Average signal-to-interference-plus-noise ratio of a generalized optimum selection combiner for non-identical independent Rayleigh fading channels in the presence of co-channel interference

A generalized optimum selection combiner selects an arbitrary number (m 2⩽m⩽L) of diversity branches with the largest signal-to-interference-plus-noise ratio (SINR) from a total of L available branches in the presence of co-channel interference (CCI), it weights and combines the selected branches to maximize the SINR for the desired user. A generalized optimum selection combiner is studied as opposed to the conventional optimum combiner, which combines all the available branches in order to achieve the best trade-off between the receiver performance and complexity in the presence of CCI. This paper presents a closed-form expression for the average SINR of this generalized optimum selection combiner for non-identical independent (non-i.i.d.) Rayleigh fading channels in the presence of one co-channel interferer. The presented SINR expression reduces to the average signal-to-noise (SNR) of a generalized diversity selection combiner with a diversity order of m when there is no co-channel interference. When the interference increases it asymptotically reduces to the average SNR of a generalized diversity selection combiner with a diversity order of m-1 as if there was no interference. The paper also derives for the multiple co-channel interferers, the trade-off between the interference cancellation and diversity gain improvement. Using a subspace approach, the paper shows that optimally combining m branches from available L branches in the presence of n co-channel interferers can eliminate n (n<m) interferers and achieves an m·n order diversity gain at the same time