Matched filter bound for multichannel diversity over frequency-selective Rayleigh-fading mobile channels

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We propose a theoretical evaluation of the matched filter bound (MFB) of L-branch antenna diversity with maximal-ratio-combining (MRC) in a frequency-selective Rayleigh-fading channel. The theoretical derivation is based on a Karhunen-Loeve expansion. Although many previous approaches of this kind have been presented in the past, we give a more general and straightforward one as our model accounts for the correlations between the L branches and between the channel taps within each branch, as well as the mismatch between the average received power per branch. The usefulness of our approach is shown through two different applications. First the benefits of a two branch receiver (L=2) using spatial or polarization diversity for the global system for mobile communication (GSM) and Interim Standard 95 (IS-95) downlink systems both using binary signaling, are compared. Second, with the use of our theoretical model, it is proved that the diversity gain is invariant by any unitary transformation. As a result, and contrary to widespread belief, polarization diversity gain is shown to be invariant by spatial rotation of the receiver antennas.