and Fig. 4 to Fig. 5, we notice that for a fixed spectral efficiency and a fixed number of transmit antennas, the addition of more receive antennas results in an increasing gap between the average analytical BER curves of the two nodes. In particular, a gap of around 4 dB between the performance of User1 and User2 with N r = 2 is increased to around 7 dB when N r = 4 and further increased to around 9 dB for N r = 8. On the other hand, given that the two nodes experience a channel gain difference of 10 dB, we know that the interference aware detector cannot reach the performance of independent detection and the SULB for the node with the better SNR. Nonetheless, the gap between their respective BER curves tends toward the difference between the channel attenuations of the two users as N r grows to infinity but can never reach it i.e. the gap tends towards 10 dB.

The addition of more transmit antennas at each of the nodes results in SNR gains for each node as can be seen when we compare Fig. 4 and Fig. 6. Interestingly, however, increasing the number of transmit antennas does not change the relative behaviour of the system, i.e. the SNR difference between the BER curves of the two nodes remains constant. This behaviour is expected when we consider that (5) is independent of N t and heavily influenced by N r . In particular, the BER of both nodes is dependent on the variance of the channel coefficients in (4) which follow a central chi-squared distribution with 2N r degrees of freedom. This variance is defined in [START_REF] Younis | Reduced Complexity Sphere Decoder for Spatial Modulation Detection Receivers[END_REF].

At this point it should be noted that while the proposed detector is jointly optimum for both nodes and does not suffer from the near-far problem, it needs full CSI from all possible transmitting antennas to each receiving antenna. Additionally, finding the optimal solution is an exponentially complex problem, i.e. if we assume each node has the same number of transmit antennas and uses the same signal constellation, then the multi user ML detector has O (M N t ) Nu computational complexity which is proven to be NP-complete [START_REF] Verdu | Computational complexity of optimum multiuser detection[END_REF]. Fortunately, recent work on sphere detection algorithms may be used to alleviate this computational cost [START_REF] Younis | Sphere Decoding for Spatial Modulation[END_REF].

V. CONCLUSION

In this work the performance of SM with simultaneous transmission was analysed. A ML detector for SM in the interference limited scenario was proposed. Its performance over uncorrelated Rayleigh fading channels was studied and a closed form solution for the upper bound of the system was provided. Numerical results verified that the proposed analysis was fairly accurate for the high SNR regions. On the one hand, increasing the number of transmit antennas at each of the nodes from 2 to 4 resulted in SNR gains of around 2 dB. This measure did not, however, have any effect on the (U 1 ) = 1 and user 2 with σ 2 (U 2 ) = 0.1. Solid lines denote the performance of user 2 with a varying number of receive antennas while dashed lines denote the performance of user 1 with a varying number of receive antennas. (U 1 ) = 1 and user 2 with σ 2 (U 2 ) = 0.1 using the interference aware detector. relative coding gain between the BER curves of the two nodes i.e. the two nodes improved their performance by the same amount. On the other hand, increasing the number of receive antennas increased the diversity of the system and decreased the error contribution of each node, thus increasing the SNR gap between the BER curves of the two nodes.

Ω (U1) = {(h 1 x 1 , h 1 x 1 ), (h 1 x 1 , h 2 x 2 ), . . . , (h 1 x 1 , h Nt x M ), (h 2 x 1 , h 1 x 1 ), . . . , (h Nt x M , h Nt x M )} (7)
The generalization of this work to a system with an arbitrary number of nodes, along with further investigation on the performance of SM in an interference limited scenario will be considered in the future. ACKNOWLEDGEMENT

We gratefully acknowledge support from the Engineering and Physical Sciences Research Council (EP/G011788/1) in the United Kingdom for this work. Professor Harald Haas acknowledges the Scottish Funding Council support of his position within the Edinburgh Research Partnership in Engineering and Mathematics between the University of Edinburgh and Heriot Watt University. Nikola Serafimovski would like to acknowledge Harald Burchardt for his advice.

Fig. 3 .

 3 Fig.3. BER for user 1 with σ 2 (U 1 ) = 1 and user 2 with σ 2 (U 2 ) = 0.1 using the interference aware detector.

Fig. 4 .

 4 Fig. 4. BER for user 1 with σ 2(U 1 ) = 1 and user 2 with σ 2 (U 2 ) = 0.1 using the interference aware detector.

Fig. 5 .

 5 Fig. 5. BER for user 1 with σ 2(U 1 ) = 1 and user 2 with σ 2 (U 2 ) = 0.1. Solid lines denote the performance of user 2 with a varying number of receive antennas while dashed lines denote the performance of user 1 with a varying number of receive antennas.

Fig. 6 .

 6 Fig.6. BER for user 1 with σ 2 (U 1 ) = 1 and user 2 with σ 2 (U 2 ) = 0.1 using the interference aware detector.


Marco Di Renzo

Fitzek Alonso Luis
email: luisg@tsc.upc.edu

Foglar Andreas

Granelli Fabrizio

Fabio Graziosi

Gruet Christophe

Harald Haas

Perez Kormentzas George

Frank H P Fitzek

Andreas Foglar

Fabrizio Granelli

Christophe Gruet

George Kormentzas

Ana I Perez

Jonathan Rodriguez

John Thompson

Christos Verikoukis

GREENET -An Early Stage Training Network in Enabling Technologies for Green Radio

Keywords: Seventh Framework Programme, Marie Curie Actions, The People Programme, Initial Training Networks, Enabling Technologies for Green Radio

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

C URRENT 4G vision envisages higher data rates and multi-standard radio interfaces to provide all users with a continuous seamless connection. The large number of foreseen devices coupled with the surge in power requirements for future emerging handsets raise significant challenges in terms of reducing the energy consumption, the amount of electromagnetic radiation, and the emissions of CO2 [1], [2].

In particular, state-of-the-art multi-standard devices have high energy requirements for maintaining two or more radio interfaces. In [START_REF] Fitzek | Cellular controlled shortrange communication for cooperative P2P networking[END_REF], it is envisaged that a dramatic increase in the energy consumption of 4G devices will make active cooling a necessity. Indeed, from the manufacturer's perspective, the issue of energy consumption is becoming a key concern since there is a continuously growing gap between the energy required by emerging radio systems and what can be actually achieved by: i) the evolution on battery technology; ii) the progress on scaling and circuit design; iii) the design of novel system level architectures; and iv) the development of novel thermal and cooling techniques. Without new approaches for energy saving, there is a significant threat that 4G mobile users will be searching for power outlets rather than for network access, thus being restricted to a single location and being forced to lose their ability to roam freely.

In typical mobile terminals for cellular systems up to half of the energy consumption comes from communicationrelated functions, such as baseband processing, RF, and connectivity procedures [START_REF] Pering | CoolSpots: Reducing the power consumption of wireless mobile devices with multiple radio interfaces[END_REF]. Therefore any reduction in the power consumption of all these functionalities can have a substantial impact on the battery lifetime. The importance of this problem has already motivated solutions and protocols designed to allow dedicated switch-off periods for energy saving and for increasing the battery lifetime [START_REF] Fitzek | Cellular controlled shortrange communication for cooperative P2P networking[END_REF].

Furthermore, the need of radio networking solutions that can greatly improve energy-and resource-efficiency does not only make commercial sense for telecommunication operators supporting sustainable and profitable business, but, more important, can be extremely beneficial for the global environment. As a matter of fact, the whole world of telecommunication and information communities is facing a more and more serious challenge: on the one hand, the request for multimedia-rich data is exploding at an astonishing speed, and, on the other hand, the emission of CO2 that is due to Information and Communication Technology (ICT) is rapidly increasing. It has been pointed out that "currently, the 3% of world-wide energy is consumed by the ICT infrastructure that causes about 2% of the world-wide CO2 emissions, which is comparable to the world-wide CO2 emissions by airplanes or one quarter of the world-wide CO2 emissions by cars" [START_REF]1st Int. Workshop on Green Wireless 2008 (W-GREEN)[END_REF]. According to [2], energy costs account for as much as half of a mobile operator's operating expenses.

Therefore, the ICT sector should set itself ambitious targets for improving its own energy and carbon footprint. Furthermore, ICT can lead to the biggest energy-efficiency gains if used in the wider economy with the aim of lowering greenhouse gas emissions, reducing power consumption, and achieving efficient recycling of equipment waste.

II. GREENET VISION

Moving from the considerations above, one of the biggest challenges for future wireless communication systems is the need to limit the energy consumption of battery-powered devices, with the aim to prolong their operational time, avoid active cooling, and reduce the environmental impact of ICT overall. Thus, within the framework of "Green Communications", a number of paradigm-shifting technical approaches can be expected, including, but not limited to, energy-efficient network architecture and protocols, energyefficient wireless transmission techniques (e.g., reduced transmission power and reduced radiation), cross-layer optimization methods, and opportunistic spectrum sharing without causing harmful interference pollution.

As a consequence, there is a clear need for new disruptive strategies and technologies to address all the aspects of energy efficiency. To mention just a few examples: i) novel physical (PHY) layer technologies seem to be required to cope with the increased complexity and power inefficiency of both single and multiple-antenna wireless communication systems; ii) advanced Medium Access Control (MAC) protocols and Radio Resource Management (RRM) procedures are required to support low energy consumption; and iii) a radical paradigm shift needs to be adopted on network routing and management to enable a significant energy saving. Although some energy-efficient solutions are today available, they usually sacrifice Quality-of-Service (QoS) to reduce power.

In GREENET, we intend to present a new vision to enable green communication and networking. The core tenet is to reduce overall the energy consumption within the challenging but indispensable framework of optimizing the system capacity and maintaining the user's QoS.

To this end, it is crucial that the next generation of researchers working in the ICT sector is aware that telecommunication and networking technologies should, at the same time, i) set themselves ambitious targets for improving their own carbon footprint, and ii) be used across all sectors of the economy and society to reduce the worldwide energy consumption. This also agrees with a recent European Commission Press Release (reference: IP/09/393, date: 12/03/2009) [1], which pushes ICT for a greener Europe and to make people more aware of how they use energy.

To achieve these goals, we believe that ICT's scientists should have a solid grasp and understanding of multidisciplinary research fields (information theory, protocol design, optimization theory, game theory, signal processing, cross-layer/holistic design, etc.) at different layers of the protocol stack. These topics, however, are unlikely to be covered even by advanced academic courses. Thus, the ambitious goal of the International Training Network (ITN) GREENET is to provide advanced training to Early Stage Researchers (ESRs) interested in using and improving the efficiency of ICT with the aim of reducing the emissions of CO2 without renouncing to the "anywhere, anytime, everywhere" requirement of several wireless applications.

A. Objectives

GREENET targets the main following objectives

B. Expected Benefits

The following long-term benefits can be expected from GREENET:

• Overall, it is expected that the research activities conducted in GREENET provide significant scientific, industrial, and economic benefits by contributing to the reduction of the energy demands in 4G handsets and related carbon emissions.

• From a scientific point of view, the design of new physical, medium access control, and routing techniques that take advantage of cooperation and cognition without security and QoS degradation represents the main distinguishable feature of GREENET.

• From an industrial point of view, the exchange of scientific results among the partners (industrial and academic) will be the fundamental enabler to create impact within standardization bodies (e.g., 3GPP, IEEE P1900.4 & 6, IEEE 802.16j, IEEE 802.15.4, ETSI, ITU, etc.), and to drive the deployment of innovative commercial solutions based on the scientific outcomes of the ITN.

• On the economic side, the know-how acquired during the activities of GREENET will be transferred to innovative products targeting "energy efficiency without QoS degradation". This will potentially open new market opportunities for European device manufacturers, service and application developers.

C. Partners

GREENET foresees the fruitful collaboration of 10 European partners, among which 3 universities, 3 research centers, 1 company, and 3 small/medium enterprises. In particular, the partners are as follows:

1) Universidad Polytecnica de Catalunya (UPC), Spain (project coordinator).

2) The University of Edinburgh, United Kingdom.

3) Università di Trento, Italy. 4) Instituto de Telecomunicac ¸ões, Portugal. 5) National Centre for Scientific Research (NCSR) Demokritos, Greece. 6) Centre Tecnolgic de Telecomunicacions de Catalunya (CTTC), Spain. 7) WEST Aquila s.r.l., Italy. 8) ACTICOM GmbH, Germany. 9) CASSIDIAN, an EADS Company, France. 10) INNOROUTE GmbH, Germany.

III. RESEARCH PROGRAM

The workplan of GREENET is articulated into 8 WorkPackages (WPs): 1 WP (WP0) devoted to the project management, 1 WP devoted to training (WP6), 1 WP (WP7) devoted to dissemination, and 5 technical WPs (WP1-WP5). In particular, the technical WPs are organized in a matrix structure where three (WP1, WP2, and WP3) "horizontal" WPs aim at studying novel breakthrough technologies at the PHY, MAC, and network (NET) layers, respectively, to improve the energy efficiency of future wireless systems, and two (WP4, WP5) "vertical" WPs aim at addressing interdisciplinary and novel paradigms, such as network cooperation and cognition, for the design of energy-efficient wireless systems in which the secure and safe delivery of data can be guaranteed with high reliability through the network.

In what follows, we provide a brief description of the research program for each technical WP (WP1-WP5).

A. WP1: Energy-Efficient and Low-Complexity PHY-layer Techniques

Multiple-antenna techniques offer a practical way to extend the communication capabilities of the next generation wireless systems [START_REF] Mietzner | Multiple-antenna techniques for wireless communications -A comprehensive literature survey[END_REF]. They can be used to accomplish a multiplexing gain, a diversity gain, or an antenna gain, thus enhancing the bit rate, the error performance, or the signal-to-noise-plusinterference ratio of wireless systems, respectively. However, the benefits of Multiple-Input-Multiple-Output (MIMO) systems cannot be achieved, unfortunately, for free. The main drawbacks of any MIMO scheme are the increase in hardware and signal processing complexity, energy consumption, and component size at the transmitter and at the receiver [START_REF] Molisch | MIMO systems with antenna selection[END_REF]. However, due to the clear advantages of MIMO techniques it must be a clear research goal to develop new approaches for multiple-antenna transmission, either centralized or distributed, to mitigate the practical limitations while retaining the key advantages.

In GREENET, we are committed to a comprehensive analysis of a new recently proposed transmission technology for MIMO systems, which promises to solve some of the issues mentioned above. It seems to be suitable for the design of energy-efficient MIMO schemes and for their actual implementation in the next generation wireless communication systems and networks. The new transmission technology is called Spatial Modulation (SM) [START_REF] Mesleh | Spatial modulation[END_REF]. Our research will encompass the development of novel modulation and coding schemes, low-complexity detection units, efficient channel estimation algorithms, and the development of novel methodologies for computing the error and capacity performance for realistic settings. More specifically, we will aim at achieving low-energy requirements via optimized coding and modulation schemes at the transmitter, opportunistic power allocation mechanisms to exploit the randomness of the wireless channel, and low-complexity implementations of detectors and channel estimators at the receiver.

B. WP2: Energy-Efficient Design of MAC and RRM Protocols

To reduce the footprint of wireless networks it is necessary to address the design of proper RRM and MAC schemes. RRM deals with assignment of radio resources to wireless devices, while MAC is related to managing the access to such shared resource. Several approaches are available in the literature targeting the study of energy-efficient MAC and RRM strategies in wireless networks [START_REF] Jones | A survey of energy efficient network protocols for wireless networks[END_REF]. However, the results available so far have pointed out that no single best strategy for energy-efficiency is today available, as well as that adaptivity is the way forward.

In GREENET, novel RRM and scheduling techniques that optimize energy efficiency with QoS constraints will be studied. Furthermore, solutions that mitigate intraand inter-cell interference will be considered. In addition, improvements in the design of MAC protocols for wireless local area networks with low energy consumption will be investigated.

C. WP3: Energy-Efficient Network-Coded Wireless Architectures

In today practical communication networks, information is delivered from a source to a destination through routing. Network nodes simply store and forward data, and processing is accomplished only at the end nodes. Network Coding (NC) breaks with this assumption: instead of simply forwarding data, the nodes may recombine several input packets into one or several output packets. The potential advantages of NC over routing include resource (e.g., bandwidth and power) and computational efficiency, as well as robustness to network dynamics [START_REF] Ahlswede | Network information flow[END_REF], [START_REF] Katti | XORs in the air: Practical wireless network coding[END_REF]. Although NC was originally proposed to maximize the throughput in wireless networks, recent results have clearly shown that it can be used as an efficient technique for energy saving by exploiting the broadcast nature of the wireless medium [START_REF] Fragouli | Efficient broadcasting using network coding[END_REF], [START_REF] Goseling | On the energy benefit of network coding for wireless multiple unicast[END_REF].

In GREENET, we aim at exploiting the NC paradigm for reducing the energy consumption of wireless communication systems and networks by adopting a cross-layer design methodology. More specifically, our main commitment will be the design of novel (cross-layer) joint channel and network decoding algorithms to improve the performance and the energy-efficiency of wireless networks. In particular, we are interested in developing novel solutions that can efficiently work over realistic fading channels and can take into account the realistic operation of cooperative networks.

D. WP4: Cooperative Networking for the Design of Energy-Efficient Wireless Networks

Recent studies have shown that using cooperation in wireless networks can significantly improve the performance and provide an intrinsic robustness against the impairments of the wireless channel [START_REF] Laneman | Cooperative diversity in wireless networks: Efficient protocols and outage behavior[END_REF]. The net result turns out to be a lower packet-error probability and a better QoS. Cooperative communications are an active field of research in various European projects (e.g., CODIV, REWIND, SMARTNet). However, effective energy-efficient cooperative solutions for wireless networks are still unavailable in the literature.

In GREENET, we aim at proposing innovative cooperative paradigms that overcome the limitations of state-of-the-art solutions. To this end, we aim at exploiting novel PHY-layer technologies (e.g., SM described in WP1) and advanced encoding functionalities at the NET-layer (e.g., NC described in WP3) for performance improvement and significant energy savings. In addition, we plan to design efficient short-range cooperative MAC protocols (as described in WP2), and Cooperative Automatic Repeat reQuest (ARQ) strategies to further reduce the energy consumption. Furthermore, the proposed solutions will be designed to be robust to possible security threats.

E. WP5: Cognitive Networking for the Design of Energy-Efficient Wireless Networks

Another promising way to improve energy efficiency of wireless systems lie in cognitive approaches in which learning is used for better adaptation [START_REF] Zhang | Cognitive radio for green communications and green spectrum[END_REF]- [START_REF] Grace | Using cognitive radio to deliver green communications[END_REF]. A Cognitive Radio (CR) is characterized by an adaptive, multi-dimensionally aware, autonomous radio system empowered by advanced intelligent functionalities, which interacts with its operating environment and learns from its experiences to reason, plan, and decide future actions to meet various needs. This approach can lead to a significant increase in radio resource (spectrum) efficiency, networking efficiency, as well as energy efficiency. Cognition can be used at the spectrum level for spectrum coexistence and interference management. Interference mitigation directly results in energy saving. Cognitive approaches can also be applied at the network layer to integrate heterogeneous networks and let energy efficiency becomes one of the primary optimization concerns to provisioning services across those networks. CR is a hot research asset in several European-funded projects, e.g., PHYDYAS, ARAGORN, CogNet, Self-NET and E3. However, none of them explicitly deal with the exploitation of CR for energy saving.

In GREENET, we target the design of cognitive algorithms and protocols, which encompass energy-efficient detection capabilities for cooperative spectrum sensing, vertical handover procedures based on context information, dynamic spectrum management, and self-organization. Furthermore, the proposed solutions will be designed to be robust to possible security threats.

IV. TRAINING PROGRAM

GREENET is committed to recruit 17 ESRs for a time period of 36 months each. Each ESR will be recruited through a competitive process, and will be supervised by more than one partner of the consortium. Each ESR will develop his/her research program within the premises of one of the partners of the ITN, and will spend a period of the duration of 6 months in the premises of at least another partner of the consortium. The training program of each ESR will be personalized through a well defined individual personal career development plan.

Training will be accomplished in many forms in the ITN:

V. CONCLUSION

In this paper, we have described GREENET, a new recentlyfunded European project that aims at designing next generation energy-efficient wireless networks. GREENET foresees the collaboration of 10 European partners equally distributed among academia, research centers, and industry, which will synergically work to provide advanced training to 17 ESRs recruited by the whole consortium. The main objective of GREENET is to design new PHY, data-link, NET protocols, along with cooperative and cognitive paradigms to reduce the carbon footprint of ICT, and, at the same time, to enable a more efficient utilization of ICT across all sectors of the economy and society with the target to minimize the worldwide energy consumption.

  1) Traditional training by means of Ph.D. courses, tutorials, seminars, workshops, and international conferences. 2) Training through research, which foresees the development of an individual research program by each ESR. 3) Complementary training, which foresees the attendance of specific courses aiming at improving presentation, paper writing, patent writing, etc. skills.

ACKNOWLEDGMENT

This work is funded by the Research Project GREENET (PITN-GA-2010-264759).