Khouloud Issiali
email: khouloud.issiali@orange.com

Valery Guillet
email: valery.guillet@orange.com

Ghais El

Gheorghe Zaharia
email: gheorghe.zaharia@insa-rennes.fr

IEEE 802.11ac Multi-User MIMO Capacity and Impact of Antenna Array Geometry based on Indoor Measurements

Keywords: MU-MIMO, IEEE 802.11ac, capacity, antenna arrays, indoor propagation measurements

Based on channel measurements conducted at 5 GHz, this paper examines the impact of transmitting antennas on the Block Diagonalization (BD) capacity gain for IEEE 802.11ac Multi-User Multiple Input Multiple Output (MU-MIMO) in Home Networks. We study in details a system with two users with two antennas each by evaluating multiple numbers as well as various geometries of transmitting antennas. The experiments reveal that Crossed Circular Array (CCA) is recommended for small sized transmitter with 8 antennas (70% of MU-MIMO capacity gain over Single User MIMO (SU-MIMO) is achieved for a 20 dB of Signal-to-Noise Ratio (SNR)). In the context of a less congested system, it has been shown that using 6 transmitting antennas arranged in Uniform Linear Array (ULA) gives a gain close to that obtained with 8 antennas. We have also shown, using measured path loss values, that the capacity gain of MU-MIMO to SU-MIMO goes beyond the double when the difference between the received power of each user is high. This is obtained in comparison with the Carrier Sense Multiple Access/Collision Avoidance (CSMA/CA) as a channel access method, 130% of gain is achieved when the gap between the received powers of each user is around 40 dB.

I. INTRODUCTION

In a Downlink (DL) Multi-User Multiple Input Multiple Output (MU-MIMO) scenario, an Access Point (AP) is equipped with multiple antennas and is simultaneously transmitting several independent spatial streams to a group of users. Each of these users is also equipped with a single or multiple antennas. The management of multiple users generates a new interference called Inter User Interference (IUI). Several studies have focused on the MU-MIMO solutions to overcome multipath propagation and IUI.

In this context, the new IEEE 802.11ac standard ratified in January 2014 normalizes the MU-MIMO processing, namely precoding techniques [START_REF] Issiali | Impact of EIRP Constraint on MU-MIMO 802.11ac Capacity Gain in Home Networks[END_REF]. The use of MU-MIMO methods aims to increase data rates above 1 Gbits/s and to improve capacity. The precoding methods can be classified according to several criteria [START_REF] Peel | Space-Time Processing for MIMO Communications (chapter:Linear and Dirty-Paper Techniques for the Multi-User MIMO Downlink[END_REF]. The criterion that has been frequently used is whether the technique is linear or not.

The non-linear techniques are known to achieve optimum capacity. Actually, it has been proven that the capacity region of the DL MU-MIMO systems is achieved with Dirty Paper Coding (DPC) method [START_REF] Lee | Dirty Paper Coding vs. Linear Precoding for MIMO Broadcast Channels[END_REF]. This technique has, however, high computational complexity. The linear method that is most explored in the literature is Block Diagonalization (BD) [START_REF] Peel | Space-Time Processing for MIMO Communications (chapter:Linear and Dirty-Paper Techniques for the Multi-User MIMO Downlink[END_REF]. The main principle of BD is to ensure zero IUI as a first step, and then to maximize capacity. Thus, with perfect Channel State Information (CSI) at the Transmitter (Tx), BD transforms a MU-MIMO system into several parallel Single User MIMO (SU-MIMO) systems after canceling the IUI. Transmit eigenbeamforming [START_REF] Bouhlel | Transmit Beamforming Analysis for MIMO Systems in Indoor Residential Environment Based on 3D Ray Tracing[END_REF] is then applied to maximize capacity. In fact, when a perfect CSI is provided at the access point, zero IUI is achievable at every receiver, enabling thereby a simple receiver at each user. However, propagation channels change over time in actual radio environments and CSI is hence not perfect. A simple channel prediction scheme to provide CSI is proposed in [START_REF] Bui | Performance Evaluation of a Multi-User MIMO System With Prediction of Time-Varying Indoor Channels[END_REF], and its effectiveness is demonstrated through simulations of Bit Error Rate (BER) performance using a measurement campaign in a meeting room.

Few articles have studied MU-MIMO capacity based on measured indoor MU-MIMO propagation channels. In a narrow indoor corridor environment, the authors in [START_REF] Rusek | Indoor multi-user MIMO: Measured user orthogonality and its impact on the choice of coding[END_REF] have analyzed DPC gain over linear processing for two single antenna receivers and reveal that this gain is almost insignificant for low and high user channel orthogonality. Studies in [START_REF] Fushiki | Experimental evaluations of multiuser MIMO with two-dimensional antenna configuration[END_REF]- [START_REF] Zheng | Performance examinations of Multi-User MIMO systems with a compact antenna cube[END_REF] have focused on achieving capacity or throughput improvement through the use of various transmitting antenna arrangements, antenna designs and antenna configurations. It has been shown in [START_REF] Zheng | Performance examinations of Multi-User MIMO systems with a compact antenna cube[END_REF] by evaluating channel capacity that a compact tripolarization antenna cube combined with a simplified pattern circuit are suitable for MU-MIMO systems with antenna selection. It has been shown in [START_REF] Fushiki | Experimental evaluations of multiuser MIMO with two-dimensional antenna configuration[END_REF], using one transmitter with 8 antennas and four single antenna receivers, that constraining the antenna arrangement to 7λ is beneficial (a gain of 12.8 % of spectral efficiency is achieved) in an indoor environment (room), where λ indicates the wavelength of carrier frequency. However, none of these articles highlights the area of use of the MU-MIMO compared to SU-MIMO, or studies in details MU-MIMO capacity gain over SU-MIMO with multiple antennas receivers based on measurements in Homes Networks.

In this article, we evaluate the MU-MIMO capacity gain over SU-MIMO using system with various transmitting antenna array geometries and with two antennas at each Receiver (Rx) in an indoor frequency selective fading environment. This is based on propagation channel measurements. The measurement campaign has been conducted in the 5.25 GHz frequency band in a residential environment typically encountered in home networks. The rest of this paper is organized as follows. Section II presents briefly the considered 802.11ac system, the BD algorithm and gives the capacity computation method for MU-MIMO and SU-MIMO systems. Section III describes the experiment and the post processing of the data. The results are provided in Section IV. Finally, the conclusion is drawn in Section V.

II. IEEE 802.11AC MULTI-USER MIMO SYSTEM AND RELATED CHANNEL CAPACITY

The studied IEEE 802.11ac MU-MIMO system based on BD precoding and its capacity are detailed in [START_REF] Issiali | Impact of Antennas and Correlated Propagation Channel on BD Capacity Gain for 802.11ac Multi-User MIMO in Home Networks[END_REF]. Hereafter, we recall capacity formulas.

A. MU-MIMO Capacity

For a MU-MIMO system with K users and n R k receiving antennas for each user k, the channel capacity for a particular propagation channel sample is expressed for each Orthogonal Frequency-Division Multiplexing (OFDM) subcarrier by [START_REF] Issiali | Impact of EIRP Constraint on MU-MIMO 802.11ac Capacity Gain in Home Networks[END_REF].

C M U -M IM O = K k=1 nR k i=1 log 2 (1 + p ik σ 2 n µ 2 ik ) (1)
where p ik is the power dedicated to the i th antenna for the k th user, µ 2 ik are the eigenvalues of the effective channel for the k th user after applying the IUI cancellation, and σ 2 n is the noise power. The total transmitted power over 20 M Hz bandwidth is equally shared among p ik and is scaled to satisfy the Equivalent Isotropically Radiated Power (EIRP) constraint of Wireless Local Area Network (WLAN) [START_REF] Issiali | Impact of EIRP Constraint on MU-MIMO 802.11ac Capacity Gain in Home Networks[END_REF], and K = 2 throughout this paper.

B. SU-MIMO Capacity

For the corresponding SU-MIMO systems and for relevant comparisons with MU-MIMO, the numbers of transmitting antennas n T and receiving antennas n R k remain unchanged. The considered SU-MIMO system applies a singular value decomposition and its capacity is computed for each OFDM subcarrier as detailed in [START_REF] Bouhlel | Transmit Beamforming Analysis for MIMO Systems in Indoor Residential Environment Based on 3D Ray Tracing[END_REF]. We denote C 1 and C 2 the provided capacities for two users respectively. The SU-MIMO capacity for a 2-user system is expressed according to the applied channel access method. We give the capacity for the following two channel access methods.

1) TDMA method:

In the literature, the SU-MIMO sum capacity is often computed considering the deterministic Time Division Multiple Access (TDMA) which allows several users to share the same frequency channel by dividing the signal into equal time slots.The TDMA SU-MIMO sum capacity, denoted C SU,T DM A , is computed using the arithmetic mean of C 1 and C 2 as can be seen in [START_REF] Peel | Space-Time Processing for MIMO Communications (chapter:Linear and Dirty-Paper Techniques for the Multi-User MIMO Downlink[END_REF]. 2) CSMA/CA method: The IEEE 802.11ac standard uses for the channel access the Carrier Sense Multiple Access/Collision Avoidance (CSMA/CA) method, where each user verifies the absence of other co-channel signals before transmitting a frame. The data frames are supposed to have equal size for each user, which implies a variable transmission duration [START_REF] Heusse | Performance anomaly of 802.11b[END_REF]. The CSMA/CA SU-MIMO sum capacity is then equal to the harmonic mean of C 1 and C 2 expressed by [START_REF] Lee | Dirty Paper Coding vs. Linear Precoding for MIMO Broadcast Channels[END_REF].

C SU,T DM A = C 1 + C 2 2 (2)
C SU,CSM A = 2 1 C1 + 1 C2 (3)

III. EXPERIMENT

In this section, we present the performed measurement for MU-MIMO channels, based on which we evaluate the performance. We first describe the measurement environment as well as the studied scenarios. Further, we introduce the measurement equipment and setup, and the post processing including the different types of transmitting antenna arrays.

A. Measurement Scenario

Fig. 1 represents the environment of the experiment. It displays a typical 3D indoor residential scene used to perform measurements [START_REF] Guillet | Over the air antenna measurement test-bed to assess and optimize WiFi performance[END_REF]. It is a typical and real middle sized apartment with a 12m × 7m surface and European building materials and furniture. The ceiling is at 2.53 m. Both Line-Of-Sight (LOS) and Non-Line-Of-Sight (NLOS) scenarios have been probed. Nevertheless, hereafter we do not study the two cases separately since both give almost identical results. Two locations of the Tx are considered, denoted as Tx1 and Tx2 in Fig. 1. For each position of Tx, multiple configurations of the two receivers are evaluated. We denote Rx 1 and Rx 2 the position for the first and the second user respectively. During the measurements, nothing moved in the environment of the experiment to keep the same measurement conditions. Finally, the obtained measurement data base corresponds to 67 various 2-users configurations.

B. Channel Measurement Setup

The MU-MIMO propagation channel is sounded using a Vector Network Analyzer (VNA) based on a frequency domain technique. We collect the S 21 parameter since the propagation channel is the device under test. The VNA, depicted in Fig. 2(a), is connected by cables of 10 m to the Tx and 20 m to each Rx. Hence, the maximum distance between the Tx and the Rx is 30 m. The VNA have probed 2048 frequency tones between 5.15 GHz and 5.40 GHz. This configuration permits a maximum propagation excess delay of 8192 ns. This delay is well above the maximum propagation delay in such environment but it is useful to estimate the noise level of the measurement data for post-processing. The high number of frequency bins allows also to improve the dynamic of the Channel Impulse Response (CIR), which is between 20 dB and 65 dB in our experiment.

We have used vertically polarized dipole antennas at the Tx and the Rx. The Tx is composed of 8 antennas arranged in Uniform Linear Array (ULA) spaced by λ/2. The transmitting antenna gain is 5.13 dBi with 60 degrees of vertical beamwidth. Two additional transmitting antennas are located at both ends to have symmetrical coupling effects as can be seen in Fig. 2(b). The distance between the center of each transmitting antenna and the ground is 1.8 m. For each user as depicted in Fig. 2(c), four antennas are arranged in a square horizontal array with a λ/2 side. The receiving antenna gain is 1.6 dBi, and the distance between the antenna center and the ground is fixed to 1.1 m. The transmitting antennas are mounted on a rotating arm to measure different antenna geometries and to take into account fast fading effects as illustrated in Fig. 2(b). A rotation step of 6 degrees is selected. We come up to a total of 480 virtual transmitting antennas as shown in Fig. 2(d). For each position of the three devices, i.e. one Tx and two Rx, the channel is of dimension 480 × 8 for each subcarrier where 8 represents the total number of receiving antennas.

Two 8-to-1 switches at the Tx and the Rx respectively, are used to select the antennas. First, the channel is measured between the first transmitting antenna and the first receiving antenna by sweeping frequencies between 5.15 GHz and 5.40 GHz stepped by 122 kHz. The selected receiving antenna for measurement is then switched using the receiving switch. Afterwards, we select the second transmitting antenna using the switch at the Tx. Note that the switching time is 5 ms for switching at the Tx and the Rx . Finally, after the 8 × 8 switching steps, the rotating arm is turned by 6 degrees. We repeat the same processing till the rotating arm returns to the first position. It takes about 20 min with the VNA to record one measurement consisting of 480 × 8 channel sweeps over 2048 tones. All equipment (switches, VNA and rotating arm) are controlled by one laptop and connected through Ethernet cables.

C. Post-Processing

The measured CIRs are afterwards calibrated using reference measurements where the transmit and receive cables or switches are directly connected to the VNA Input-Output. For our analysis, the calibration takes into consideration the switches, the antenna connectors, and the cables. The collected CIRs have a dynamic arranged between 20 dB and 60 dB depending on whether the Rx is near or far from the Tx. The measurement noise level is estimated from the non physical delay area of the average Power Delay Profile (PDP). We force the corresponding CIR complex samples with an average power below this noise level to 0 and also the sample corresponding to a dynamic greater than 30 dB in order to process measurements with a comparable dynamic between 20 and 30 dB.

The IEEE 802.11ac OFDM signal is divided into subcarriers with a subcarrier spacing equal to 312.5 kHz. Since the indoor propagation channel is frequency flat on such a small bandwidth, we choose the first measured frequency sample to be the multiple of 122 kHz which is the closest to the subcarrier spacing of IEEE 802.11ac (312.5 kHz). We exploit multiple IEEE 802.11ac 20 M Hz subchannels (up to 10 bands for 250 M Hz probed by the VNA) as well as angular positions (up to 60 transmit angular positions) in order to have representative statistical results .

IV. EXPERIMENTAL RESULTS

The measured data allows to study various types of transmitting antenna geometries. This article presents MU-MIMO results based on normalized and non-normalized propagation channels.

A. Impact of Transmitting Antennas considering a Normalized Channel

In this section, the effect of transmitting antennas (number and geometry of antennas) on MU-MIMO system with two receivers with two antennas each is analyzed based on a normalized channel. The reason of using the normalization is to keep only fast-fading effects so that the average Signal-to-Noise Ratio (SNR) at the receiving antennas is set to a fixed value and can be easily adjusted as a parameter. The applied channel normalization in this article implies that the average propagation loss is set to 0 dB for both users [START_REF] Issiali | Impact of Antennas and Correlated Propagation Channel on BD Capacity Gain for 802.11ac Multi-User MIMO in Home Networks[END_REF]. The SNR is defined as SN R = EIRP/σ 2 n where EIRP = 23 dBm for this study, and is set to 20 dB. The aim is to assess the impact of transmitting antenna configuration on the BD capacity gain over SU-MIMO and to give recommendations to optimize MU-MIMO performance. To highlight the MU-MIMO capacity gain over SU-MIMO, most graphs below show the average of MU-MIMO to SU-MIMO capacity ratio. For 2 users, the optimal capacity gain value is 2 [10] for TDMA system.

1) Number of transmitting antennas: Fig. 3 gives the average of MU-MIMO to SU-MIMO capacity ratio versus the number of transmitting antennas arranged in an ULA. It also includes 10% (q 10 ) and 90% (q 90 ) confidence intervals as a reference. The first observation drawn from Fig. 3 is that the MU-MIMO capacity gain over SU-MIMO grows logarithmically with the number of transmitting antennas. It changes from 1.27 to 1.7 for the residential environment, i.e. around 43% of capacity gain. For 4 transmitting antennas, the quantile q 10 of capacity gain is less than 1. This can be explained by the fact that we cannot benefit from transmit beamforming gain since the number of transmit antennas is the same as the total number of spatial streams.

Fig. 4 shows the average capacity values for MU-MIMO and SU-MIMO systems. The capacity value for MU-MIMO increases more rapidly than SU-MIMO. It achieves 24 bits/s/Hz versus 14 bits/s/Hz for SU-MIMO with 8 transmitting antennas. In order to optimize the MU-MIMO capacity gain and have a less congested system, we recommend using 6 transmitting antennas in a system with two receivers and two antennas for each receiver. If we aim at reaching higher capacities, using 8 transmitting antennas allows 2 bits/s/Hz of capacity increase.

2) Different antenna geometries for 8 transmitting antennas: Before comparing the performance of MU-MIMO to SU-MIMO, we first define the analyzed antenna geometries. We evaluate a Tx with 8 antennas arranged in ULA, Crossed Circular Array (CCA) with 0.5λ spacing, and Irregular Circular Array (ICA) with different radiuses as illustrated in Fig. 5. In Fig. 5(b), the antennas are placed on the same circle and 48 degrees is a multiple of the angular step of 6 degrees. Four radiuses are considered: 0.5λ, 1λ, 2λ and 3λ. We denote them respectively: ICA 0.5λ, ICA 1λ, ICA 2λ, ICA 3λ. Note also that the results are presented based on the two-user channel correlation coefficient explored in [START_REF] Issiali | Impact of Antennas and Correlated Propagation Channel on BD Capacity Gain for 802.11ac Multi-User MIMO in Home Networks[END_REF]. Fig. 6 gives the average of MU-MIMO to SU-MIMO capacity ratio versus the average correlation coefficient. The highest MU-MIMO capacity gain over SU-MIMO is achieved with antennas arranged in CCA with relatively small correlation coefficient value. This confirms the results of [START_REF] Fushiki | Experimental evaluations of multiuser MIMO with two-dimensional antenna configuration[END_REF] of reducing the span of an antenna array. All of the simulated geometries show small correlation. This is explained by the number of the transmitting antennas [START_REF] Issiali | Impact of Antennas and Correlated Propagation Channel on BD Capacity Gain for 802.11ac Multi-User MIMO in Home Networks[END_REF]. In terms of capacity values, as in Fig. 7, we achieve 23.45 bits/s/Hz with the CCA geometry, which is very close to the highest one shown in the graph with ULA but with a greater span.

B. Non Normalized Channel using 6 transmitting antennas arranged in ULA

In this section, we consider the propagation channel including its measured path loss on 20 M Hz bandwidth. The EIRP is equal to 23 dBm. The noise power is set to -93 dBm. The number of transmitting antennas is set to 6 arranged in ULA geometry. The SU-MIMO capacity is expressed considering the two channel access methods mentioned above: TDMA and CSMA/CA. We consider the average received power at each user in dBm. Fig. 8 shows the average of MU-MIMO to SU-MIMO capacity ratio versus the difference of the received powers ∆P . We observe that when ∆P is below 15 dB, both channel access methods give almost the same results. Nevertheless, compared to SU-MIMO CSMA/CA method, it is advantageous to group users with larger ∆P and use MU-MIMO: the capacity gain can be greater than 2. Actually, if C 1 is very small compared to C 2 , then C SU,CSM A is penalized by C 1 [START_REF] Heusse | Performance anomaly of 802.11b[END_REF] which is not the case of C M U -M IM O . We also notice that the capacity gain in all cases is higher than 60% in a 12m × 7m apartment with a 23 dBm EIRP. This proves the benefit of using the MU-MIMO method rather than applying the classical eigen-beamforming of the SU-MIMO.

V. CONCLUSION

We have investigated the impact of transmitting antenna geometry on the BD capacity gain for 802.11ac MU-MIMO in home networks. The results are based on measured propagation channel for two users with two antennas each. We have given in this article recommendations to optimize MU-MIMO capacity in terms of number and geometry of transmitting antennas. We have also studied the advantage of path loss difference on the BD capacity gain over SU-MIMO. In particular, in a typical indoor apartment with a 23 dBm EIRP, MU-MIMO is better than SU-MIMO based on CSMA/CA, the capacity gain goes beyond the double since SU-MIMO based on CSMA/CA is penalized when the gap between the received power of each user is high. Furthermore, we will perform a comparison between these results and the ones based on the MU-MIMO correlated channel model specified for 802.11ac. Besides, the impact of the receiving antennas number might be analyzed.

Figure 1 .

 1 Figure 1. The indoor environment: 2 positions of Tx with 12 positions of Rx.

  Tx: 480 virtual antennas.

Figure 2 .

 2 Figure 2. Measurement equipment.

Figure 3 .

 3 Figure 3. Average of MU-MIMO to SU-MIMO capacity ratio versus the number of transmitting antennas.

Figure 4 .

 4 Figure 4. MU-MIMO and SU-MIMO capacity values.

Figure 5 .

 5 Figure 5. Antenna geometries.

Figure 6 .

 6 Figure 6. Average of MU-MIMO to SU-MIMO capacity ratio versus the average correlation coefficient.

Figure 7 .

 7 Figure 7. MU-MIMO capacity values versus the average correlation coefficient.

Figure 8 .

 8 Figure 8. MU-MIMO to SU-MIMO capacity ratio versus ∆P .


Appasamy Murugaiyan

Methods in Historical linguistics Evidences from Tamil epigraphic

come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Why and how languages change over time have been the major concerns of the historical linguistics. Any language, as a living entity, is subject to change. Historical linguistics is the field of linguistic research that is interested in the study of temporal variationdiachronic changes. How ever, diachronic and synchronic linguistic studies are complementary to each other. In Historical linguistics, we are interested in the complex interaction between the synchronic and diachronic aspects of the language. In short, historical linguistics aims at 1) understanding the principles and factors that cause changes in language and 2) describing the history of a given language. Here we would study two different but related aspects of linguistic variation: temporal (Historical linguistics) and social (historical sociolinguistics). In general, historical linguistics deals about the changes that occurred in languages over time (temporal variation). The linguistic analysis of inscriptions and classical and ancient literary texts will shed light on the historical linguistics of Tamil and will try to fill a gap in the historical linguistics of the Dravidian family of languages.

The Dravidian comparative linguistics in the last few decades has arrived at excellent results at different levels of language change: phonology, morphology and etymology. However, the field of historical syntax remains to be explored in detail. Change or variation in word order type is one of the most important areas in the study of historical linguistics and language change.

TAMIL INSCRIPTIONS

There are inscriptions of many ages, carved in Tamiḻ-Brāhmī, Vaṭṭeḻuttu, Tamiḻ and Grantha scripts. The inscriptions in Tamil Nadu can be divided either chronologically or typologically into different groups. They can be broadly classified into three groups, known as (1) Tamiḻ-Brāhmī inscriptions (TBI), (2) Hero Stone Inscriptions (HSI) and (3) Temple Tamil inscriptions (TTI) (that include copper plates and other Inscriptions). The vast corpus of Tamil inscriptions shows the gradual development of the Tamil epigraphic culture. The earliest of the Tamil inscriptions written in Tamiḻ-Brāhmī script and so named as Tamiḻ-Brāhmī inscriptions (TBI), date from 300 BCE up to 500 CE. These short inscriptions carved on the rocks and in the natural caves, on pot shreds and coins have been studied in detail by Mahadevan (2003). The HSI comes immediately after the (TBI) both chronologically and typologically. The HSI, short memorial or funerary texts, are limited in number and are distributed mainly in the northern part of Tamil Nadu. Finally, the TTI are the structurally developed diverse monumental inscriptions carved on the walls of the temples and span from 5 th century up to 19 th CE. The TTI inscriptions contain mostly descriptions of donations (of lands, ornaments, jewellery, cows, goats, statues and images) made to temples, village assemblies, their maintenance, administration. From the expansion of Chola (8 th to 14 th CE), epigraphy flourished everywhere, and inscriptions in Tamil are literally innumerable.

LINGUISTIC ANALYSIS

An in-depth linguistic analysis of Tamil epigraphic texts will show how the Tamil language used in Tamil inscriptions constitutes an important diachronic evidence of both sociolinguistic and linguistic evolution. I will concentrate on the following three aspects:  Historical sociolinguistics: Maṇipravāḷa style and the development of Tamil as Inscriptional Language  Historical linguistics, Syntax and Information structure  Construction of a fine-grained linguistic database and illustrate how "corpus analysis" can help us mapping the process of language change and language use.

Historical sociolinguistics:

Historical sociolinguistics is the study of the relationship between language and society in the past. It aims to identify how extra linguistic factors induce changes in the grammatical structure of a language (syntax, phonology, and lexicon) over time. This topic will deal about Bilingualism, language contact, development of Maṇipravāḷa style and the emergence of Tamil as "Inscriptional Language". We will study some of the bilingual inscriptions in Tamil and show the functions of the Indo Aryan (Prakrit and Sanskrit) and the Tamil languages in the early Tamil epigraphic texts. We will study the nature of contact between these two major Indian language families and the development of the Maṇipravāḷa style in the epigraphic texts.

In this regard, importance will be given to the study of the sociolinguistic aspects of creation of Tamil technical terms. This part will show one aspect of the specific features of the Tamil as inscriptional language.

Historical linguistics, Syntax and Information structure:

What type of linguistic model would offer an understanding and interpretation of a variety of ancient texts that is preserved only in "writing"? How to describe the (synchronic) linguistic structure of a language at a given point in the past? How to find out and account for the linguistic changes that have occurred during the past few centuries?

One possible solution would be to device a conceptual framework based on semantics and pragmatics, which would be more appropriate to delve into the meaning, intended in the text.

Since the 19th century, there has been a regular paradigm shift in linguistic theory and in the study of languages (from philology to structuralism, generative, functional, etc.). This paradigm shift has provided us with a handful of analytical tools, enabling us to view the discourse (written and spoken) from a new perspective; it has also shown us that texts are more than strings of sentences. Pioneering studies in this direction have made it clear that it is necessary to take into account semantic and communicative dimensions in the description of languages. (Kibrik 1997).

The place of different constituents in these propositions is controlled by information structure and other contextual considerations. Lambrecht suggests that the formal structure of sentences is related to the communicative situations in which sentences are used. He states that "this relationship is governed by principles and rules of grammar, in a component called information structure" (Lambrecht 1994 p.334).

Based on the above principles, this topic will study the morphological and syntactic structures of the Tamil epigraphic texts. We will concentrate on the case system, word order variation and predicate structure in the Tamil epigraphic texts.

Historical linguistics, Linguistic database and Corpus analysis

During the last few decades, corpora analysis and database have drastically changed the linguistic analysis and the study of languages. This is even more true in the case of historical linguistics. Because the use of quantitative data alone will allow the identification of specific language changes and to study the historical evolution of languages. In this topic, we will discuss about the construction of a fine-grained linguistic database and illustrate how "corpus analysis" can help us mapping the process of language change.

In this topic we will discuss about preparation of corpus, data entry, inventory of parts of speech tag set (POST), interlinear glossing of texts and other language specific issues in the construction of a linguistic database. This topic will try to illustrate how linguistic corpora can be used as readily available evidence for mapping language, language development and language variation in time and space.