Probability of Error of Linearly Modulated Signals with Gaussian Cochannel Interference in Maximally Correlated Rayleigh Fading Channels

Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2010, Article ID 193183, 13 pages doi:10.1155/2010/193183 Research Article Probability of Error of Linearly Modulated Signals with Gaussian Cochannel Interference in Maximally Correlated Rayleigh Fading Channels Luca Rugini and Paolo Banelli Department of Electronic and Information Engineering, University of Perugia, Via G. Duranti 93, 06125 Perugia, Italy Correspondence should be addressed to Luca Rugini, Received 30 November 2009; Revised 12 May 2010; Accepted 30 June 2010 Academic Editor: Guosen Yue Copyright © 2010 L. Rugini and P. Banelli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We evaluate the probability of error of linearly modulated signals, such as phase-shift keying (PSK) and quadrature amplitude modulation (QAM), in the presence of Gaussian cochannel interference (CCI) and Rayleigh fading channels. Specifically, we assume that the fading channel of the CCI is maximally correlated with the fading channel of the signal of interest (SOI). In practical applications, the maximal correlation of the CCI channel with the SOI channel occurs when the CCI is generated at the transmitter, such as the multiuser interference in downlink systems, or when a transparent repeater relays some thermal noise together with the SOI. We analytically evaluate the error probability by using a series expansion of generalized hypergeometric functions. A convenient truncation criterion is also discussed. The proposed theoretical approach favorably compares with alternative approaches, such as numerical integration and Monte Carlo estimation. Among the various applications of the proposed analysis, we illustrate the effect of nonlinear amplifiers in orthogonal frequency-division multiplexing (OFDM) systems, the downlink reception of code-division multiple-access (CDMA) signals, and the outdoor-to-indoor relaying of Global Positioning System (GPS) signals. 1. Introduction Thermal noise, fading channels, and cochannel interference (CCI) are among the main sources of performance degradation in wireless communication systems. For fading channels, the theoretical evaluation of the system performance has been extensively explored in the technical literature (see [1, 2], and the references therein), mainly in terms of symbol-error probability, equivalently known as symbolerror rate (SER), and of bit-error probability, also called bit-error rate (BER). In the last decades, the BER analysis has been extended to include the presence of faded CCI. Krishnamurthi and Gupta have investigated the BER of QPSK and 8-PSK when the signal of interest (SOI) and a single interferer are affected by independent Rayleigh fading channels [3]. Beaulieu and Abu-Dayya have evaluated the BER of QPSK when the SOI is subject to Nakagami fading and the interferer is affected by Rayleigh fading [4]. The BER analysis in Nakagami fading channels has been subsequently extended by Aalo and Zhang to multiple interferers, whose CCI can be modeled as Gaussian, under the assumption that the SOI employs differential PSK [5]. The BER of BPSKmodulated SOI with multiple CCI subject to Rayleigh fading has been studied also in the presence of multiple receive antennas [6–8]. The common feature of all the mentioned research studies is that the fading experienced by the CCI is independent of the fading experienced by the SOI. However, in many practical scenarios, the fading channel of the CCI and the fading channel of the SOI are highly correlated [9, 10]. In some important cases, this correlation is at maximum level, for example, when both the SOI and the CCI are subject to the same fading channel. For instance, this scenario happens when the CCI is generated at the transmitter, such as the multiuser interference in code-division multipleaccess (CDMA) downlink systems [11]. Other examples of 2 EURASIP Journal on Wireless Communications and Networking transmitter-generated CCI include the nonlinear distortion caused by the high-power amplifier in orthogonal frequencydivision multiplexing (OFDM) systems [12, 13], and the thermal noise produced by the front-end of a transparent transponder that relays Global Positioning System (GPS) signals from outdoor to an indoor receiver [14]. In all these scenarios, the CCI is well modeled by a Gaussian random variable. Despite the nonnegligible number of scenarios of interest, there have been few theoretical studies about the BER performance in the presence of CCI that is subject to the same fading channel of the SOI. Recently, Beaulieu and his coworkers have analyzed the BER performance when the SOI and the CCI experience correlated Rayleigh fading, assuming multiple receive antennas and maximal ratio combining [15, 16]. However, the analysis of [15, 16] is valid only for BPSKmodulated SOI, and for multiple interferers that use BPSK; therefore, the obtained results are not valid when the CCI is Gaussian. In this paper, we develop a SER analysis for linear modulations in Rayleigh fading channels, when the CCI is modeled as Gaussian at the decision variable. The proposed analysis can be employed in order to predict the maximum amount of interference that can be tolerated at the receiver, given a fixed performance requirement. We focus on maximally correlated fading channels, that is, we assume that the CCI is subject to the same fading channel that affects the SOI. Specifically, we analytically assess the error probability by using a series expansion of generalized hypergeometric functions [17]. Different aspects of the proposed formula are considered, such as, alternative expressions, series truncation criterion, BER with Gray coding, and effect of phase errors. We compare the proposed analysis with two alternative approaches, that is, numerical and statistical. The numerical approach uses Laguerre-Gauss quadrature [18] to evaluate the SER expressed as a single integral of a real variable. The statistical approach estimates the SER by means of a Monte Carlo method that shares many similarities with semianalytic evaluation [19]. We show that the proposed theoretical method enjoys a better accuracy with respect to both numerical and statistical methods, and that our theoretical results can accurately predict the SER performance in many different scenarios. Specifically, we focus on three applications: OFDM systems subject to highpower amplifier nonlinearities, CDMA detectors impaired by multiuser interference in downlink transmissions, and GPS receivers aided by outdoor-to-indoor relays. However, our analysis is quite general, since it can be applied to any communication system that is impaired by Gaussian CCI generated at the transmitter, when the channel experiences Rayleigh fading. Note that for some particular cases, the CCI gene (...truncated)