Efficient Channel Shortening Equalizer Design
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Efficient Channel Shortening Equalizer Design Richard K. Martin School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14853, USA Email: [email protected]
Ming Ding Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX 78712-1084, USA Email: [email protected]
Brian L. Evans Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX 78712-1084, USA Email: [email protected]
C. Richard Johnson Jr. School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14853, USA Email: [email protected] Received 6 February 2003 and in revised form 9 June 2003 Time-domain equalization is crucial in reducing channel state dimension in maximum likelihood sequence estimation and intercarrier 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. Keywords and phrases: multicarrier modulation, channel shortening, time-domain equalization, efficient computation, symmetry.
1. INTRODUCTION Channel shortening, a generalization of equalization, has recently become necessary in receivers employing multicarrier modulation (MCM) [1]. MCM techniques like orthogonal frequency division multiplexing (OFDM) and discrete multitone (DMT) have been deployed in applications such as the wireless LAN standards IEEE 802.11a and HIPERLAN/2, digital audio broadcast (DAB) and digital video broadcast (DVB) in Europe, and asymmetric and very-high-speed digital subscriber loops (ADSL, VDSL). MCM is attractive due to the ease with which it can combat channel dispersion, provided that the channel delay spread is not greater than the length of the cyclic prefix (CP). However, if CP is not long enough, the orthogonality of the subcarriers is lost, causing intercarrier interference (ICI) and intersymbol interference (ISI).
A well-known technique to combat the ICI/ISI caused by the inadequate CP length is the use of a time-domain equalizer (TEQ) in the receiver front end. The TEQ is a finite impulse response filter that shortens the channel so that the delay
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