Generalized diversity combining (GDC), also known as hybrid selection/maximal
ratio combining or generalized selection combining, is a low-complexity
diversity combining technique by which a fixed subset of a large number of
available diversity channels is chosen and then combined using the rules of maximal
ratio combining. In this paper, we analyze the performance of GDC on
time-correlated Rayleigh fading channels with noisy channel estimates.
We derive expressions for the probability of error for
various linear modulation schemes with coherent detection, as a function of the
channel estimation parameters, the number of channels, and
the number of channels to combine.
Throughout the paper, using a fundamental approach to obtain the
decision statistic at the combiner output, a number of new expressions for
the error probabilities are obtained in a rigorous way,
along with a presentation of their performance with imperfect channel estimation.
The final expressions are simple, and have the same complexity of
evaluation as that for the channel with only additive Gaussian noise.
Our results, while correcting various inaccuracies in the recent literature,
show that imperfect channel estimates cause a significant degradation of the receiver
performance.