PCC: Principal components combining for dense correlated multipath fading environments

Spread spectrum transmissions and RAKE receivers are known to alleviate the effects of random fading. In the context of future wideband/ultra-wideband systems, both estimation accuracy and receiver complexity are adversely affected when the number of channel parameters increases. As an alternative to generalized selection combining schemes, which have received a great deal of attention over the last couple of years, this work introduces a new class of diversity schemes that trade off optimally diversity gain with receiver complexity. The basic idea is to exploit the information on the channel statistics in selecting a linear mapping that reduces the channel order while minimizing the loss in terms of diversity gain. We prove that the optimal linear mapping amounts to projecting the received data onto the channel's principal components obtained by the eigenvectors of the channel correlation matrix corresponding to the Q strongest eigenvalues. We then derive closed-form expressions for the average combined signal-to-noise ratio and the average symbol error rate for various modulation schemes operating in dense Nakagami-m correlated multipath fading environments of practical interest.