Performance analysis of linear diversity-combining schemes on Rayleigh fading channels with binary signaling and Gaussian weighting errors

Abstract

In this paper, we analyze the error probability performance of maximal-ratio combining (MRC), equal-gain combining (EGC), selection combining (SC), and generalized-selection combining (GSC) diversity schemes with coherent binary phaseshift keying (BPSK) signaling on Rayleigh fading channels with Gaussian channel-estimation errors. We first show that, with weighting errors, averaging the conditional probability of error with the density function of the instantaneous signal-to-noise ratio (SNR) at the output of the combiner yields a lower bound on the exact probability of error. Later, we derive the exact probability of error for MRC, EGC, SC, and GSC diversity schemes and show that, for the case of nonnegative values of the in-phase correlation coefficient between the actual and the estimated channel gains, the exact probability of error with weighting errors is the same as that of the case with perfect channel estimation, but with the average SNR per diversity branch γ, for the case of perfect channel estimation, replaced by the effective SNR γ ρ , due to weighting errors. The effective SNR is a function of both γ and ρ, the magnitude of the normalized cross correlation between the actual and the estimated channel gains. Finally, we show that, as ρ → 0, the average probability of error approaches 0.5, irrespective of the order of diversity and the diversity-combining rule.

Error Probability for L-branch Coherent BPSK Equal Gain Combiners over Generalized Rayleigh Fading Channels

“…Using this expression for U(x) in (10), and substituting back in (9) and simplifying, we have (11) in (8), the probability of error for equal gain combiners over Generalized Rayleigh fading channels is…”

“…Annavajjala et al [11] consider the error probability performance of MRC, EGC, SC and generalized selection combining (GSC) diversity schemes with coherent BPSK signaling on Rayleigh fading channels with Gaussian channel estimation errors. The exact probability for MRC, EGC, SC, and GSC diversity schemes with weighting errors is the same as that for the case with perfect channel estimation with average SNR per diversity branch when the in-phase correlation coefficient between the actual and the estimated channel gains is non-negative.…”

Exact Error Rate Analysis of MIMO-MRC System under Cochannel Interference and Imperfect Channel State Information

“…Some works that take into account the imperfect CSI scenario in the performance of MIMO-MRC systems can be found in [18][19][20][21][22][23]. The works in [18] and [19] analyzed the performance of MIMO-MRC systems in the presence of Gaussian channel estimation errors in i.i.d.…”

“…The works in [18] and [19] analyzed the performance of MIMO-MRC systems in the presence of Gaussian channel estimation errors in i.i.d. Rayleigh fading channels.…”

Using Delayed Feedback for Antenna Selection in MIMO Systems

“…Simulation results on the loss in the achievable capacity of the hybrid selection MRC system due to CSI imperfections is presented in [8]. The error probability of Generalized Selection Combining is presented in [9], where it was shown that estimation errors lead to a bounded loss in Signal to Noise Ratio (SNR) compared to the perfect CSI case. The effect of channel estimation error on a MIMO OFDM system employing antenna selection is analyzed in [10].…”