CHAPTER 4 PERFORMANCE ANALYSIS OF THE ALAMOUTI STBC BASED DS-CDMA SYSTEM

89 CHAPTER 4 PERFORMANCE ANALYSIS OF THE ALAMOUTI STBC BASED DS-CDMA SYSTEM 4.1 INTRODUCTION This chapter investigates a technique, which uses antenna diversity to achieve full transmit diversity, using an arbitrary number of transmit antennas for secure communications, and to improve the system performance by mitigating interference. The work is focussed on the performance of DS- CDMA systems over the Rayleigh, Rician and AWGN fading channels, in the case of the channel being known at the receiver. The diversity scheme used in the analysis is the Alamouti STBC scheme. Using analytical and simulation approach, we have shown that the STBC CDMA system has increased performance in cellular networks. We also compared the performance of this system with that of the typical DS-CDMA system, and shown that the STBC and multiple transmit antennas for the DS-CDMA system, provide performance gains without any need of extra processing. The evaluation and comparison of the performances of the DS-CDMA system in the AWGN, Rician and the Rayleigh fading channels are provided. In this chapter, fading channel STBC DS-CDMA system has been implemented and analyzed. And the analysis is made under two conditions, by assuming (i) Two transmit and One receiving antenna and (ii) Two transmit and two receiving antennas. Both the schemes in the AWGN, Rayleigh and Rician fading channels have been analyzed. Using the analytical

90 and simulation approach, it is shown that the latter case is advantageous over the traditional CDMA system, including better BER performance and lower complexity. It has been observed that the BER performance of the system is improved with antenna diversity schemes. The simulation results show that the BER performance is better, using the Alamouti scheme under the AWGN and Rician channel, whereas it is worse under the Rayleigh fading channel. In general, the BPSK scheme should have the least priority compared to the other mapping schemes, while considering spectral efficiency, bandwidth and bit rate support. Because, if one bit is transmitted per symbol, as with BPSK, then the symbol rate would be the same as the bit rate. If two bits are transmitted per symbol, as in QPSK, then the symbol rate would be half of the bit rate. The Channels perform in the following order, in terms of the best (less SNR requirement) to the worst (more SNR requirement) to maintain the required BER: AWGN, Rician and Rayleigh. 4.2 ALAMOUTI STBC SCHEME 4.2.1 Space Time Multiuser CDMA System The STBC is an effective transmit diversity technique, used to transmit symbols from multiple antennas, which ensures that transmission from various antennas is orthogonal, as has been depicted by Tarokh et al (1999) and Blogh & Hanzo (2002). Wireless transmission with a high data rate, as well as diversity and coding gain, is quite achievable using the STBC, which combats fading in wireless communications. The STBC is a highly efficient approach to signaling within wireless communication, that takes the advantage of the spatial dimension by transmitting a number of data streams, using multiple co-located antennas as has been reported by Goldsmith (2001).

91 The main feature of the STBC is the provision of full diversity with a very simple, yet effective encoding and decoding mechanisms. Here, Sij is the modulated symbol to be transmitted from antenna j in time-slot i. There should be T time-slots, nt number of transmit antennas, and nr number of receive antennas. This block is usually considered to be of length T. We consider two diversity schemes for our analyses: 1. Scheme-I: two transmit antennas, one receive antenna 2. Scheme-II: two transmit antennas, two receive antennas 4.2.2 Scheme-I: Two transmit antennas, one receive antenna Figure 4.1shows the basic two-branch transmit Alamouti scheme, with only one antenna at the receiver. This particularly simple and prevalent scheme, with two transmit antennas and one receive antenna, uses simple coding, which is the only STBC that can achieve its full diversity gain, without any change in the data rate. As per Alamouti s scheme, the transmitter sends out data in groups of two bits. The scheme may be analyzed

92 ŝ 0 ŝ 1 Figure 4.1 Two-branch transmit Alamouti scheme 4.2.2.1 The Encoding and Transmission Sequence At a given symbol period, two signals, transmitted from two antennas, antenna zero and antenna one, are denoted by and simultaneously. During the next symbol period, signal ( ) is transmitted from antenna zero, and signal is transmitted from antenna one, where stands for a complex conjugate operation. The encoding is done in space and time (and hence, space-time coding). The assumption made for this scheme is that, the channel state remains fairly constant over the transmission of two consecutive symbols as has been reported by Alamouti (1999) & Antony et al (2004). It can be clearly understood from Table 4.1.

93 Table 4.1 Transmission sequence in two-branch transmit Alamouti scheme Antenna 0 Antenna 1 t s s t+t - s* s * Assuming that fading is constant across two consecutive symbols, the channel at time t, may be modeled as ( ) ( + ) = (4.1) ( ) ( + ) = (4.2) where, T is the symbol duration. be expressed as The received signals, and at time T and t + T respectively, can = ( ) + (4.3) = ( + ) + (4.4) where, and are complex random variables representing the receiver noise and interference. 4.2.2.2 The Combining Scheme The combiner builds the following two combined signals that are sent to the maximum likelihood detector

94 ( + ) (4.5) ( + ) (4.6) 4.2.2.3 The Maximum Likelihood Decision Rule The combined signals obtained above are sent to the ML detector, in order to obtain the symbol decision. In the case of PSK or BPSK, the detection rule can be expressed as follows: d 2 (s 0, s i ) d 2 (s 0, s k ), where i k => choose symbol s i. It is interesting to note that the signals at the output of the combiner are equivalent to the signals obtained in the two-branch MRRC, as depicted in Figure 4.1. That is the reason why it is affirmed, that the Alamouti scheme with two-branch transmit diversity is equal to the twobranch MRRC, in terms of the diversity order. A slight difference is that the noise components are rotated; however, this fact does not affect the SNR. 4.2.3 Two-branch transmit with M receivers Under some circumstances, when the air channel presents bad characteristics, or when it is possible to implement more than one antenna at the receiver, the use of a higher order of diversity could be interesting. The order that we would get in a system with two-transmit antennas and N receive antennas is 2N. In this section, a detailed view of the two-transmit and two receive antennas is given, with the aim of simplicity, but the generalization can easily be done in the case of using any number of antennas. Figure 4.2 shows the scheme in this particular case. 4.2.3.1 The Encoding and Transmission Sequence The encoding and transmission sequence for this configuration is identical to the case discussed in Section 4.1.2.1. The channel at time t can be modeled by complex multiplicative distortions, ( ), ( ), ( ), ( ),

95 between transmit antenna zero and receive antenna zero, transmit antenna one and receive antenna zero, transmit antenna zero and receive antenna one, transmit antenna one and receive antenna one, respectively. symbol time. Table 4.2 shows the signal notation for each antenna in each Table 4.2 Notation of received signals at the receive antennas Antenna 0 Antenna 1 Receiving antenna 0 h 0 h 2 Receiving antenna 1 h 1 h 3 Figure 4.2 Two-branch transmit with two receive antennas scheme

96 can be written as, Assuming that fading is constant across two consecutive symbols, it ( ) ( + ) = (4.7) ( ) ( + ) = (4.8) ( ) ( + ) = (4.9) ( ) ( + ) = (4.10) where, T is the symbol duration. The received signals can then be expressed as + (4.11) + (4.12) + (4,13) + (4,14) The complex random variables,,, and represent the receiver thermal noise and interference. 4.2.3.2 The Combining Scheme The combiner builds the following two combined signals, which are sent to the maximum likelihood detector (4.15) (4.16)

97 The combined signals seen above are equal to those obtained using a four-branch MRRC. Hence, the diversity order obtained with the two schemes is the same. Another property is that the combined signals of the receive antennas are simply the addition of the combined signals from each receive antenna, so it is possible to implement a combiner for each antenna and then simply sum the output of each combiner. 4.3 CHANNEL MODEL The Channel is a physical medium between the transmitter and receiver. This channel results in the random delay or random phase shift of the original signal. The AWGN channel model has been explained in the last chapter. The Rayleigh and Rician fading channels can be modeled as follows: 4.3.1 Fading in Communication Channels In wireless communication systems, the radio frequency signal propagates from the transmitter to the receiver via multiple different paths, due to reflectors existing in the wireless channel and the obstacles. These multipaths are caused by the mechanisms of diffraction, reflection and scattering from structures, buildings and other obstacles existing in the propagation environment, as has been studied by Andersen et al (1995). As shown in Figure 4.3, multipath propagation is described by the Line of Sight (LOS) path and Non Line of Sight (NLOS) paths. Figure 4.3 Multipath Propagation

98 When the mobile unit is considered far from the base station, there is no LOS signal path, and reception occurs mainly from the indirect signal paths. These multiple paths have different propagation lengths, and thus will cause time delay, amplitude and phase fluctuations in the received signal. And hence, the multipath propagation effect can be mainly described in terms of delay spread and fading, as reported by Sklar (1997). When the multipath signal waves are out of phase, the reduction of the signal strength at the receiver can occur. This causes significant fluctuations in the received signal amplitude, and leads to a phenomenon known as multipath fading or small scale fading. A representation of multipath fading is shown in Figure 4.4. Figure 4.4 Representation of Multipath Fading Rayleigh fading is also called Small-scale fading because if a large number of multiple reflective paths is present, and there is no LOS signal component, the envelope of the received signal is statistically described by the Rayleigh distribution. When there is a dominant non fading signal component present, such as an LOS propagation path, the small scale fading envelope is described by the Rician distribution and, thus, is referred to as Rician fading, which has been investigated by Rappaport (2002).

99 When the mobile unit is moving, there is a shift in the frequency of the transmitted signal along each signal path, due to its velocity. This phenomenon is known as the Doppler shift. Signals traveling through different paths can have different Doppler shifts, corresponding to the different rates of change in phase. The difference in the Doppler shifts between different signal components contributing to a single fading signal component, is known as the Doppler spread. Channels with a large Doppler spread have signal components, that are each changing independently in phase over time, as has been pointed out by Tse & Viswanath (2005). If the Doppler spread is significant, relative to the bandwidth of the transmitted signal, the received signal will undergo fast fading. On the other hand, if the Doppler spread of the channel is much lesser than the bandwidth of the baseband signal, the signal undergoes slow fading, as has been reported by Shankar (2002). So, the terms slow and fast fading refer to the rate, at which the magnitude and phase change imposed by the channel on the signal, change. Because multiple reflections of the transmitted signal may arrive at the receiver at different times, this can result in inter-symbol interference (ISI) due to the crashing of bits into one another. This time dispersion of the channel is called multipath delay spread, and is an important parameter to assess the performance capabilities of wireless communication systems, as has been stated by Manninen & Lempiainen (2002). 4.3.2 Modeling of Rayleigh Fading As stated previously, Rayleigh fading results from the multiple Non Line of Sight paths of the signal propagating from the transmitter to the receiver. If the transmitted signal s(t) is assumed to be an unmodulated carrier, then it can be written as: ( ) = cos (2 ) (4.17)

100 where, f c is the carrier frequency of the radio signal. The received signal, after propagation over N scattered and reflected paths, can be considered as the sum of N components with random amplitude and phase for each component. Thus, when the receiving station is assumed to be stationary, the received signal r(t) can be written as ( ) = cos (2 + ) (4.18) where, a i is a random variable corresponding to the amplitude of the i th signal component, and i is another uniformly distributed random variable, corresponding to the phase angle of the i th signal component. Using the trigonometric identity: cos( + ) = cos.cos sin.sin (4.19) equation (4.18) can be re-written in the form: ( ) = cos(2 ). (2 ). (4.20) Equation (4.20) can be expressed as r(t) =X.cos(2 ) -Y.sin(2 ) (4.21) where, = (4.22) = (4.23) X and Y can be considered as two identical and independent Gaussian random variables when N tends to a large value. Equation (4.25) represents the received Radio frequency signal, when the receiver is assumed to be stationary. If the mobile unit is moving at a speed of v meters/second

101 relative to the base station, the received signal will acquire a frequency Doppler shift. The maximum Doppler shift is given by = (4.24) The instantaneous frequency Doppler shift is dependent on the angle of arrival of the incoming signal path component, as shown in Figure 4.5. Figure 4.5 A Mobile Unit Moving at Speed v The instantaneous value of the Doppler shift f di can be expressed as: = (4.25) where i is the angle of arrival for the i th path signal component. signal becomes: On the other hand, the instantaneous frequency of the received RF = + cos (4.26) Accordingly, the received signal can be expressed in the form: ( ) = cos (2 ( + ) + ) (4.27) Equation (4.27) can alternatively be written in another form, using the trigonometric identity (4.19):

102 ( ) = cos (2 ). cos(2 + ) (2 ). (2 + ) (4.28) The received signal can also be formulated as: ( ) = cos(2 ). ( ) sin(2 ). ( ) (4.29) where: ( ) = cos (2 + ) (4.30) ( ) = (2 + ) (4.31) and =. X(t) is the in-phase component, and Y(t) is the quadrature component of the received signal. It is seen from equation (4.29) that the received signal is like a quadrature modulated carrier. The envelope of the received signal is given by: ( ) = [ ( ) + ( ) ] (4.32) It can be shown that the probability density function (pdf) of the envelope A(t) of the received signal is Rayleigh distributed, as has been illustrated by Papoulis (1991). The instantaneous power of the received signal is given by: P(t) = X (t) 2 + Y(t) 2 (4.33) On the other hand, the average value of the received power P av is the statistical mean of P(t):

103 P av = mean[p(t)] = P(t) (4.34) At the receiver side, the in-phase and quadrature components X(t) and Y(t) can be obtained by demodulating the received signal r(t). 4.3.3 Modeling of Rician Fading When the received signal consists of multiple reflective paths, plus a significant LOS component, the received signal is said to be a Rician faded signal, because the probability density function of the RF signal's envelope follows Rician distribution, as has been illustrated by Couch (2001). The received RF signal in this case can be written as: ( ) =. cos(2 ( + ) ) + cos(2 ( + ) + ) (4.35) where K LOS -amplitude of the direct (LOS) component, f d - frequency Doppler shift in the LOS path, and f di - frequency Doppler shift along the i th NLOS path signal component. In terms of the in-phase and quadrature components, the received signal can be written as: ( ) =. cos(2 ( + ) ) + cos(2 ). ( ) + sin(2 ). ( ) (4.36) where X(t) and Y(t) are the equations given by (4.30) and (4.31) respectively. 4.4 SYSTEM MODEL AND DESCRIPTION Figure 4.6 presents the block diagram of the Alamouti STBC based DS-CDMA communication system, with antenna diversity. The system model can be explained as follows:

104 4.4.1 Transmitter Part At the transmitter, the data generated from a random source, consists of a series of ones and zeros. The Modulation process is used to convert the data input bits into a symbol vector. The QPSK scheme is used to map the bits to symbols. Then, these PSK symbols are the input to the STBC encoder. properties: Modulation techniques are expected to have three positive a. Good Bit Error Rate Performance Modulation schemes should be able to achieve a low bit error rate in the presence of fading, Doppler spread, interference and thermal noise. b. Power Efficiency Power limitation is one of the crucial design challenges in portable and mobile applications. Power efficiency can be increased by using Nonlinear amplifiers. However, non-linearity may degrade the BER performance of some modulation techniques. Constant envelope modulation techniques are used to prevent the regeneration of the spectral side lobes during nonlinear amplification c. Spectral Efficiency The power spectral density of the modulated signals should have a narrow main lobe and fast roll-off of the side lobes. Spectral efficiency is measured in units of bits/sec/hz. The Walsh Hadamard codes are used for spreading and despreading the modulated sequence. The spreading factors of 4,8 and 16 are used for spreading.

105 Figure 4.6 Block Diagram for the simulated Alamouti STBC based CDMA system The application of the STBC in the DS-CDMA multi-user communication system is considered, and presented the simulation results for the performance of DS-CDMA channels with STBC. Figure 4.6 shows the transmitter and receiver models with two transmit antennas at the base station and one receive antenna at the remote unit, and two transmit antenna and two receive antennas at the receiver. In our simulations, the output of each STBC was spread by the Walsh Hadamard code of length 64. The spread signals from different users for the same transmit antenna were summed up, before they were transmitted from antennas 1 and 2 at the base station, respectively. A matched filter is used to decorrelate the received signal. The output of the matched filter is fed to the STBC decoder.

106 4.4.2 Signal Model for DS-CDMA Based on the Alamouti Scheme Consider the discrete time complex baseband model for the downlink channel of a single cell direct sequence CDMA system. As before, there are K users in the system and the base station employs long spreading codes. We consider the Alamouti transmit diversity scheme with two transmit antennas, as shown in Figure 4.7. Figure 4.7 Block diagram of the transmitter with the Alamouti scheme Let b k [m] be the m th symbol of transmission to mobile station k, independent and identically distributed (i.i.d.). It is assumed that the quadrature phase shift keying signaling is used. That is, b k [m] {±1±j}. Then, the outputs of the space time encoder, as has been reported by Alamouti (1998), become: ( ) [2 ] = [2 ] (4.37)

107 ( ) [2 + 1] = [2 + 1] (4.38) ( ) [2 ] = [2 + 1] (4.39) ( ) [2 + 1] = [2 + 1] (4.40) where ( ) [ ] is the data symbol from the transmit antenna i to the k th user. From the Figure 4.7, it is observed that the same user spreading sequence is used for the data symbol ( ) [ ]. That is, [ + ] = ( ) [ + ] i=1, 2 (4.41) [ + ] is the k th user long spreading sequence. It is also assumed that the long spreading sequence is normalized as [ + ] =. For coherent combining and channel estimation at the receiver, two different orthogonal pilot spreading sequences ( ( ) [ ], = 1,2), with different pilot symbols ( ) [ ], = 1,2) can be transmitted through two transmit antennas. Assume that the complex channel attenuations associated with each pair of transmit and receive antennas are time-invariant. Then, the received signal at the j th receive antenna can be written as: ( ) [ + ] = [ ] ( ) [ + ] + ( ) [ + ] (4.42) where, ( ) [ + ] = ( ) [ + ] + ( ) [ + ]

108 ( ) [ + ] = ( ) [ ] [ + ] ( ) [ + ] = ( ) [ ] ( ) [ + ] In the vector notation, J 1 received signal vector can be written as: [ ] = ( ) [ ] + [ ] (4.43) where the channel matrix H i, the received signal vector r[n], the transmitted signal vector u (i) [n], and the noise vector n[n] are given by =, = 12,, (4.44) where, = ( [0] [1]. [ 1]) Furthermore, [ ] = ( ( ) [ ] ( ) [ ] ) (4.45) ( ) [ ] = ( ( ) [ ]. ( ) [ + 1]) [ ] = ( ( ) [ ]. ( ) [ ]) where, ( ) [ ] is the received signal at receive antenna J, and ( ) [ ] is the baseband transmission signal from transmit antenna i. 4.5 RESULTS AND DISCUSSION The aim of this chapter is to review the performance of the DS- CDMA system, using two different diversity schemes. For this, some assumptions are made. The first assumption is that the total power transmitted

109 by the two antennas in the Alamouti scheme, is equal to the power that the unique antenna in the MRRC scheme would transmit. Another assumption is that fading along all the paths between the transmit and receive antennas is mutually uncorrelated, and follows a Rayleigh distribution. Moreover, it is supposed that the average power received in every single receive antenna is the same, and that the receiver has a perfect knowledge of the channel. 4.5.1 Performance of Alamouti STBC (2 Tx & 1 Rx) based DS- CDMA system over Rayleigh channel Figure 4.8 shows the BER performance for the coded DS-CDMA system using Alamouti s STBC technique (ntx=2 & nrx=1) in the Rayleigh fading condition. It is assumed that the receiver has a perfect knowledge of the channel condition. It is clear that Alamouti s STBC technique using two transmitting antennas and one receiving antenna for the CDMA system, is the same as that of the system which uses the Maximum ratio Combiner, using two transmitting antennas and one receiving antenna. And both the schemes are better than the typical DS-CDMA system. It is also observed that transmit diversity has a 13 db advantage at BER of 10-3, when compared to the system without transmit diversity. If the transmitted and received power for these two cases is the same, then the performance would be identical. At a BER of 0.01, there is a 9 db improvement in the SNR obtained, as compared to that without Alamouti diversity.

110 10-1 without Alamouti With MRC Alamouti ntx=2 nrx=1 10-2 10-3 10-4 10-5 0 5 10 15 20 25 SNR (db) Figure 4.8 BER vs E b /N o for Alamouti STBC (2 Tx & 1 Rx) based DS- CDMA system over Rayleigh fading channel If the performance of the Alamouti scheme in diversity terms is equal to that of the MRRC, why are the two-branch transmit Alamouti results 3dB under the MRRC? The reason is, one of the assumptions that have been made, is that each antenna transmits half the power; so, in total, the power radiated by the two antennas is the same as the power radiated by the single antenna in of MRRC. If each of the antennas in the Alamouti scheme would transmit the same power as the single antenna, the results would overlap. The most important conclusion we can get from this graph is the fact, that the Alamouti scheme provides the same performance as the MRRC, independent of the codification and modulation used.

111 4.5.2 Performance of Alamouti STBC (2 Tx & 1 Rx) based DS- CDMA system over Rician fading channel Figure 4.9 presents a comparison of the performance of the typical DS- CDMA system, the system using Maximal Ratio Combiner technique and the CDMA system implementing Alamouti s STBC technique. 10-1 without Alamouti With MRC Alamouti ntx=2 nrx=1 10-2 10-3 10-4 10-5 0 5 10 15 20 25 SNR (db) Figure 4.9 BER vs E b /N o for Alamouti STBC (2 Tx & 1 Rx) based DS- CDMA system over Rician channel When Alamouti s STBC technique is used for the CDMA system, in the Rician fading channel, the performance drastically improves by around 8 db at BER of 10-5 due to the presence of LOS component (direct path). This

112 means, that it will require less power to transmit for same BER for CDMA system using Alamouti s STBC technique. It can be explained alternatively, that transmitting signals at the same power will give a better BER for the CDMA system with Alamouti s STBC technique, than for the typical CDMA system. It is evident that E b /N 0 is decreased for the CDMA system, when Alamouti s scheme is used. The capacity of any system is inversely proportional to E b /N 0, which indicates that the capacity increases while using Alamouti s scheme. 4.5.3 Performance of Alamouti STBC (2 Tx & 2 Rx) based DS- CDMA system over Rayleigh fading channel Figure 4.10 shows the BER performance for the coded DS-CDMA system, using Alamouti s STBC technique (ntx=2 & nrx=2) in Rayleigh fading condition. Here, the BER plots are shown for both systems, with and without the antenna diversity scheme. The BER of 10-3 is obtained for 3dB, while considering Alamouti s STBC technique (ntx=2 & nrx=2), whereas the same BER is obtained for 11 db with the MRC technique. And hence, an 8 db improvement in SNR is obtained. While comparing it without the Alamouti technique, a 21 db SNR improvement is obtained, because at 24 db, the BER of 10-3 is obtained. The BER performance of the simulation result without the diversity scheme is worse than that with the diversity scheme, and the BER performance is improved dramatically in low SNR, but not in high SNR. In low SNR, white Gaussian noise dominates the BER, which can be improved by enhancing the SNR; but in high SNR, the error due to phase estimation dominates the BER, which cannot be improved by simply enhancing the SNR.

113 10-1 without Alamouti With MRC Alamouti ntx=2 nrx=2 10-2 10-3 10-4 10-5 0 5 10 15 20 25 SNR (db) Figure 4.10 BER vs E b /N o for Alamouti STBC (2 Tx & 2 Rx) based DS- CDMA system over Rayleigh fading channel 4.5.4 Performance of Alamouti STBC (2 Tx & 2 Rx) based DS- CDMA system over Rician fading channel Figure 4.11 shows the simulated performance of the Alamouti STBC technique (ntx=2 & nrx=2) in Rician fading channel. It shows the performance from 0 db to 25 db where upto10 5 bits are transmitted. The BER of 10-3 is obtained for 2.5 db, while considering Alamouti s STBC technique (ntx=2 & nrx=2), whereas the same BER is obtained for 11 db with the MRC technique. And hence, 8.5 db improvement in SNR is obtained. While comparing it without the Alamouti technique, 21.5 db SNR improvement is obtained, because at 24 db, the BER of 10-3 is obtained.

114 10-1 without Alamouti With MRC Alamouti ntx=2 nrx=2 10-2 10-3 10-4 10-5 0 5 10 15 20 25 SNR (db) Figure 4.11 BER vs E b /N o for Alamouti STBC (2 Tx & 2 Rx) based DS- CDMA system over Rician fading channel Table 4.3 shows that, in the presence of Rayleigh fading channel, the BER of 0.0016 is achieved for the SNR value of 10 db, using the Alamouti STBC (ntx=2 & nrx=1) encoding, whereas the BER of 0.0014 is achieved for the SNR value of 6 db, using the same encoding technique in the presence of AWGN and Rician channel. Thus, a lower BER is obtained when Alamouti encoding is used.

115 Table 4.3 BER values of STBC DS-CDMA system for the above two schemes upto SNR values of 10 db SNR (db) ntx=2 & nrx=1 Rayleigh Rician fading fading channel channel ntx=2 & nrx=2 Rayleigh Rician fading fading channel channel 0 0.0581 0.0352 0.0055 0.0043 1 0.0440 0.0235 0.0033 0.0024 2 0.0328 0.0145 0.0018 0.0013 3 0.0239 0.0086 0.0010 0.0007 4 0.0169 0.0049 0.0005 0.0004 5 0.0118 0.0027 0.0003 0.0002 6 0.0081 0.0014 0.0001 0.00009 7 0.0055 0.0007 0.00008 0.00007 8 0.0037 0.0004 0.00006 0.00005 9 0.0025 0.0002 0.000032 0.00002 10 0.0016 0.0001 0.000014 0.0000098 Also from Table 4.3, in the presence of Rayleigh fading channel, the BER of 0.0003 is achieved for the SNR value of 5 db using Alamouti s STBC (ntx=2 & nrx=2) technique, whereas for the SNR of 4 db in the presence of Rician fading channel, the BER value is.0004. In the presence of Rayleigh channel, the BER of 0.001 is achieved for the SNR value of 3 db using Alamouti s STBC, whereas for the SNR of 2 db in the presence of Rician channel, the BER value is.0013. Hence 1 db improvement in the SNR is obtained when compared to the Rayleigh channel due to the presence of line of sight component in Rician fading channel.

116 4.5.5 Performance comparison of extended Alamouti STBC based DS-CDMA system over Rician fading channel Figure 4.12 shows the BER performance for the coded DS-CDMA system, using multiple antennas of Alamouti s STBC technique in AWGN and Rician fading condition. Here, the BER plots are shown for three different cases, with various number of receiving antenna diversity. The BER of 10-4 is obtained for 6 db, while considering Alamouti s STBC technique (ntx=2 & nrx=2), whereas the same BER is obtained for 2 db and 1 db for (ntx=2 & nrx=4) and (ntx=2 & nrx=6) respectively. And hence, 4 db to 5 db improvement in SNR is obtained. While comparing it without the Alamouti technique, 18 db SNR improvements is obtained, because at 24 db, the BER of 10-3 is obtained. 10-2 Alamouti based DS-CDMA ntx=2 nrx=2 Alamouti based DS-CDMA ntx=2 nrx=4 Alamouti based DS-CDMA ntx=2 nrx=6 10-3 10-4 10-5 10-6 0 1 2 3 4 5 6 7 8 9 10 SNR(dB) Figure 4.12 BER vs E b /N o comparison of extended Alamouti STBC based DS-CDMA system over AWGN and Rician channel

117 Table 4.4 BER values of STBC DS-CDMA system for the three different diversity schemes upto SNR values of 10 db BER values in the presence of AWGN & Rician channel SNR (db) ntx=2 & nrx=2 ntx=2 & nrx=4 ntx=2 & nrx=6 0 0.004 0.000585 0.00025 1 0.0024 0.000345 0.000135 2 0.0012 0.000145 0.00006 3 0.0007 0.000095 0.00002 4 0.0004 0.000065 0.00001 5 0.0002 0.000015 0.000005 6 0.0001 0.00001 0.0000016 7 0.00004 0.000005 0.0000002 8 0.00001 0.0000025 0.00000005 9 0.000005 0.0000014 0.00000003 10 0.000001 0.0000004 0.000000012 From Table 4.3, in the presence of Rician and AWGN channel, the BER of 0.000005 is achieved for the SNR value of 9 db using Alamouti s STBC (ntx=2 & nrx=2) technique, whereas the same BER is obtained for the SNR of 7 db and 5 db when receiver diversity increases as 4 and 6 respectively. Similarly, BER rate of 0.0002 is obtained for 5 db while Alamouti s STBC (ntx=2 & nrx=2) technique is assumed. Approximately, the same BER is obtained for 2 db and 0 db respectively for receiver diversity increases from 4 to 6. Hence, a maximum of 5 db improvement in the SNR is obtained when receiver diversity increases from 2 to 6. 4.5.6 Capacity Analysis Determining the capacity of the communication channel is very important in order to satisfy the quality of service requirements. Capacity

118 determines the maximum limit of data that can be transmitted over the channel. Shannon defined capacity as the mutual information maximized over all possible input distributions. The main theoretical aspect of MIMO is one of channel capacity. The Shanon s capacity theorem for a simple RF channel is: = (1 + ) (4.46) where C= capacity (bits/s), B=bandwidth (Hz), N= signal to noise ratio. The above capacity equation is widely used and refers to a system with one transmitter and one receiver (with possibly added diversity, but ultimately combined into one receiver); now we consider a system of N M antennas: N transmitters, and M receivers. The H-matrix is a matrix [H ij ] defines complex throughput correlation parameters (with amplitude and phase) from each transmit antenna i to each receive antenna j. The new capacity equation for MIMO systems is = 1 + ( ) (4.47) where n is the number of independent transmit/receive channels (which is no greater than min(n,m)), and reflects the number of sufficiently uncorrelated paths, S i are the signal power in channel i, N- the noise power, and 2 i (H) are singular values of the H matrix.

119 35 30 25 Shannon Capacity MIMO, ntx=nrx=2 MIMO, ntx=nrx=4 MIMO, ntx=nrx=5 MIMO, ntx=nrx=6 MIMO Capacity 20 15 10 5 0 2 4 6 8 10 12 14 16 18 20 SNR(dB) Figure 4.13 MIMO capacity: capacity curves versus average SNR at receiver; M = M R =M T Figure 4.13 shows the performance of the MIMO system in which SNR and Capacity are considered. In the above figure four different numbers of receiving antennas are considered. Figure 4.13 shows that as the SNR increases the capacity also increase, so at 20 db SNR the capacity for ntx= nrx = 6 is 35 bits/s/hz. Figure 4.13 implies that the Shannon channel capacity for the higher SNR is higher than the case of low values of SNR, which means that the system operating in higher SNR has more ability to admit new users without any disconnection in the service for the old users. The channel capacity difference between the five cases becomes larger after a 12 db SNR, the Figure 4.13 also shows that at a lower SNR values the five curves is relatively close to each other. When the Alamouti based CDMA system is compared with the work reported by Ahlen (2002), 4G IP based wireless systems, the spectral

120 efficiency difference for single user is 4.8 bps/hz is obtained. So as the number of user increases, the spectral efficiency also increases correspondingly. And also when compared with the capacity of wireless system, there is a gradual increase in spectral efficiency at each and every points of SNR value. 4.6 CONCLUSION In this chapter, the STBC DS-CDMA system has been implemented and analyzed. Using the analytical and simulation approach, it has been shown that using the STBC in the DS-CDMA system is advantageous over the traditional CDMA system, including a better BER performance and lower complexity. Both the schemes in AWGN channel, Rayleigh Fading channel and Rician Fading channel have been analyzed. The Alamouti scheme has been used as the antennal diversity. It has been observed that the BER performance of the system is improved with antenna diversity schemes. The simulation results show that the BER performance is better, using the Alamouti scheme under the Rician fading channel, whereas it is worse under Rayleigh fading channel. The channels perform in the following order, in terms of the best (less SNR requirement) to the worst (more SNR requirement) to maintain the required BER: AWGN, Rician and Rayleigh. The main conclusions of this chapter are as follows: 1. With two transmit antennas and one receive antenna, the Alamouti technique is comparable to the MRRC, with two receive antennas and one transmit antenna, in terms of diversity.

121 2. Using the receive diversity results in larger performance gain than using additional transmit antennas. 3. When there is a strong line-of-sight component available, signal fading is negligible and space-time coding will not provide any performance gain. 4. A 3 db of disadvantage from the BER performance in comparison with the MRRC, is obtained. That is because each antenna transmits half the power in order to maintain the total radiated power. 5. Generalisation can be done by adding more receive antennas. In this case, the diversity order reaches up to 2N. 6. Low computation complexity, similar to MRRC. 7. Soft fail advantages, and multiple transmission branches assure communication, when one of them is disrupted.