On the SNR penalty of MPSK with hybrid selection/maximal ratio combining over i.i.d. Rayleigh fading channels

Closed-form expressions that lower and upper bound the penalty of hybrid selection/maximal ratio combining relative to maximal ratio combining (MRC) for M-ary phase-shift keying (MPSK) modulation are proved. The bounds offer simple-to-evaluate explicit expressions, and are typically within 0.6 dB for hybrid systems with diversity order up to eight that use at least two branches, yet are independent of signal-to-noise ratio (SNR). Contrary to conclusions conjectured in a previously published paper, it is proved that the SNR penalty is not a constant, independent of SNR. It is also shown that previous estimates of the performance losses of selection diversity relative to MRC underestimate or lower bound the losses for MPSK modulation systems, and that the true loss can be significantly larger than previously believed. An upper bound to this loss is also obtained.

[1]  Moe Z. Win,et al.  On the energy capture of ultrawide bandwidth signals in dense multipath environments , 1998, IEEE Communications Letters.

[2]  Mohamed-Slim Alouini,et al.  Performance of coherent receivers with hybrid SC/MRC over Nakagami-m fading channels , 1999 .

[3]  John G. Proakis,et al.  Digital Communications , 1983 .

[4]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[5]  Laurence B. Milstein,et al.  Average SNR of a generalized diversity selection combining scheme , 1999, IEEE Communications Letters.

[6]  Moe Z. Win,et al.  Analysis of hybrid selection/maximal-ratio combining in Rayleigh fading , 1999, IEEE Trans. Commun..

[7]  M. Win,et al.  Analysis of hybrid selection/maximal-ratio combining of diversity branches with unequal SNR in Rayleigh fading , 1999, 1999 IEEE 49th Vehicular Technology Conference (Cat. No.99CH36363).

[8]  A. Shiryaev,et al.  Probability (2nd ed.) , 1995, Technometrics.

[9]  Sven Zeisberg,et al.  BER performance of a hybrid SC/MRC 2DPSK RAKE receiver in realistic mobile channels , 1994, Proceedings of IEEE Vehicular Technology Conference (VTC).

[10]  A. G. Greenhill,et al.  Handbook of Mathematical Functions with Formulas, Graphs, , 1971 .

[11]  Moe Z. Win,et al.  Performance of RAKE reception in dense multipath channels: implications of spreading bandwidth and selection diversity order , 2000, IEEE Journal on Selected Areas in Communications.

[12]  Chintha Tellambura,et al.  Error rates for Nakagami-m fading multichannel reception of binary and M-ary signals , 2001, IEEE Trans. Commun..

[13]  Laurence B. Milstein,et al.  Comparison of diversity combining techniques for Rayleigh-fading channels , 1996, IEEE Trans. Commun..

[14]  H. Piaggio.  Differential Geometry of Curves and Surfaces , 1952, Nature.

[15]  Norman C. Beaulieu,et al.  New results on selection diversity , 1998, IEEE Trans. Commun..

[16]  Mohamed-Slim Alouini,et al.  Average SNR of dual selection combining over correlated Nakagami-m fading channels , 2000, IEEE Communications Letters.

[17]  Moe Z. Win,et al.  Virtual branch analysis of symbol error probability for hybrid selection/maximal-ratio combining in Rayleigh fading , 2001, IEEE Trans. Commun..

[18]  Moe Z. Win,et al.  Virtual path analysis of selective RAKE receiver in dense multipath channels , 1999, IEEE Communications Letters.

[19]  Khaled Ben Letaief,et al.  Antenna diversity combining and finite-tap decision feedback equalization for high-speed data transmission , 1998, IEEE J. Sel. Areas Commun..