Abstract
Time-domain equalization is crucial in reducing channel state dimension in maximum likelihood sequence estimation and inter-carrier and intersymbol interference in multicarrier systems. A time-domain equalizer (TEQ) placed in cascade with the channel produces an effective impulse response that is shorter than the channel impulse response. This paper analyzes two TEQ design methods amenable to cost-effective real-time implementation: minimum mean square error (MMSE) and maximum shortening SNR (MSSNR) methods. We reduce the complexity of computing the matrices in the MSSNR and MMSE designs by a factor of 140 and a factor of 16 (respectively) relative to existing approaches, without degrading performance. We prove that an infinite-length MSSNR TEQ with unit norm TEQ constraint is symmetric. A symmetric TEQ halves FIR implementation complexity, enables parallel training of the frequency-domain equalizer and TEQ, reduces TEQ training complexity by a factor of 4, and doubles the length of the TEQ that can be designed using fixed-point arithmetic, with only a small loss in bit rate. Simulations are presented for designs with a symmetric TEQ or target impulse response.
Highlights
Channel shortening, a generalization of equalization, has recently become necessary in receivers employing multicarrier modulation (MCM) [1]
We show how to exploit this symmetry in computing the minimum mean square error (MMSE) target impulse response (TIR), adaptively computing the maximum shortening SNR (MSSNR) time-domain equalizer (TEQ), and in computing the frequency-domain equalizer (FEQ) in parallel with the TEQ
In [15], it was shown that the MMSE target impulse response becomes symmetric as the TEQ length goes to infinity, and in Section 5.2, it was shown that the infinite-length MSSNRUNT TEQ is an eigenvalue of a symmetric centrosymmetric matrix, and is expected to be symmetric
Summary
A generalization of equalization, has recently become necessary in receivers employing multicarrier modulation (MCM) [1]. In [3], Falconer and Magee proposed a minimum mean square error (MMSE) method for channel shortening, which was designed to reduce the complexity in maximum likelihood sequence estimation (MLSE). Melsa et al [5] proposed the maximum shortening SNR (MSSNR) method, which attempts to minimize the energy outside the window of interest while holding the energy inside fixed. This approach was generalized to the min-ISI method in [9], which allows the EURASIP Journal on Applied Signal Processing residual ISI to be shaped in the frequency domain. This paper examines the MSSNR and MMSE methods of channel shortening.
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