Diversity Analysis for Linear Equalizers over ISI Channels

It has been shown in the literature that, with zero-padding prefix (ZPP), the optimum diversity gain of frequency selective channels can be obtained by uncoded signals and zero forcing (ZF) equalizers. In this paper, we derive two important results about linear equalizers over frequency selective channels: 1) With cyclic prefix and any rate-1 unitary precoding, which includes the uncoded/coded-OFDM/SCFDMA systems as special cases, linear equalizers can only obtain order-1 diversity; and 2) Although linear equalizers can achieve the optimum diversity order with zero-padding prefix and uncoded signals, the required SNR (signal-to-noise ratio) is an increasing function of the symbol-length. The second result implies that we may not be able to take advantage of the diversity gain in practice due to the high SNR requirements. Special cases are also investigated to gain some physical insights about the effects of different prefixes on the performance of linear equalizers. The results in this paper can be utilized in the design of up/down-link LTE systems with linear equalizers.