Antoine Stephan
email: antoine.stephan@ens.insa-rennes.fr

Jean-Yves Baudais

Jean-François Hélard
email: jean-francois.helard@insa-rennes.fr

Adaptive Spread Spectrum Multicarrier Multiple-Access for UWB Systems

Keywords: Multicarrier CDMA, resource allocation, spread spectrum multicarrier multiple-access (SS-MC-MA), ultrawideband (UWB), wireless access. I

Ultra-wideband (UWB) has emerged as an exciting technology for short range, high data rate wireless personal area networks (WPAN) applications. The multiband orthogonal frequency division multiplexing (MB-OFDM) scheme is one of the main candidates for WPAN standardization. In this paper, we propose a new UWB waveform based on a spread spectrum multicarrier multiple-access (SS-MC-MA) scheme that respects the OFDM parameters of the MB-OFDM solution. Then, we suggest an efficient low-complexity resource allocation algorithm that maximizes the total system throughput. Furthermore, we dynamically distribute the time-frequency codes that provide frequency hopping between users, in order to improve our system performance. We show that our proposed system transmits data at much higher attenuation levels and higher throughputs compared to the MB-OFDM system. Consequently, we conclude that our proposed system can be advantageously exploited for high data rate UWB applications.

INTRODUCTION

Ultra-wideband (UWB) technology has attracted significant interest in wireless communications since 2002 when the Federal Communications Commission (FCC) agreed on the allocation of a 3.1-10.6 GHz spectrum for unlicensed use of UWB devices [START_REF]First report and order, revision of part 15 of the commission's rules regarding ultra-wideband transmission systems[END_REF]. The FCC regulations are very stringent since UWB spectrum overlays other existing spectrum allocations. In order to reduce interference with these existing services, the FCC imposed a power spectral density (PSD) limit of -41.25 dBm/MHz. The IEEE 802.15.3a wireless personal area networks (WPAN) standardization group proposed a very high data rate physical layer based on UWB signaling [START_REF][END_REF], since UWB can provide high data rate at low cost and relatively low power consumption. The main multiple-access techniques considered by the group are a pulse radio transmission which uses directsequence code-division multiple-access (DS-CDMA), and a multiband orthogonal frequency division multiplexing (MB-OFDM) supported by the Multiband OFDM Alliance (MBOA) [START_REF][END_REF]. The MBOA solution appears to be a very competitive candidate due to its ability to mitigate interference and to achieve high data rate. Other techniques based on a multicarrier code-division multiple-access (MC-CDMA) scheme have also been proposed in the literature in order to reach much higher data rate [START_REF] Tung | MMSE receiver for multicarrier CDMA overlay in ultra-wide-band communications[END_REF].

In the UWB environment, the channel response varies slowly in time and can be considered as quasi-static. Previous resource allocation studies have been proposed for the MBOA model [START_REF] Xu | Power allocation for multi-band OFDM UWB communication networks[END_REF]. In this paper, we propose a new UWB waveform based on a spread spectrum multicarrier multiple-access (SS-MC-MA) scheme [START_REF] Stephan | Resource allocation for multicarrier CDMA systems in ultra-wideband communications[END_REF] respecting the OFDM parameters of the MBOA solution, and we propose an efficient low-complexity resource allocation algorithm applied to the SS-MC-MA scheme in order to maximize the total system throughput, while respecting the FCC regulations. Furthermore, we propose a new technique that maximizes the throughput by dynamically distributing the time-frequency codes that provide frequency hopping between users. This paper is organized as follows. Section II presents the multiband OFDM solution, followed by a description of our proposed SS-MC-MA scheme. Section III details the resource allocation algorithm applied to the SS-MC-MA scheme. Section IV describes the dynamic distribution of the timefrequency codes. Simulation results showing the interest of our proposed system in UWB applications are given in Section V before the conclusion in Section VI.

II. SYSTEM MODEL

A. Multiband OFDM solution

The MBOA solution for UWB systems design is based on the combination of an OFDM modulation with a multibanding approach, which divides the 7.5 GHz UWB spectrum into 14 sub-bands of 528 MHz each [START_REF] Batra | TI physical layer proposal for IEEE 802.15 task group 3a[END_REF], as seen in Fig. 1. These subbands are then regrouped into 5 channels. Multibanding reduces power consumption and lowers cost since the information is processed over much smaller bandwidth, while taking benefit of the frequency diversity linked to the total bandwidth. Initially, most of the studies have been performed on the first 3 sub-bands (3.1-4.8 GHz). The multiband UWB system provides data rates ranging from 53.3 Mbps to 480 Mbps. The OFDM scheme consists of 128 subcarriers, out of which 100 are assigned to data tones. The modulation used is a quadrature phase-shift keying (QPSK), which leads to the transmission of 200 bits per OFDM symbol. The useful duration of each OFDM symbol is 242 ns, This work was supported by France Télécom R&D/RESA/BWA, within the contract 46136582. leading to a subcarrier frequency spacing of 4.125 MHz. A zero-padding cyclic prefix of duration 60.61 ns is added at the end of each OFDM symbol to cope with the inter-symbol interference (ISI). An additional guard interval of 9.47 ns is added for the sub-bands' hops.

The MBOA solution offers potential advantages for UWB applications, e.g., the signal robustness against channel selectivity and the efficient exploitation of the energy of every signal received within the prefix margin. However, this solution suffers from various limitations in a multi-user and multi-piconet context. When the first 3 sub-bands are considered, conflicts between users start as soon as we add a fourth user to the cell, whereas cells of up to 6 simultaneous users are being considered in the MBOA proposal. Moreover, this solution lacks in the ability to allocate sub-bands and power optimally since the sub-bands are not assigned to each user according to his channel condition, and the transmitted power is equally distributed among sub-bands without any power adaptation.

B. Proposed SS-MC-MA scheme

Some studies have proposed to use a MC-CDMA waveform by adding a CDMA scheme to the OFDM solution with a spreading in the frequency domain, in order to improve the system performance. The resource allocation becomes more flexible due to the addition of a spreading sequence. Furthermore, the spreading in the frequency domain improves the signal robustness against the frequency selectivity of the UWB channel, and against the narrowband interference, since the signal bandwidth could become much larger than the bandwidth of the interference.

To improve the system performance, we propose a SS-MC-MA scheme [START_REF] Kaiser | A flexible spread-spectrum multi-carrier multiple-access system for multi-media applications[END_REF]. SS-MC-MA consists in assigning to each user a specific block of subcarriers according to a frequency division multiple-access (FDMA) scheme, whereas with MC-CDMA, resource sharing is realized by assigning to each user different individual codes transmitted over the whole available bandwidth. The SS-MC-MA system benefits from the performance and advantages of the MC-CDMA system while improving the resource allocation flexibility. With SS-MC-MA, symbols are transmitted simultaneously on a specific subset of subcarriers by the same user and undergo the same distortions. Self-interference (SI), which replaces the multiple access interference (MAI) obtained with MC-CDMA, can be easily compensated by mono-user detection with only one complex coefficient per subcarrier.

The proposed SS-MC-MA scheme is applied to UWB while respecting the OFDM parameters of the MBOA solution in order not to increase the system complexity significantly. At a given time, each user is allocated a group of 100 subcarriers equivalent to one of the first 3 MBOA sub-bands of 528 MHz bandwidth. Each sub-band is then divided into several blocks b, each of them including a number of subcarriers equal to the spreading code length L and linked by a spreading code C b . The constellations used are the QPSK (similar to MBOA), as well as the 8-QAM and 16-QAM in order to better fit the channel capacity. Besides, the radio-frequency frond-end of the MBOA solution is maintained.

C. Channel model

The channel model used for our resource allocation is the one adopted by the IEEE 802.15.3a committee for the evaluation of UWB physical layer proposals [START_REF] Foerster | Channel modeling sub-committee report final[END_REF]. It is a modified version of the Saleh-Valenzuela model for indoor channels [START_REF] Saleh | A statistical model for indoor multipath propagation[END_REF], which fits the properties of measured UWB channels. A lognormal distribution is used for the multipath gain magnitude. In addition, independent fading is assumed for each cluster and each ray within the cluster. Moreover, four different channel models (CM1 to CM4) are defined for the UWB system modeling, each with arrival rates and decay factors chosen to match different usage scenarios and to fit line-of-sight (LOS) and non-line-of-sight (NLOS) cases.

III. PROPOSED ALLOCATION ALGORITHM

In this paper, we propose an efficient resource allocation algorithm for our proposed SS-MC-MA waveform, whose objective is to maximize the total system throughput with a PSD constraint fixed by the FCC regulations. The channel response varies slowly in time and can be considered as quasistatic during one frame. Hence, we can assume that the channel state information (CSI) is available at the transmitters.

The throughput in bits per symbol of an OFDM system is derived from Shannon theorem by

∑ ∈         + = S k k k OFDM N P H Γ R 0 2 2 1 1 log , ( 1
)
where S is the group of used subcarriers, Г the signal-to-noise ratio (SNR) gap, known as the normalized SNR, H k and P k the frequency-domain response and the transmitted power density of the k th subcarrier respectively, and N 0 the noise density.

The total throughput in bits per symbol of a SS-MC-MA system using a zero-forcing detection is given from [START_REF] Crussière | Adaptive spread spectrum multicarrier multiple access over wirelines[END_REF] by

∑ ∑ ∑ = = ∈ - -               + = B b C c b c S k k MA MC SS b b N P H L Γ R 1 1 0 , 2 2 2 1 1 1 log , ( 2
)
where B is the number of blocks, C b the number of codes per block b, L the spreading code length, and P c,b the power density of code c within block b.

The throughput maximization study is divided into two steps. First, we consider an infinite granularity case where the throughput R is allowed to have real non-integer values, and then we consider a finite granularity case where the throughput values must be integer since we have discrete modulation orders. In the infinite granularity case, by imposing a constraint on the PSD, the optimization problem can be described as

∑∑ ∑ = = ∈               + B b C c b c S k k b b N P H L Γ 1 1 0 , 2 2 2 1 1 1 log max , (3)
with P the PSD constraint of -41.25 dBm/MHz. To maximize the system throughput for a given PSD, the L subcarriers with the largest response amplitude should be selected.

To solve the optimization problem, we introduce the Lagrange multipliers λ in ( 3) and ( 4). We find that

C P P b c / , =
and L C = .

(5)

Consequently, the maximum reachable throughput in bits per block b in the infinite granularity case becomes

              + = ∑ ∈ 0 2 2 * 1 1 1 log N P H L Γ L R b S k k b , (6)
and the maximum reachable throughput in bits per code c becomes

[ ] L c L R R b b c : 1 * * , ∈ ∀ = . ( 7
)
Since we have discrete modulation orders, the throughput per code must always have integer values. An optimal solution for this problem is given in [START_REF] Crussière | Adaptive spread spectrum multicarrier multiple access over wirelines[END_REF] and it shows that an optimal throughput distribution would be to allocate  

  ( )   1 2 / / * * - = - L R L R b b L n . (8)
Hence, the discrete throughput in bits per code becomes

  [ ]   [ ]      + ∈ ∀ = ∈ ∀ + = . : 1 / : 1 1 / * , * , L n c L R R n c L R R b b c b b c (9)
The power density per code is then given by ( )

∑ ∈ - Γ = b b c S k R k b c H N L P 1 2 , 2 0 2 , , (10)
and the total discrete throughput in bits per block b becomes

    ( )   ( )     ( )   ( ). / ) 1 2 ( 1 / ) 1 2 ( * / / * / / * * * * L R L L L R L R b L R L R b L R L R b b b b b - - + + - = - - (11)

IV. TIME-FREQUENCY CODES EXPLOITATION

A. TFC distribution

In the MBOA proposal, unique logical channels corresponding to different piconets are defined by using different time-frequency codes (TFC) for each band group. These codes provide frequency hopping from a band to another at the end of each OFDM symbol. Fig. 2 represents a realization of the TFC, where the first OFDM symbol of the first user is transmitted on Band 1, the second symbol on Band 2 and the third on Band 3. The proposition described by the MBOA norm consists in choosing the TFC regularly without taking into consideration the channel response state of each user for each of the first 3 MBOA sub-bands. In our study, we use a dynamic TFC (DTFC) distribution, different from the distribution of the MBOA norm, which consists in selecting for every 3 consecutive OFDM symbols the optimal repartition of the 3 users on the 3 sub-bands that maximizes the SS-MC-MA system margin.

We consider 3 users, and consequently 3 TFC codes, distributed on the first 3 bands of the MBOA solution. Over a given OFDM symbol period T, each user occupies one of the 3 available sub-bands. To find the number of unique possible distributions of the TFC over 3 consecutive periods T, we have a combinational problem. In fact, over one period, we have a permutation with order and without repetition of 3 users on 3 bands. The total number of possible permutations is then given by

6 ! ) ( / ! = - = k n n p
, with 3 = n the number of bands and 3 = k the number of users. Hence, there are 216 possible permutations over 3 periods. But within each band, we do not take into consideration the users' order in time, thus the number of unique permutations is reduced to 55. We should notice that we have a total of 9 different channel responses in the system, since each user has 3 different channel responses corresponding to 3 bands.

B. Algorithm implementation

After having described the bit loading algorithm of the proposed SS-MC-MA scheme and the dynamic TFC distribution for system throughput maximization, we combine these 2 techniques into a single algorithm and we apply it to the first 3 sub-bands of the MBOA solution. The total number of blocks per sub-band is equal to   L N / , where 100 = N is the number of used subcarriers. This algorithm can be implemented as follows:

Figure 3 .

 3 Figure 3. Total system throughput with a 4-QAM in the case of a PSD constraint per OFDM symbol for CM2 and CM4 channel models.

Figure 4 .

 4 Figure 4. Total system throughput with a 4-QAM in the case of a mean PSD constraint per 3 OFDM symbols for CM1 channel model.

Figure 5 .Figure 6 .

 56 Figure 5. Total system throughput with a 16-QAM in the case of a PSD constraint per OFDM symbol for CM2 and CM4 channel models.

=

,

with n given from [START_REF] Kaiser | A flexible spread-spectrum multi-carrier multiple-access system for multi-media applications[END_REF], symbol throughput:

3) For

V. SIMULATION RESULTS

In this section, we present the simulations performed on the first 3 sub-bands of the MBOA solution using the proposed adaptive SS-MC-MA system, with and without the dynamic TFC (DTFC). The spreading code length used is the optimal one with 16 = L , which gives the highest system throughput. First, the algorithm is used to maximize the total system throughput. The simulations are performed by considering the case of a PSD constraint per one OFDM symbol (Fig. 3), and the case of a mean PSD constraint per three OFDM symbols where the PSD measuring is made on 3 symbols (Fig. 4). In the second case, if a user is occupying a sub-band for only onethird of the time, his PSD could be 3 times larger than the average PSD defined by the MBOA norm (-41.25 dBm/MHz). Fig. 3 represents the total system throughput per 3 OFDM symbols for different channel attenuation levels, with a 4-QAM modulation. With the MBOA system using CM2 channel model, the 3 users are able to transmit information ( 1800 200 3 3 = × × bit/3×symbol) at attenuation levels lower than 31 dB. At attenuation levels from 32 to 35 dB, only 2 users are able to transmit (1200 bit/3×symbol), at levels from 36 to 41 dB only 1 user is able to transmit (600 bit/3×symbol), and at levels higher than 46 dB no one is able to transmit. When we consider an adaptive SS-MC-MA system, the throughputs are much higher at high attenuation levels, e.g. the throughput of 1200 bit/3×symbol is reached at 35 dB level with MBOA, whereas with SS-MC-MA it can be reached at 71 dB, and at 35 dB the system has a throughput of 1800 bit/3×symbol. Moreover, the system is able to transmit at an attenuation level of 93 dB. Besides, when we apply the TFC distribution algorithm to the adaptive SS-MC-MA system, the throughput increases more as we can see in Fig. 3.

From Fig. 4, we notice that even with a mean PSD constraint per 3 symbols, the adaptive SS-MC-MA system outperforms MBOA, and when we use the DTFC distribution, the total throughput increases more. Similar results are obtained with the different channel models (CM1-CM4). Fig. 5 represents an adaptive SS-MC-MA system using a 16-QAM modulation. This system also outperforms MBOA and is able to transmit data at an attenuation level of 92 dB.

This algorithm is also used to maximize the throughput of the user which has the most critical channel response. Fig. 6 gives the throughput of the critical user for CM2 and CM4 model. We notice that with MBOA using CM2 model, this user is only able to transmit information at attenuation levels lower than 31 dB whereas with adaptive SS-MC-MA, he can even transmit at 92 dB.

VI. CONCLUSION

In this paper, we proposed a low-complexity resource allocation algorithm applied to a SS-MC-MA waveform which is new in high data rate UWB applications, and which respects the OFDM parameters of the MBOA solution in order not to increase the system complexity significantly. The proposed system aims at maximizing the total throughput while taking into consideration the WPAN environment and respecting the FCC regulations. Furthermore, we proposed a dynamic distribution of the time-frequency codes which increases the system performance since with the MBOA solution the TFC are distributed regularly without taking into consideration the channel response state of each user for each band. We found that our proposed system outperforms the MBOA system and transmits information at much higher attenuation levels with higher throughputs. Hence, we conclude that our proposed system can be advantageously exploited for high data rate UWB applications.


Antoine Stephan
email: antoine.stephan@ens.insa-rennes.fr

Jean-Yves Baudais
email: jean-yves.baudais@insa-rennes.fr

Jean-François Hélard
email: jean-francois.helard@insa-rennes.fr

ADAPTIVE MULTI-CARRIER SPREAD-SPECTRUM WITH DYNAMIC TIME-FREQUENCY CODES FOR UWB APPLICATIONS

Keywords: Multi-carrier spread-spectrum, resource allocation, UWB

In this paper, we propose a spread spectrum multi-carrier multiple-access (SS-MC-MA) waveform for high data rate UWB applications, taking into consideration the European UWB context. This new UWB scheme respects the parameters of the multiband orthogonal frequency division multiplexing (MB-OFDM) technique which is one of the candidates for wireless personal area networks (WPAN) standardization. We optimize the spreading code length and the number of codes in our proposed scheme in order to maximize the system range for a given target throughput. Furthermore, we dynamically distribute the time-frequency codes that provide frequency hopping between users in order to improve our system range. We show that our adaptive system transmits information at much higher attenuation levels and with larger throughput than the ones of the MB-OFDM proposal. Hence, we conclude that our proposed system can be advantageously exploited for UWB applications.

Introduction

Ultra-wideband (UWB) has emerged as an exciting technology for short range, high data rate wireless communications since 2002 when the Federal Communications Commission (FCC) agreed on the allocation of a 3.1-10. [START_REF] Stephan | Resource allocation for multicarrier CDMA systems in ultra-wideband communications[END_REF] GHz spectrum for unlicensed use of UWB devices [START_REF]First report and order, revision of part 15 of the commission's rules regarding ultrawideband transmission systems[END_REF]. The FCC imposed a power spectral density (PSD) limit of -41.25 dBm/MHz in order to reduce interference with existing spectrum allocations.

One of the main multiple-access techniques considered by the IEEE 802.15.3a standardization group is a multiband orthogonal frequency division multiplexing (MB-OFDM) supported by the Multiband OFDM Alliance (MBOA) [START_REF][END_REF], [START_REF] Batra | Design of multiband OFDM system for realistic UWB channel environments[END_REF]. In this paper, we propose a new UWB waveform based on a spread spectrum multi-carrier multiple-access (SS-MC-MA) scheme while respecting the OFDM parameters of the MBOA solution and taking into consideration the European UWB context. Then, we optimize the spreading code length and the number of codes of the proposed scheme in order to maximize the system range. These optimizations do not take into account the channel coding scheme. Furthermore, we propose an allocation algorithm that maximizes the system range by dynamically distributing the time-frequency codes that provide frequency hopping between users.

This paper is organized as follows. Section 2 presents briefly the multiband OFDM solution, followed by a description of our proposed SS-MC-MA scheme. Section 3 studies the SS-MC-MA system optimization for range maximization. Section 4 describes the dynamic TFC algorithm applied to the SS-MC-MA scheme. Simulation results showing the interest of the proposed adaptive scheme in UWB applications are given in Section 5, followed by the conclusion in Section 6.

2.

System model

Multiband OFDM in the European context

The MBOA solution is based on the combination of an OFDM modulation with a multibanding approach, which divides the 7.5 GHz UWB spectrum into 14 sub-bands of 528 MHz each. The OFDM scheme consists of 128 subcarriers, out of which 100 are assigned to data tones. The modulation used is a quadrature phase-shift keying (QPSK), which leads to the transmission of 200 bits per OFDM symbol. The MBOA solution offers potential advantages for UWB applications, e.g., the signal robustness against channel selectivity and the efficient exploitation of the energy of every signal received within the prefix margin.

Initially, most of the studies have been performed on the first 3 sub-bands (3.1-4.8 GHz). The FCC PSD limit of -41.3 dBm/MHz was imposed on the whole 14 sub-bands, whereas with the European Electronic Communications Committee (ECC) regulations of March 2006 much lower PSD limits were imposed on the UWB spectrum, except on the 6-8.5 GHz range where a similar -41.3 dBm/MHz limit was considered [START_REF]ECC Decision of 24 March 2006 on the harmonised conditions for devices using Ultra-Wideband (UWB) technology in bands below 10.6 GHz[END_REF]. Hence, we perform our studies on sub-bands 7, 8 and 9 (6.33-7.92 GHz) of the MBOA solution.

Proposed SS-MC-MA scheme

To improve the system performance, we propose a SS-MC-MA scheme which consists in assigning to each user a specific block of subcarriers [START_REF] Kaiser | A flexible spread-spectrum multi-carrier multiple-access system for multi-media applications[END_REF]. This scheme is applied to UWB while respecting the OFDM parameters of the MBOA solution [START_REF] Stephan | Resource allocation for multicarrier CDMA systems in ultra-wideband communications[END_REF]. The spreading is in the frequency domain in order to improve the signal robustness against the frequency selectivity of the UWB channel and against narrowband interference. If we consider 3 users transmitting simultaneously, at a given time each user is allocated a group of 100 subcarriers equivalent to one of the 3 sub-bands (7, 8 and 9) of 528 MHz bandwidth. Each sub-band can be divided into several blocks, each of them including a number of subcarriers equal to the spreading code length. In addition, the only modulation used is the QPSK as with the MBOA solution.

Channel model

The channel model used for our study is the one adopted by the IEEE 802.15.3a committee for the evaluation of UWB physical layer proposals [START_REF] Foerster | Channel modeling sub-committee report final[END_REF]. It is a modified version of the Saleh-Valenzuela model for indoor channels, fitting the properties of measured UWB channels. A lognormal distribution is used for the multipath gain magnitude. In addition, independent fading is assumed for each cluster and each ray within the cluster. Moreover, four different channel models (CM1 to CM4) are defined for the UWB system modeling, each with arrival rates and decay factors chosen to match different usage scenarios and to fit line-of-sight (LOS) and non-line-of-sight (NLOS) cases.

SS-MC-MA system optimization

The SS-MC-MA system optimization is divided into 2 steps. First, we will find the optimal number of blocks that maximizes the system margin for a target throughput, and then we will optimize the code length and the number of codes in order to maximize the system range with lower variable throughput.

The throughput of an OFDM system in bits per symbol is derived from Shannon theorem by

∑ ∈ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = S k k k OFDM N E h Γ R 0 2 2 1 1 log , ( 1
)
where S is the group of used subcarriers, Γ the signal-to-noise ratio gap (normalized SNR), h k and E k the frequency-domain response and the transmitted power density of the k th subcarrier respectively, and N 0 the noise density. The total throughput in bits per symbol of a SS-MC-MA system using a zero-forcing detection is given by [START_REF] Crussière | Adaptive linear precoded DMT as an efficient resource allocation scheme for power line communications[END_REF] ∑∑ ∑ ∑∑ ∑

= = = = = = - - ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + = = = B b C c b c L i b i b B b C c b c B b b MA MC SS b b b N E h L Γ R R R 1 1 0 , 1 2 , 2 2 1 1 , 1 | | 1 1 1 log , ( 2
)
where (

B
Using the Lagrange multipliers in ( 2) and ( 3), we find that the optimal solution which maximizes the system throughput would be to have

b L C C E E b b b b c ∀ = =
, and / , . Moreover, in the UWB context, the modulations used are limited to a QPSK. Thus, the UWB throughput in bits per symbol becomes

∑ ∑ ∑ = = = ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + ≤ = B b L i b i b b B b b UWB N E h L Γ L L R b 1 0 1 2 , 2 1 | | 1 1 1 log 2 . ( 4
)
Property 1: The throughput R UWB is only reachable if the expected value

3 1 | | 1 E 2 , ≤ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ b i h , ( 5
) with 0 2 , 2 , / | | | | N Γ E h h b i b i = .
Proof: From (4) we can write

∑ ∑∑ = = = ≤ B b b B b L i b i L h b 1 1 1 2 , 3 | | 1 . ( 6
)
If n is the total number of used subcarriers, then

n L b b = ∑ and (6) becomes 3 1 | | 1 1 1 1 2 , ≤ ∑∑ = = B b L i b i b h n . (7)
■

Optimization of the number of blocks

In this study, we want to find the optimal number of blocks B that maximizes the SS-MC-MA system margin with a fixed modulation and a fixed target throughput (200 bit/symbol). Let b γ be this margin per block.

From (4), we can write ( )

∑ ∑ ∑ = = = ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + = = = B b L i b i b b B b b UWB b h L L L n R 1 1 2 , b 2 1 | | / 1 1 1 log 2 2 γ (8)
and

( ) ∑ = = b L i b i b b h L 1 2 , | | / 1 3 1 γ . ( 9
)
Theorem 1: To maximize the noise margin of the SS-MC-MA system, and consequently the system range, a code length equal to the number of useful subcarriers should be used, i.e. one single SS-MC-MA block should be used. We have

∑ ∑ ∑∑ = = = = + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = = B b b B b b b B b L i b i n L h b 1 1 1 1 2 , | | 1 α α α α α
. Thus, we find that 0

min

. Thus, n L = maximizes the margin, i.e. the optimal choice for a given throughput is to use a spreading code length equal to the total number of useful subcarriers which is equal to 100 in the UWB context. ■ Consequently, it is not necessary to know the channel coefficients at the transmitter side to distribute the subcarriers between the blocks, since all these subcarriers are used within the same single block. Furthermore, this theorem shows that the SS-MC-MA noise margin can never be lower than the OFDM noise margin. This is due to the energy gathering capability of SS-MC-MA which can exploit, contrarily to OFDM, the residual energy conveyed by each subcarrier. The SS-MC-MA system range is therefore larger than the OFDM system range.

Range improvement with variable throughput

Now, we optimize the code length L and the number of codes N in order to maximize the system range when the UWB throughput of 200 bit/symbol is not reachable at high attenuation levels.

In a general approach with variable throughput, the number of codes N can be lower than the code length L and Theorem 1 is not applicable anymore. In this case, a multiple blocks configuration has to be considered and each block can exploits its own code length L b . But finding the optimal block sizes amounts to resolving a complex combinational optimization problem that can not be reduced to an equivalent convex problem. Then, no analytical solution exists and optimal solution can only be obtained following exhaustive search [START_REF] Crussière | Adaptive linear precoded DMT as an efficient resource allocation scheme for power line communications[END_REF]. In order to avoid prohibitive computations, we assume a single block configuration system.

Maximizing the system range is equivalent to maximizing the system throughput. The optimal non-integer throughput for the single block system is given by

( ) ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + = ∑ = L i i h L L R 1 2 2 | | / 1 1 log . ( 10
)
Theorem 2: With a QPSK modulation and a PSD constraint of

E E L c c ≤ ∑ =1
, the optimal number of codes that can be used for a given spreading code length L is

( ) ⎣ ⎦ 3 / 1 2 / - = L R L N
, with R given by (10).

Proof: With the optimal number of codes N, the PSD constraint should be respected, whereas with 1 + N codes, it shouldn't. Hence, N should satisfy the following 2 conditions

( ) ( ) ( ) ( ) ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ < - + - - = - ≥ - - - = - ∑ ∑ + = = , 0 1 2 1 1 2 , 0 1 2 1 2 2 / 1 1 2 / 1 α α α α N L E E N L E E L R N c c L R N c c (11) with ∑ = = L i i h N L 1 2 0 2 | | Γ / α . From (11), ( ) 3 / 1 2 / - ≤ L R L N and ( ) 1 3 / 1 2 / - - > L R L N . Hence, ( ) ⎣ ⎦ 3 / 1 2 / - = L R L N . ■
From (10) and Theorem 2, since the number of codes cannot be larger than the code length, the maximum reachable throughput for a given L becomes

( ) ( ) ( ) ⎪ ⎪ ⎭ ⎪ ⎪ ⎬ ⎫ ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ⎥ ⎥ ⎥ ⎥ ⎦ ⎥ ⎢ ⎢ ⎢ ⎢ ⎣ ⎢ × = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ⎥ ⎦ ⎥ ⎢ ⎣ ⎢ - × = ∑ = L h L L L L R L i i L R , | | / 1 3 min 2 , 1 2 3 min 2 1 2 2 / . (12)
Finally, the maximum reachable throughput with the optimal code length becomes

( ) { } L R R N L≤ ≤ = 1 max max . ( 13
)

Time-frequency codes exploitation

In the MBOA solution, unique logical channels corresponding to different piconets are defined by using different time-frequency codes (TFC) for each sub-band group. These codes provide frequency hopping from a sub-band to another at the end of each OFDM symbol. The configuration proposed by the MBOA solution consists in choosing the TFC regularly without taking into consideration the channel response state of each user for each sub-band. In our study, we use a dynamic TFC (DTFC) distribution, different from the distribution of the MBOA solution, in order to maximize the SS-MC-MA system range.

We consider 3 users, and consequently 3 TFC codes, distributed on subbands 7, 8 and 9 of the MBOA solution. Over a given period T equivalent to the duration of an OFDM symbol, each user occupies one of the 3 available sub-bands. To find the number of unique possible distributions of the TFC over 3 successive periods T, we consider a combinational problem: over one period, we have a permutation with order and without repetition of 3 users on 3 sub-bands. Moreover, within each sub-band, the users' order in time is not taken into consideration. We find that the number of unique permutations is equal to 55. In addition, we have a total of 9 different channel responses in the system, since each user has 3 different channel responses corresponding to 3 sub-bands.

Simulation results

In this section, we present the simulations performed on sub-bands 7, 8 and 9 of the MBOA solution using the proposed SS-MC-MA scheme and taking into consideration the European context.

Fig. 1 represents the total throughput per OFDM symbol of a single user over CM1 channel model for different channel attenuation levels, before applying the dynamic TFC algorithm. With the MBOA solution, the total throughput of 200 bit/symbol is not reachable at attenuation levels higher than 38 dB, whereas with the proposed SS-MC-MA scheme using a single block of length 100 = L

, we are able to transmit 200 bit/symbol at an attenuation level of 53 dB (15 dB larger range). Moreover, when we optimize the code length L and the number of codes N of the SS-MC-MA system, we are able to transmit data at much higher attenuations (81 dB), and the reachable range and throughput with adaptive SS-MC-MA are always larger than the ones of an adaptive OFDM system. The number of QPSK modulated subcarriers can vary from 100 to 0 with the called adaptive OFDM scheme, whereas with the MBOA solution the number of active subcarriers is always equal to 100. The optimal values of L and N that maximize the range of the adaptive SS-MC-MA system for different attenuation levels are given in Fig. 2. We can notice that at high attenuations, N is lower than L.

Fig. 3 and Fig. 4 represent the total system throughput per 3 OFDM symbols for 3 users over CM1 channel model. In Fig. 3, with the MBOA system using the TFC defined by the solution, the 3 users are able to transmit ( 1800 200 3 3 = × × bit/3×symbol) at attenuation levels lower than 41 dB. At attenuation levels from 41 to 43 dB, only 2 users are able to transmit (1200 bit/3×symbol), at levels from 44 to 49 dB only 1 user is able to transmit, and at levels higher than 49 dB no one is able to transmit. When applying the dynamic TFC (DTFC) algorithm to the MBOA system, the system range increases more than 5 dB, and when applying it to the SS-MC-MA scheme, the system range becomes around 20 dB larger than the MBOA system range. In Fig. 4, the same TFC algorithm is applied to the adaptive OFDM system and to the optimized SS-MC-MA system with variable code length L and variable number of codes N. We notice that the adaptive SS-MC-MA system is able to reach an 89 dB attenuation level. Moreover, with the DTFC applied to the SS-MC-MA system, the reachable range becomes larger, and for a given attenuation level, the throughput is improved. Similar results are obtained with CM2, CM3 and CM4 channel models.

Conclusion

In this paper, we proposed a SS-MC-MA waveform which is new for high data rate UWB applications and which respects the OFDM parameters of the MBOA solution, taking into account to the European UWB context. Then, we optimized the spreading code length and the number of codes in order to maximize the system range. Furthermore, we proposed an allocation algorithm which maximizes the system range by distributing the timefrequency codes dynamically, contrarily to the MBOA solution where the time-frequency codes are distributed regularly without taking into consideration the channel response of each user for each sub-band. We showed that the SS-MC-MA system is able to transmit information at attenuation levels much higher than the attenuation limits of the OFDM solution. These optimizations did not take into account the channel coding scheme. However, the performance comparison of the final systems with channel coding shows that our proposed adaptive SS-MC-MA scheme and proposed TFC algorithm can be advantageously exploited for high data rate UWB applications. These improvements can be obtained without changing the radio-frequency front-end compared to the MBOA solution.

  is the number of blocks, C b the number of codes used for block b, L b the code length of block b, E c,b the power allocated to code c of block b,

Proof:

  We want to maximize the minimum value of b

.

  Let γ be the noise margin of the SS-MC-MA system with one block, and let b' be such that

Figure 1 .Figure 3 .

 13 Figure 1. Total throughput of a single user system.

Figure 2 .

 2 Figure 2. Optimal adaptive SS-MC-MA configuration.

Figure 4 .

 4 Figure 4. Total throughput of a 3-users system with adaptive schemes.

Acknowledgment

The authors would like to thank France Télécom R&D/RESA/BWA which supports this study within the contract 46136582.

Code length and number of codes Code Length L Number of codes N


Antoine Stephan
email: antoine.stephan@ens.insa-rennes.fr

Jean-Yves Baudais

Jean-François Hélard
email: jean-francois.helard@insa-rennes.fr

Efficient Allocation Algorithms for Multicarrier Spread-Spectrum Schemes in UWB Applications

Keywords: Multiband OFDM, multicarrier spreadspectrum (MC-SS), resource allocation, UWB

In this paper, we propose a multicarrier spread spectrum (MC-SS) waveform for high data rate UWB applications, taking into account the American and the European UWB contexts. This new waveform for UWB is presented as an evolution of the well known Multiband OFDM Alliance (MBOA) solution and does not increase the system complexity significantly. First, we optimize the number of spreading codes to maximize the system range for a fixed QPSK constellation. Secondly, we use variable constellation orders and we propose a low-complexity resource allocation algorithm that maximizes the system throughput. We show that our adaptive MC-SS system transmits information at much higher attenuation levels and with higher throughput compared to the MBOA solution, and can be advantageously exploited for UWB applications.

I. INTRODUCTION

Ultra-wideband (UWB) technology has attracted considerable interest in short range, high data rate wireless communications since 2002 when the Federal Communications Commission (FCC) agreed on the allocation of a 3.1-10. [START_REF] Foerster | Channel modeling sub-committee report final[END_REF] GHz spectrum for unlicensed use of UWB devices [START_REF]First report and order, revision of part 15 of the commission's rules regarding ultra-wideband transmission systems[END_REF]. The FCC regulations are very stringent and require very low transmitted power since the UWB spectrum overlays other existing spectrum allocations.

One of the multiple-access techniques considered by the IEEE 802.15.3a standardization group is a multiband orthogonal frequency division multiplexing (MB-OFDM) supported by the Multiband OFDM Alliance (MBOA) [START_REF][END_REF]. Some studies have proposed to use a multicarrier codedivision multiple-access (MC-CDMA) waveform by adding a CDMA scheme to the OFDM solution with a spreading in the frequency domain, in order to improve the system performance [START_REF] Schmidt | Ultra wideband transmission based on MC-CDMA[END_REF]. In this paper, we propose a multicarrier spread-spectrum (MC-SS) scheme, known as linear precoding OFDM (LP-OFDM), which respects the OFDM parameters of the MBOA solution in order not to increase the system complexity significantly. This MC-SS technique improves the signal robustness against frequency selectivity and narrowband interferences.

An analytical study focusing on the optimization of the spreading function is presented. More precisely, the intrinsic characteristics and capabilities of the spreading function are highlighted and allocation algorithms are developed to improve the system performance. Two cases are considered for the optimization study. First, we consider a fixed quadrature phase-shift keying (QPSK) constellation as in the MBOA solution, and we find the optimal spreading code length and number of codes that maximize the noise margin, and consequently the system range. Secondly, in order to further improve the system throughput, we consider variable constellation orders as QPSK, 8-QAM (quadrature amplitude modulation) and 16-QAM. The UWB channel response varies slowly in time and can be considered quasi-static. Hence, we assume that the channel state information (CSI) is available at the transmitter. We propose a low-complexity resource allocation algorithm that distributes energy, bits and codes efficiently across the spectrum in order to achieve higher throughput, under a power spectral density (PSD) constraint. Simulations are performed by considering the American and the European UWB context. The optimization study does not take into account the channel coding scheme, but the performance comparison of the final systems with channel coding shows that the adaptive MC-SS can be advantageously exploited for UWB applications This paper is organized as follows. Section II presents the proposed MC-SS scheme. Section III details the MC-SS optimization study and describes the proposed resource allocation algorithms, first in the case of a fixed QPSK constellation and secondly in the case of variable constellation orders. Simulation results showing the interest of the proposed adaptive scheme in UWB applications are given in Section IV, followed by the conclusion in Section V.

II. SYSTEM MODEL

The MBOA solution is based on the combination of an OFDM modulation with a multiband approach that divides the 7.5 GHz UWB spectrum into 14 sub-bands of 528 MHz each. The OFDM scheme consists of 128 subcarriers, out of which 100 are assigned to data tones. The constellation used is a QPSK, which leads to the transmission of 200 data bits per OFDM symbol. Initially, most of the studies have been performed on the first 3 sub-bands (3.1-4.8 GHz). The FCC imposed a PSD limit of -41. [START_REF] Schmidt | Ultra wideband transmission based on MC-CDMA[END_REF] the 6-8.5 GHz range where a similar limit value of -41.3 dBm/MHz was considered [START_REF]ECC Decision of 24 March 2006 on the harmonised conditions for devices using Ultra-Wideband (UWB) technology in bands below 10.6 GHz[END_REF]. Hence, when we consider the European context, we perform our studies on sub-bands 7, 8 and 9 (6.33-7.92 GHz) of the MBOA solution (Fig. 1). To improve the system performance, we propose a MC-SS scheme which consists in assigning to each user a specific block of subcarriers [START_REF] Kaiser | A flexible spread-spectrum multicarrier multiple-access system for multi-media applications[END_REF]. This scheme is applied to UWB while respecting the OFDM parameters of the MBOA solution. The spreading is applied in the frequency domain in order to improve the signal robustness against frequency selectivity of the UWB channel and against narrowband interference. The MC-SS system benefits from the performance and advantages of the MC-CDMA system while improving the resource allocation flexibility. With the MC-SS scheme, symbols are simultaneously transmitted by the same user on a specific subset of subcarriers and undergo the same distortions. Selfinterference (SI), which replaces the multiple-access interference (MAI) obtained with MC-CDMA, can be easily compensated by single user detection with only one complex coefficient per subcarrier.

A schematic representation of the sub-bands distribution of the MC-SS scheme is depicted in Fig. 2. At a given time, each user is allocated a group of 100 data subcarriers equivalent to one of the MBOA sub-bands of 528 MHz bandwidth, in order not to increase the system complexity compared to MBOA. Each sub-band is then divided into several blocks b, each of them including a number of subcarriers equal to the spreading code length L. Note that in this figure, the subcarriers linked by the same spreading codes are adjacent to simplify the schematic representation, whereas in reality they are not necessarily.

The channel model used for our study is the one adopted by the IEEE 802.15.3a committee for the evaluation of UWB physical layer proposals [START_REF] Foerster | Channel modeling sub-committee report final[END_REF]. It is a modified version of the Saleh-Valenzuela model for indoor channels, fitting the properties of measured UWB channels. A lognormal distribution is used for the multipath gain magnitude. In addition, independent fading is assumed for each cluster and each ray within the cluster. Moreover, four different channel models (CM1 to CM4) are defined for the UWB system modeling, each with arrival rates and decay factors chosen to match different usage scenarios and to fit line-of-sight (LOS) and non-line-of-sight (NLOS) cases.

III. MC-SS SYSTEM OPTIMIZATION

In this section, the objective is to properly handle the spreading process so that the system performance is improved. The spreading function brings some additional parameters which are the number N and the length L of the spreading sequences to use. These parameters constitute new degrees of freedom in terms of system configuration and can be optimally chosen as proposed in this part. In order to focus on the study of the precoding function, the only spreading and OFDM functions are considered here, and other functions of the global transmission chain are not taken into account.

The MC-SS system optimization is divided in 2 cases. First, we consider a fixed constellation order of QPSK as in MBOA and we optimize the number of codes in order to maximize the system range. Then, in order to get higher throughput, we propose a resource allocation algorithm with variable constellation orders.

The throughput in bits per symbol of an OFDM system is derived from Shannon theorem by

∑ ∈         + = S k k k OFDM N E h Γ R 0 2 2 1 1 log , ( 1
)
where S is the group of used subcarriers, Γ the signal-tonoise ratio (SNR) gap, h k and E k the frequency-domain response and the transmitted power density of the k th subcarrier respectively, and N 0 the noise density. The total throughput in bits per symbol of a MC-SS system using a zero-forcing (ZF) detection is given by [START_REF] Crussière | Adaptive linear precoded DMT as an efficient resource allocation scheme for power line communications[END_REF] ,

2 1 1 0 2 1 , 1 log 1 1 b N B n b SS MC MA L b n i i b E L R Γ N h - - = = =       = +         ∑∑ ∑ , ( 2
)
where

E E E b = ≤ ≥ ∀ ∑ , ( 3
)
where E is the PSD limit defined by the FCC or the ECC.

A. Fixed QPSK constellation

We consider K data subcarriers per sub-band and a fixed QPSK constellation as in the MBOA solution. For a fixed target throughput of 2K bits per symbol, it is demonstrated in [START_REF] Stephan | Adaptive multicarrier spread-spectrum with dynamic time-frequency codes for UWB applications[END_REF] that to maximize the noise margin of the MC-SS system, a code length L equal to the total number of useful subcarriers K should be used. Consequently, one single block system should be considered. Now, we optimize the code length and the number of codes in order to maximize the system throughput and the system range when the throughput of 2K bits per symbol is not reachable at high attenuation levels.

In a general approach with variable throughput, the number of codes can be lower than the code length. In this case, a multi-block configuration has to be considered and each block can exploit its own code length. But finding the optimal block sizes amounts to resolving a complex combinational optimization problem that can not be reduced to an equivalent convex problem. Then, no analytical solution exists and optimal solution can only be obtained following exhaustive search [START_REF] Crussière | Adaptive linear precoded DMT as an efficient resource allocation scheme for power line communications[END_REF]. In order to avoid prohibitive computations, we assume a single block configuration system.

Maximizing the system range is equivalent to maximizing the system throughput. Using Lagrange multipliers to solve (2) under constraint (3), we find that the optimal solution which maximizes the non-integer system throughput would be to consider

, / n b b E E N = and b N L = , b ∀ .
Then, the optimal non-integer throughput for the single block system becomes

( )            + = ∑ = L i i h L L R 1 2 2 | | / 1 1 log , ( 4
) with 0 2 2 / | | | | N Γ E h h i i =
and h i the frequency-domain response of the i th subcarrier of the single block sub-band. , the optimal number of codes that can be used for a given spreading code length L is ( )

  3 / 1 2 / - = L R L N
, with R given by (4).

Proof: Let N be the optimal number of spreading codes that maximizes the system range. Thus, when the system is using N codes, the PSD constraint has to be respected, whereas when it is using 1 + N codes, the constraint should not be respected anymore. Therefore, N should satisfy

( ) ( ) ( ) ( ) / 2 1 1 / 2 1 2 1 2 1 0, 1 2 1 2 1 0, N R L n n N R L n n L N E E L N E E α α α α = + =  - = -- -≥    +  - = -- -<   ∑ ∑ (5) with 2 0 2 1 / | | L i i N L h Γ α = = ∑ . From (5), ( ) 3 / 1 2 / - ≤ L R L N and ( ) 1 3 / 1 2 / - - > L R L N .
Hence, ( )

  3 / 1 2 / - = L R L N .
From ( 4) and Theorem 1, since the number of codes can not be larger than the code length, the maximum reachable throughput for a given code length L becomes ( ) ( )

. , | | / 1 3 min 2 1 2 2                           × = ∑ = L h L L R L i i (6)
Finally, the maximum reachable throughput with the optimal code length becomes

( ) { } max 1 max L K R R L ≤ ≤ = . (7)
A low-complexity algorithm that derives the optimal number of codes N is applied to the MC-SS system using a fixed QPSK constellation. This algorithm can be advantageously exploited for high attenuation levels since it increases the system range significantly when the channel response is critical, as shown in Section IV. In addition, these improvements can be obtained without changing the radiofrequency front-end of the MBOA solution.

B. Variable constellations

Here, we move away from the MBOA proposal by considering variable constellations (QPSK, 8-QAM and 16-QAM) in order to reach higher throughput. We propose a resource allocation algorithm that distributes energy, bits and codes efficiently across the spectrum in order to maximize the total system throughput under a PSD constraint.

By considering a multi-block context, the maximum reachable non-integer throughput in bits per block b is derived from (4)

              + = ∑ = 0 1 2 , 2 | | 1 1 1 log N E h L Γ L R L i b i b , (8)
and the maximum throughput in bits per code n becomes [ ] , / 1 :

n b b R R L n L = ∀ ∈ . ( 9
)
Since we have discrete constellation orders, the throughput per code must always have integer values. An optimal solution for this problem is given in [START_REF] Crussière | Adaptive linear precoded DMT as an efficient resource allocation scheme for power line communications[END_REF]. It shows that an optimal throughput distribution would be to allocate 

 1 / + L R b bits to m codes and   L R b /
bits to the remaining L m -codes, where m is an integer number given by ( )

/ / 2 1 b b R L R L m L -      = -     . (10)
Hence, the discrete throughput in bits per code becomes

[ ] [ ] , , / 1 1: / 1:
.

n b b n b b R R L n m R R L n m L  = + ∀ ∈       = ∀∈ +       (11)
The power density per code for block b is then given by (

| n b L R n b i i b N Γ P L h = = - ∑ , ) , 0 , 2 2 1 , 2 1 |
and the total discrete throughput in bits per block b becomes

      L R L L R b L R L R b b b / ) 1 2 ( / / + - = - . ( 13
)
This algorithm increases the system throughput considerably when applied to an MC-SS scheme with variable constellations. Consequently, the MC-SS system range is improved compared to MBOA and the adaptive system is able to transmit data at very low attenuation levels.

IV. SIMULATION RESULTS

In this section, we present the simulations performed on sub-bands 1, 2 and 3 (American context, 3.16-4.75 GHz) and sub-bands 7, 8 and 9 (European context, 6.33-7.92 GHz) of the MBOA solution.

Fig. 3 and Fig. 4 represent the results of the throughput optimization for a fixed QPSK constellation in the American context. The total throughput per OFDM symbol of a single user over CM1 channel model is given in Fig. 3, for different channel attenuation levels. With the MBOA solution, the total throughput of 200 bit/symbol is not reachable at attenuation levels higher than 46 dB, whereas with the proposed MC-SS scheme using a single block of length 100 = L

, we are able totransmit 200 bit/symbol until a 61 dB level (15 dB larger range). Moreover, when we optimize L and N for the MC-SS system, we are able to transmit data at much higher attenuations (until 84 dB), and the reachable range with adaptive MC-SS is always larger than the range of an adaptive OFDM system. With the called adaptive OFDM scheme, the number of QPSK modulated subcarriers can vary from 100 to 0, whereas with the MBOA solution the number of active subcarriers is always equal to 100. The optimal values of L and N that maximize the range of the adaptive MC-SS system are given in Fig. 4. We can notice that at high attenuations, the optimal value of N is not necessarily equal to L. Hence, the algorithm is very efficient at high attenuation levels. Moreover, the radio-frequency front-end of the MBOA solution is maintained.

Fig. 5 and Fig. 6 represent the throughput of a single user when variable constellation orders are considered (QPSK, 8-QAM and 16-QAM), for the American and European contexts, respectively. When the resource allocation algorithm is applied to the MC-SS scheme, the throughput is equal to 400 bit/symbol at low attenuation levels. At high attenuation levels, the adaptive MC-SS range is always larger than the adaptive OFDM range (around 10 dB at critical attenuation levels). This is due to the energy gathering capability of MC-SS which can exploit, contrarily to OFDM, the residual energy conveyed by each subcarrier. Similar results are obtained for the different channel models (CM1 to CM4). In this case, since we are using 8-QAM and 16-QAM constellations, one or two additional bits are needed for the analog-to-digital conversion. Hence, the radio-frequency front-end complexity is not increased significantly compared to MBOA.

V. CONCLUSION

In this paper, we proposed a multicarrier spread-spectrum waveform which is new for high data rate UWB applications and which respects the OFDM parameters of the MBOA solution in order not to increase the system complexity significantly. First, while considering a fixed QPSK constellation, the spreading code length and the number of codes were optimized to maximize the system range. Furthermore, we used variable constellation orders and we proposed a low-complexity resource allocation algorithm in order to maximize the system throughput. We showed that the adaptive MC-SS system is able to transmit information at attenuation levels much higher than the attenuation limits of the MBOA solution. These optimizations did not take into account the channel coding scheme. However, the performance comparison of the final systems with channel coding shows that our proposed adaptive MC-SS scheme can be advantageously exploited for high data rate UWB applications. In addition, the proposed system complexity is not increased significantly compared to MBOA.

Fig. 1 .

 1 Fig. 1. PSD mask (FCC and ECC) and sub-bands distribution of the MBOA solution.

  B is the number of blocks, N b the number of codes per block b, L the spreading code length, h i,b the frequencydomain response of the i th subcarrier in block b, and E n,b the power density of code n within block b, with the constraint

Theorem 1 :

 1 With a QPSK constellation and a

Fig. 3 .

 3 Fig.3. System throughput with the optimal number of codes and a fixed QPSK constellation, over CM1 model (American context).

Fig. 5 .

 5 Fig. 5. System throughput with variable constellation orders, after applying the resource allocation algorithm over CM2 model (American context).

Fig. 4 .

 4 Fig. 4. Optimal adaptive MC-SS configuration with a fixed QPSK constellation, over CM1 model (American context).

Fig. 6 .

 6 Fig.6. System throughput with variable constellation orders, after applying the resource allocation algorithm over CM3 model (European context).

ACKNOWLEDGEMENT

The authors would like to thank France Télécom R&D/RESA/BWA which supports this study within the contract 46136582.

Code length and number of codes Code Length L Number of codes N