Southwest Jiaotong University,

Performance of a wireless link is evaluated with turbo coding in the presence of Rayleigh fading with single transmitting antenna and multiple receiving antenna. QAM modulator is considered with maximum likelihood decoding. Performance results show that there is a significant improvement in required signal to noise ratio (SNR) to achieve a given BER. It is found that the system attains a coding gain of 14.5 dB and 13 dB corresponding to two receiving antenna and four receiving antennas respectively over the corresponding uncoded system. Further, there is an improvement in SNR of 6.5 dB for four receiving antennas over two receiving antennas for the turbo coded system.


INTRODUCTION
The increasing demand for high data rates in wireless communications due to emerging new technologies makes wireless communications an exciting and challenging field [1][2].Turbo code is the most exciting and potentially important development in the coding theory which is capable of achieving near Shannon capacity performance [3][4][5].Diversity technique can be applied to minimize the effect of fading in a wireless channel.Space time block coding is found to be an effective means to combat fading in a multipath propagation environment [6][7].In [6][7], it is found that use of two transmit antenna and multiple receive antennas and space time block coding provides remarkable performance improvement.The use of space-time block coding with concatenating turbo product codes is also recently reported .Instead of using STBC, the performance of a wireless link may be improved by applying turbo coding in a SIMO configuration.In this paper, performance analysis of a wireless link with turbo coding in conjunction with multiple receiving antenna diversity is presented for a rayleigh fading channel with single input multiple output (SIMO) configuration.Performance result is presented in terms of bit error rate for multiple receiving antenna diversity schemes.Computer simulation is carried out to evaluate the performance result.

II. SYSTEM MODEL
The block diagram of the system under consideration is shown in Fig. 1 and Fig. 2. The data is turbo encoded with frame size 1024, with the following generator matrix with code rate ½ and modulated by a 64 QAM modulator before transmission.At the receiving end, signal is received by multiple receiving antennas.The detail block diagram of the combiner is shown in Fig. 3.
If the symbol transmitted by transmit antenna is s1, then the signal received by the receiving antennas can be written as: Where h 1… h n and η 1….. η n represent the channel coefficients and additive white noise for IF link.
The combiner combines received signals which are then sent to the maximum likelihood detector.If we consider two receiving antennas, then received signal r 0 and r 1 are fed to combiner and then combiner generates the following signal [6]: (1) for more then two receive antenna then r 0 , r 1, r 2 , r 3 ---------------r  s can be achieved using the decision metric [7] (3) Over all possible values of s1.We expand the above equation and delete the terms that are independent of the code words and observe that the above minimization is equivalent to minimizing [7] The above can be rewrite: (4) Thus the minimization of (1) and in turn is equivalent to minimizing the decision metric [7] (5) for detecting s1.Output of the combiner is demodulated using a coherent demodulator.Decoding of the turbo coded bits are carried out following the MAP decoding algorithm.

IV. RESULT AND DISCUSSION
Computer simulation is carried out to find the bit error rate (BER) performance of a wireless transmission system with turbo coding with multiple receiving antennas.The results are evaluated for several combinations of t x and r x antennas with and without Turbo coding.The plots of BER as a function of SNR (E s /N o ) are shown in fig. 3. It is found that there is a significant improvement in required SNR for achieving a given BER with two receiving antenna compared to four receiving antennas of a turbo coded system.The coding gain is found to be 6.5 dB at BER 10 -6 of a turbo coded system for two receiving antenna compared to four receiving antennas.There is also significant improvement with turbo code compared to the uncoded system.For two receiving antennas, the coding gain is found to be 14.5 dB and for four receiving antennas, the coding gain is found to be 13 dB at BER 10 -6 over the uncoded system with same numbers of receiving antenna.Thus the effectiveness of turbo coding is more significant for higher number of receiving antenna.

Fig. 1 .
Fig. 1. : Block diagram of a wireless link with turbo coding and multiple receiving antennas (a) Transmitter (b) Receiver

Figure 2 .
Figure 2. Block diagram of receiver with multiple receiving antennas and turbo decoder.

Figure 1 .
Figure 1.Block diagram of transmitter with turbo encoder and one transmit antenna

Figure 3 . 11 r
Figure 3. Receive diversity with one transmit antenna and two receive antenna