The problem of designing nonuniformly-spaced tapped-delay-tine equalizers (NU-E) for sparse multipath channels is addressed. First, analytical expressions that explicitly indicate the tap positions and tap values of the infinite-length, T-spaced linear equalizers (LE) and decision feedback equalizers (DFE) under the zero-forcing (ZF) and minimum mean square error (MMSE) criteria are derived using the conventional matched receive filter (MF) and a square root raised cosine (SRRC) receive filter that is matched to a SRRC transmit filter. For both receive filter systems, the ZF-LE and the MMSE-LE for sparse multipath channels are nonuniformly-spaced with identical tap positions, but the ZF-DFE and MMSE-DFE are uniformly-spaced. Next, two suboptimum tap allocation algorithms based on the positions of large magnitude taps in the infinite-length, T-spaced equalizers are proposed for designing finite-length, T- and T/2-spaced MMSE NU-LE and NU-DFE. Results have shown that the proposed NU-E exhibit superior performance over uniformly-spaced tapped-delay-line equalizers (U-E) for the same number of taps, and only a small loss in SNR when compared to U-E with a large number of taps. Moreover, the SRRC receive filter is found to be a better front-end receive filter than the MF when used together with an appropriately-designed NU-E. A simple method that assigns extra T/2-spaced taps to improve the timing insensitivity of the proposed NU-E is also included.
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