226 IETE JOURNAL OF RESEARCH | VOL 57 | ISSUE 3 | MAy-JUN 2011 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Performance of L-MRC Receiver over Equally Correlated Hoyt Fading Channels Rupaban Subadar and P. R. Sahu Department of ECE, IIT Guwahati, Guwahati, Assam, India ABSTRACT Performance of an L branch maximal raio combining receiver has been analyzed in equally correlated Hoyt fading channels. For the combiner output signal-to-noise raio, analyical expressions for the probability density funcion, its average value, nth moment and outage probability have been obtained. Further, for the MRC receiver, expressions for average bit error rate for binary, coherent, and noncoherent modulaions have been presented. Both numerical evaluaion and computer simulaion results have been generated to validate analyically obtained expressions. Numerical results have been ploted to illustrate the efect of channel correlaion and L on the receiver performance. Keywords: Average bit error rate, Equal correlaion, Hoyt fading channel, MRC receiver, Outage probability. IETE JR_16_10R3 1. INTRODUCTION Among performance analysis of diversity combining receivers over fading channels, analysis of correlated fading cases are always on demand and have been found to be challenging. Hoyt fading, which is observed in satellite links and other fading channels, characterizes severe fading types ranging between one-sided Gaussian and Rayleigh [1]. Performance of maximal ratio combining (MRC) and EGC receivers over Hoyt fading channels are presented in [2–7]. Most of this works are on independent fading channels, where as in [7], performance analysis of a dual maximal ratio combining (MRC) receiver over correlated Hoyt fading channels has been presented. In practice obtaining independent spatial fading channels for diversity combining is dificult due to the size limitation of wireless communication devices. Hence in this paper, we have analyzed the performance of an L-MRC receiver over correlated Hoyt fading channels. Performance evaluation of the MRC receiver requires the probability density function (PDF) of the combiner output signal-to- noise ratio (SNR). For correlated L Hoyt random variables (RVs) this PDF is not known in an usable mathematical form. However, using the Hoyt RV model in [8] and an useful analytical result of [9], we demonstrate that it is possible to obtain an expression for this PDF of the MRC receiver for the special case of equally correlated Hoyt RVs. Equal or constant correlation model has been discussed in [1] and [10], where correlation coeficient r m,n =r for " m ≠ n and 1 ≤ m, n ≤ L. In practice, this correlation model can be observed in diversity reception by an array of three antennas placed on an equilateral triangle or by closely placed antennas (other than linear arrays) [11]. In this paper, using the obtained PDF of MRC output SNR EQ1 EQ2 we derive mathematical expressions for the moment of the output SNR and outage probability of the combiner. Further, for the MRC receiver, we derived an expression for the average bit error rate (ABER) for the binary, coherent, and noncoherent modulation schemes. The paper is organized as follows. In Section 2, we introduce the channel and receiver and in Section 3, we present an analysis of the MRC receiver. Numerical and simulation results have been presented in Section 4 followed by conclusion in Section 5. 2. CHANNEL AND RECEIVER The channel has been assumed to be slow, frequency nonselective, with Hoyt fading statistics. The receiver has been provided with L antennas for spatial diversity reception of fading signals. The complex low pass equivalent of the signal received by the l th antenna, l=1, 2,…, L, over one bit duration Tb can be expressed as rt e st n t l l j l l () () ( ), = + a f (1) where s(t) is the transmitted bit signal with energy E b and n l (t) is the complex Gaussian noise having zero mean and two-sided power spectral density 2N 0 . The RV f l denotes the instantaneous phase and a l is the Hoyt distributed fading amplitude having PDF given by [1] p q q e I q q l l l q q l l l l ( ) ( ) ( ) ( ) = + - È Î Í Í ˘ ˚ ˙ ˙ - + 1 1 4 2 1 4 0 4 2 2 2 2 2 2 W W W a , , l ≥ 0 (2) where Ω l =E[a 2 l ], q l Œ [0, 1] is the Hoyt fading parameter and I 0 (∙) is the modiied Bessel function of the irst kind 1 2