Performance of Multiuser MIMO Communication System using Chirp ...

Performance of Multiuser MIMO Communication System using Chirp Modulation Muhammad Ajmal Khan, Raveendra K. Rao, Xianbin Wang Department of Electrical and Computer Engineering Western University, London, Ontario, Canada, N6A 5B9. Abstract-Multiple-Input and Multiple-Output (MIMO) sys­ tem is widely recognized as an effective means to combat the effects of multipath fading in wireless communications. In this paper, we propose the use of chirp modulation technique in a MIMO system, as the modulated signals have inherent interfer­ ence rejection capability and immunity against Doppler shift and fading due to multipath propagation. The performance of chirp­ based MIMO system is examined using Monte Carlo simulations over Rayleigh fading channel. For example, it is shown that

a simple 2

x 2 MIMO system can offer a significant gain in performance relative to maximal ratio combining (MRC) using

chirp modulation. Next, a multiuser MIMO (MU-MIMO) system is proposed, where each user is assigned a unique orthogonal chirp signal that efficiently modulates each user's incoming data as well as identifies them at the receiver. Numerical results show that chirp modulation is very effective in MU-MIMO system in eliminating the effects of multiple-access interference (MAl).

I.

INTRODUCTION

The future wireless communication systems are aimed at providing extremely high-speed data transmission to support high speed Internet, high quality multimedia and high defini­ tion streaming videos, where the concept of MIMO technology has emerged as a key factor to achieve high data rates and to increase system's reliability in harsh wireless channels without increasing bandwidth and transmit power [1]. MIMO system consists of an array of antennas employed at the transmitter as well as at the receiver, with each antenna separated by some distance in space. By introducing multiple antennas, the possibilities are increased that at least one antenna at the transmitter or receiver does not experience multipath fading [2] [3]. A linear chirp is a sinusoidal signal whose frequency varies linearly with time. The chirp rate is used to encode information in the modulating signal and is the basis of conventional chirp modulation, which is a nonlinear modulation scheme in con­ trast to PSK and QAM. Chirp modulation does not necessarily employ coding and produces a transmitted signal bandwidth much greater than the bandwidth of the information signal being sent. Furthermore, chirp modulation, a spread spectrum type of modulation that is robust to multipath interference, can realize higher processing gains and have been used in wireless communications to improve the performance due to its anti-jamming characteristic [4] [5]. The conventional chirp signals have been widely used in radar and sonar applications. Chirp signals have also been used in various other applications such as combating multipath interference [6], spread spectrum techniques [7], modulation in multiple-access schemes [8]­ [10], equalization [11], and channel estimation [12]. In recent

years, chirp modulation has been used in IEEE 802.15.4a standard [13]. Kocian and Dahlhaus [14] analyzed the combination of chirp modulation and code-division multiple access (CDMA) over both frequency-nonselective and -selective fading chan­ nels using Monte Carlo simulations with zero cross-correlation assumption between two chirp signals which led the results to lower bound of the performance. In a similar fashion, Liu [15] proposed the use of chirp modulation with zero cross­ correlation in ultra-wideband (U WB) scheme. Gupta et. al. [16] analyzed chirp modulation in a frequency-hopped CDMA system. Dutta et. al. [17] proposed chirp modulation along with FSK and PSK schemes to obtain interference robust radio communication in the presence of partial band interfer­ ence over AWGN channel. Jeong et. al. [18] suggested two RAKE receiver architectures for chirp spread spectrum system and evaluated performance using computer simulations. Chirp modulation in fading channels as well as in the maximum ratio combining (MRC) diversity system has been investigated in [19] [20], and closed-form error probability expressions have been derived. Several other studies [21] [22] have focused on chirp modulation. Chirp spread spectrum (CSS) have been widely analyzed for applications in multiuser systems such as in [23]-[25], where authors have successfully applied CSS with unique chirp rate as well as multi-chirp rate in multiuser environment. Most studies in MIMO system has been accomplished us­ ing linear modulations such as PSK, QAM, etc. [26]. However, no research is available in the literature on MIMO system using chirp modulation. In this paper, we propose to employ chirp modulation in MIMO system in order to integrate the inherent advantages of chirp signals and MIMO system. Also, a multiuser MIMO system is proposed using chirp spread spectrum, where each user is assigned a unique chirp signal in order to identify at the receiver. The major challenge in a mul­ tiuser system is to minimize the multiple-access interference (MAl) to improve the system's performance. In this work, we exploit the orthogonality of the chirp signals using their cross­ correlation properties, as described in [23], which provides a unique chirp rate in order to reduce MAL We evaluate the proposed systems for two transmit and two receive antennas. The contributions of the paper are (i) implementation of chirp modulation in MIMO system, (ii) multiuser MIMO system using chirp spread spectrum, and (iii) performance analysis of the proposed systems using Monte Carlo simulations. The paper is organized as follows: Section II describes the chirp spread spectrum (CSS) system. System models of MIMO and multiuser MIMO using chirp modulation are explained

in Sections III and IV, respectively. Performance analysis of the proposed systems is presented in Section V. The paper is concluded in Section VI. II.

consider User k and User m with the CSS signals and Sm(t;bm), respectively.

sk(t;bk) sm(t;bm)

LINEAR CHIRP SPREAD SPECTRUM SY STEM

A chirp (also known as frequency modulated) signal is a sinusoidal signal whose frequency varies with time. Mathe­ matically, linear chirp signal is represented by [23] [27]

=

=

Sk(t;bk)

V2f;ej27rbkQkt2 V2f;ej27rbmQmt2

(4)

The signal energy is given by [3]: (5)

(1) where a is the chirp rate (or frequency modulated rate). The instantaneous frequency of the chirp signal is given by f(t) 2a t and the bandwidth is B f(T) 2aT. In binary chirp modulation, a positive chirp rate (i-e. up-chirp signal) is used to represent bit +1 and a negative of the same rate is used (i-e. down-chirp signal) to represent bit -1. Thus, the transmitted baseband signal with the information bit b E ±1 can be represented as =

=

The cross correlation between the two signals is given by [23] [28]:

=

(2) In multiuser system, a unique chirp rate is assigned to each user to transmit synchronously in the system, as shown in Figure l. For a K-user system, the baseband signal for the kth user is defined by

T 1 r Sk(t;bk)s:n,(t;bm)dt JESkEsm Jo -bmQm)T2 sinc [(bkO!k - bmO!m) T2 ] j7r(bkQk e

Pk,m(bk,bm) =

=

(6)

where * denotes conjugate of the signal. It has been noticed that the correlation in (6) contains sinc term, which plays an important role to minimize the correlation. Thus, the possible three scenarios are following [23]:

Scenario

1: When signals of users are orthogonal, MAl is minimum and thus, the signals have zero cross correlation. Therefore, setting (6) to zero gives

(7) k

=

1,2,. . . ,K.

where ak is the chirp rate assigned to user k and the information bits of user k.

(3)

bk E ±1

Then,

is

ak ± am

=

Cl ' T2

Cl

=

±1, ±2,...

(8)

Scenario

B

Kmaxf,

'- User 5 '-

Information bit - - - Information bit --

= =

+1 -1

2: For the same user transmission, it is required to distinguish between two different data bits that is between up-chirp and down-chirp of the same user. Thus, up-chirp and down-chirp of the same user should have zero cross correlation.

User 5 User 4

which gives

User 3

(10) User 2

,

-

o

Time

bk '-

=

'-

' ...... �er 1

....... ....... - _ ....... _ _

When same user transmits the same information bit (i-e. bm), the autocorrelation becomes unity, Pk,k(bk,bk) 1.

=

,,-, - - - - ---- ---� ::::::., .......

.......

'

T

Fig. 1: Unique Chirp Rates for Multiuser CSS in TF Plane.

Chirp rates should be assigned to the users in such a way as to minimize the cross correlation between their signals. The conditions on the chirp rates are demonstrated below in order to minimize the cross correlation and thus, minimizing multi­ ple access interference (MAl) among users [23]. Specifically,

In order to reduce MAl in the multiuser CSS system, unique chirp rates to each user is assigned using (8) and (10). Therefore, the unique chirp rate is assigned to kth user in a K-User system as follows [23]

ak

=

2k - 1 2T2 '

k

=

1,2,. . . ,K.

(11)

The total bandwidth required for the multiuser system from (11) is obtained as BK 20!KT (2K -l ) /T, which gives the maximum number of users, the system can support, as [23] =

=

(12)

In order to reduce MAl as well as to utilize the whole available bandwidth B, the chirp rates are assigned as below [23] ex 2k - 1 2k - 1 BT (13) k 2T2 BK 2T 2 2K - 1

l�J

=

=

l

J

The conditions presented in this section are used to calcu­ late unique chirp rate for each user throughout this paper. III.

MIMO SYSTEM USING CHIRP MODULATION

The system block diagram of proposed MIMO commu­ nication system using chirp modulation is shown in Figure 2. MIMO system is equipped with NT transmit antennas and N R receive antennas. The input data is assumed to be a sequence of binary digits from an equally likely and statistically independent data source. These binary digits are input into serial to parallel converter and mapper in order to get NT streams of data as well as to map digit + 1 to +1 and o to -1. Then, each stream of data is used as the input to a chirp modulator that transforms data bit + 1 to up-chirp signal (a positive chirp rate signal) and -1 to down-chirp signal (a negative chirp rate signal). The modulated signals are simulta­ neously transmitted from NT transmit antennas over NT x NR independent fading channels, where each fading channel is assumed to be uncorrelated from each other. Consequently, the signal received at each receive antenna is a noisy superposition of the NT transmitted signals corrupted by independent zero­ mean additive white Gaussian noise (AWGN). We assume the noise to be statistically independent from channel to channel and independent of the fading amplitude. The received signal is demodulated and detected coherently using the assigned chirp signal to decide which data was trasnmitted. The perfect knowledge of the channel state information (CSI) is also assumed to be available at the receiver but transmitter has no information of the channel.

density No/2, and H(t) is an NR x NT matrix that contains the elements hnrn, (t), 1 � nt � NT, 1 � nr � NR, which denote the channel gains between transmit antennas nt and receive antennas nr at time t. The channel is assumed to be constant for at least one symbol period. IV.

MULTIUSER MIMO SYSTEM USING CSS

Figure 3 depicts the system block diagram of proposed multiuser MIMO (MU-MIMO) communication system using chirp spread spectrum (CSS) with K synchronous users. Each user is equipped with two transmit antennas while receiver at the base station is equipped with two receive antennas. In contrast to single user MIMO, a unique chirp rate is assigned to each user in the proposed MU-MIMO system using (13) in order to reduce MAL The received signal is de-spreaded with the assigned chirp rate and decorrelator detector is employed to decide each user's data.

User 2 Data ii,

Fig. 3: System Model of Multiuser MIMO using Chirp Mod­ ulation. Input Data

MIMO Chirp Processing

Serial to Parallel

Output Data

Fig. 2: System Model of MIMO using Chirp Modulation.

Let sn, (t) denote the transmitted signal over antenna 1 � nt � NT. The transmitted signal can be written as:

nt,

(14) The received signal, r(t) £ h(t) r2(t) NR receive antennas, can be written as:

r(t)

... rNR(t)]T

for

(15) H(t) * S(t) + n(t) T n(t) £ [nl (t) n2(t) ... nNR(t)] is the noise vector elements, nnr (t), 1 � nr � N R, denote independent =

where whose additive white Gaussian noise (AWGN) with power spectral

v.

NUMERICAL RESULTS

In this section, we present the performance of the proposed systems obtained through computer simulations. Numerical results are obtained by Monte Carlo simulations using over 107 samples for information bits and the generation of the fading envelopes at each signal-to-noise ratio (SNR). All users are assumed to transfer data synchronously and their data is detected at the receiver coherently. Figure 4 depicts the error performance of MIMO system using chirp modulation over Rayleigh fading channel. The per­ formance result of single antenna and two-receive maximum ratio combining (MRC) diversity using chirp modulation is also shown for comparison. It is shown that chirp modulation can be incorporated in MIMO system in order to exploit advantages of both the systems. Also, the proposed system provides performance improvement due to spatial diversity of MIMO compared to receive diversity. The performance of multiuser MIMO system using chirp modulation for different number of users (K 1,3, and 5) is =

10

°

r-----,---�==�=====c==� -e--- 2 x 2 MIMO -A- 1 x 1 (No Diversity) -a-- 1 x 2 (MRC Diversity)

modulation scheme. The system was then extended to the case of a multiuser MIMO communication system. In the proposed multiuser MIMO system, chirp spread spectrum was employed and unique chirp rates were assigned to each user to identify user's data. MAl, a potential problem that degrades the multiuser system's performance, has been significantly reduced using proper chirp rates based on the orthogonal conditions.

REFERENCES

� 10 L--------L--------L--------L---L----�------� o -10 10 20 30 40

EblNO [dB]

Fig. 4: MIMO using Chirp Modulation over Rayleigh Fading Channel.

shown in Figure 5. Chirp rates to each user is assigned using the conditions in (13). It is evident from this figure that 3-, and 5-User MIMO system have performance close to I-User system, which verifies that MAl has been reduced by using chirp rate conditions. 10

°

r-----.----.---.�==�====� - + -1 User - * - 3 Users ...t:. . . 5 Users

� 10 L-----�-----L--�--L--� 15 o 25 -10 20 -5

Fig. 5: Multiuser MIMO using Chirp System for various Users over Rayleigh Fading Channel.

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CONCLU SION

Chirp modulation, a non-linear modulation scheme, has been successfully incorporated in MIMO communication sys­ tem, in this paper. The performance of the proposed MIMO system using chirp modulation has been evaluated for two­ transmit two-receive MIMO system. A comparison of this performance with those of single antenna chirp modulation system and two-receive diversity chirp modulation system shows significance of using multiple antennas using chirp

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