ظرفیت و خطای تجزیه و تحلیل عملکرد احتمال برای سیستم های MIMO MC DS-CDMA در محیط محو η-μ

In this paper, we investigate the effect of multiple input multiple output (MIMO) systems on the performance of the multicarrier direct sequence code division multiple access (MC DS-CDMA) system operating over independent identically distributed (i.i.d) η–μ flat fading environment in terms of average error probability and average channel capacity. We derive the instantaneous signal to interference noise ratio (SINR) at the output of the receiver. Hence, based on moment generating function (MGF) approach, we obtain the probability density function (PDF) of the instantaneous SINR. Closed form expressions of average error probabilities for the system are developed and expressed in Appell's and Lauriccella's hypergeometric functions. Furthermore, we achieve exact expression of average channel capacity for the system. Finally, we validate our results using Monte Carlo simulation technique and also compare with those already available in the literature.

Multicarrier direct sequence code division multiple access (MC DS-CDMA) is a digital modulation and multicarrier technique which results from a combination of orthogonal frequency division multiplexing (OFDM) and direct sequence code division multiple access (DS-CDMA). Due to the research on it for the last decade or more, the MC DS-CDMA system has become an important multicarrier communication system for the fourth generation (4G) wireless communication system [1]. The operation of this system is based on time domain spreading code or combination of time domain and frequency domain spreading codes respectively. Hence, original data stream is serial to parallel converted and spread using spreading code in time domain and then each subcarrier is modulated differently with each of the data stream [2]. The frequency separation between two adjacent subcarraiers is 1/Tc, where Tc is the chip duration. Furthermore, the application of multiple input multiple output (MIMO) systems to wireless communication systems (MC DS-CDMA) can substantially increase the channel capacity and lower the symbol or bit error probability without any increase in the transmission power or expansion of the required bandwidth. On the other hand, wireless communication systems will be highly complex in structure and costly due to the involvement of multiple radio frequency (RF) devices. Therefore, the hand held mobile terminals may accommodate a small number of antennas due to the size and power limitation [3]. In this case, the antennas are connected to both ends forming multiple input multiple output MC DS-CDMA (MIMO MC DS-CDMA) system. Thus, at the transmitter end, space time coding is utilized to spread information across the antennas and allow the receiver to achieve transmit diversity. This, however, maximizes the diversity gain of the wireless communication system over fading channels [4]. The space time block codes (STBC) are employed to orthogonalize the MIMO wireless channels; i.e., STBC simplify maximum-likelihood decoding by decoupling the vector detection problem into a simpler scalar detection problem [5]. Therefore, the operation of the system is of special interest for the asynchronous reverse link of wireless mobile communication system based on Alamouti techniques [6]. In [7], the performance of MC DS-CDMA system is investigated using space time spreading in forward link when random signature sequences are employed. Yang and Hanzo [8], examined the issues of parameters design and bit error rate (BER) performance of broadband multicarrier DS-CDMA system over frequency selective Rayleigh fading channels using space time spreading assisted transmit diversity. The operation of the system is based on time domain spreading, time domain and frequency domain spreading combined was considered. Sourour and Nakagawa [9], proposed a new multicarrier direct sequence code division multiple access system and investigated its BER performance analysis based on conventional matched filter receiver and RAKE receiver for each subcarrier. In [10], Yang and Hanzo studied the BER performance of the generalized MC DS-CDMA system over multipath Nakagami-m fading channels. The effect of space between two adjacent subcarriers on the system performance was also considered. The comparison based on the operations of MC DS-CDMA, multitone (MT) DS-CDMA and orthogonal multicarrier (OMC) DS-CDMA systems over multipath Nakagami-m fading was also taken into account. Elnoubi and Hashem [11] examined the BER performance of MC DS-CDMA system over MIMO Nakagami-m multipath fading channels. The impact of the RAKE receiver in conjunction with MRC was also considered. In [12], Han and Paichard investigated the influence of imperfect channel estimation on MIMO MC CDMA system performance in terms of bit error rate. Closed-form expression for BER using MGF technique was derived. Yang [13] studied the BER performance of the multiantenna MC DS-CDMA system over correlated time selective Rayleigh fading channels. The space time spreading technique based on the family of orthogonal variables spreading factor code was proposed in order to attain time diversity. In [14], Lodhi et al. looked into the performance of STBC and cyclic delay diversity for MC CDMA system operating over Nakagami-m fading channels with correlated subcarriers. Closed-form expression of average BER (ABER) for M-ary digital modulation techniques was derived. The authors [15] derived new expression for probability density function of the sum of non-identical independent squared η–μ random variables and apply it to consider the performance of the asynchronous DS-CDMA system over η–μ fading channels. The evaluation of the system operation was in terms of outage probability, average channel capacity and average error probability respectively. Sagias et al. [16] explored the performance of the DS-CDMA system over Rayleigh fading channel based on average Shannon capacity. Generalized selection combining method for RAKE receiver was employed. As can be seen from many reported literature on performance of MC DS-CDMA system over fading channels, the fading distributions employed mostly are Rayleigh, Rician, Nakagami-q, Nakagami-m and Weibull respectively. In this paper we investigate the performance of MIMO MC DS-CDMA system in terms of average error probability and ergodic channel capacity over independent identically distributed (i.i.d) η–μ fading channels. We derive the instantaneous signal to interference noise ratio (SINR) at the output of the receiver. Hence, we employ moment generating function (MGF) based method for obtaining the probability density function (PDF) of the instantaneous SINR. In addition, we derive the closed form expressions of average error probabilities for the system by averaging the coherent digital modulation techniques over the PDF of the instantaneous SINR and express them in Appell's hypergeometric or Lauricella's hypergeometric functions, respectively. These closed-form expressions are new. Furthermore, the average channel capacity is achieved by averaging the Shannon Hartley capacity over the PDF of the instantaneous SINR of the received signal. The remainder of the paper is organized as follows. System and channel models are described in the next section. In Section 3, we discuss in detail the derivation of the instantaneous signal to interference noise ratio (SINR) and its probability density function (PDF). The derivation of the average error probability for the system is carried out in Section 4 while that of average channel capacity is outlined in Section 5. Numerical results and discussion are placed in Section 6. Finally, we conclude the paper in Section 7.

We investigated the performance of the MIMO MC DS-CDMA system over independent identically distributed (i.i.d) η–μ flat fading channels in terms of two metrics, average error probability and average channel capacity. Closed form expressions of average error probabilities for the system were derived based on moment generating function approach and expressed in Appell's and Lauricella's hypergeometric functions. In addition, average channel capacity expression was also obtained. Based on developed closed form expressions, we have analyzed the performance of the system over η–μ fading channels. The numerical results show that the system performance improvement is gained with increasing order of antenna diversity and also increasing value of the fading parameter μ. On the other hand, the performance of the system becomes inferior when the constellation size of the digital modulation techniques increases and also when the number of users increases as well. We compared our results with already existing ones in the literature and found to agree well. Furthermore, Monte Carlo simulation technique was employed to validate the results. Finally, it has been verified that Nakagami-q, Nakagami-m and Rayleigh fading distributions are special cases of the generalized η–μ fading distribution.