Capacity analysis of Rayleigh fading channels in low signal-to-noise ratio regime for maximal ratio combining diversity because of combining errors

In this research work, the authors derive closed-form expressions for capacity per unit bandwidth (spectrum efficiency) of correlated Rayleigh fading channels under maximal ratio combining diversity at low signal-to-noise ratios (SNRs). Spectrum efficiency expressions are derived for M diversity branches under adaptation policies, such as: (i) optimal power and rate adaptation (OPRA) policy, (ii) optimal rate adaptation (ORA) policy and (iii) truncated channel inversion with fixed rate (TIFR) policy. Even at low SNRs, if space diversity is exercised using a single-input multiple-output system, spectrum efficiency achieved is higher compared with that achieved when signals are uncorrelated and have no diversity. This forms the focal point of this study. Analytical results show accurately that OPRA policy provides highest capacity over other adaptation policies. The spectrum efficiency for the three policies and outage probability for the low SNR case are derived, plotted and analysed in detail in this work.