Design of Transmitter and Receiver Filters for Decision Feedback Equalization

Salazar, Andres C.

doi:10.1002/j.1538-7305.1974.tb02755.x

Cited by 13 publications

(4 citation statements)

References 3 publications

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“…We apply the separation of variables technique, starting by forcing the denominator in (5) to a minimum. 2 Thus, we have (6) Upon substitution of (6) into (5) we can write (7) hence (8) where (9) denotes the optimal effective channel IR. Now we may rewrite (8) as (10) Equation 10is a generalized eigenvalue problem, and is given by the eigenvector 11corresponding to the largest eigenvalue .…”

Section: A Joint Optimization Proceduresmentioning

confidence: 99%

“…In [6], it was shown that for the finite-impulse response (FIR) filter design under the minimum mean-square error (MMSE) criterion Cholesky factorization has to be used, the finite-dimensional analog of spectral factorization used in the infinite length case. The MMSE metric is not the only metric available for filter synthesis, as other authors, notably Salazar [7], Gerstacker [8], and Falconer et al [9] have shown that the maximization of the signal-to-noise ratio (SNR) metric is also suitable. In this letter, we use the concept of maximization of SNR in the least-squares (LS) sense, combined with a FIR prefilter with both causal and anticausal taps.…”

Section: Introductionmentioning

confidence: 99%

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Joint optimization of FIR prefilter and channel estimate for sequence estimation

Olivier

Xiao²

2002

IEEE Trans. Commun.

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We provide simple analytical results for the coefficients of a finite-impulse response (FIR) prefilter and the effective channel impulse response (IR) for use in cellular communication systems. We show that using a FIR filter with both causal and anticausal filter taps, it is possible to find the jointly optimized impulse response, such that the signal-to-noise ratio is maximized in the least-squares sense. We show via computer simulation for 8-ary phase-shift keying in enhanced data rates for global evolution (EDGE) that the joint optimization of the prefilter and IR produces results similar to the minimum mean-square error decision-feedback equalizer prefilter in thermal noise, but yields gain in colored noise.

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Section: A Joint Optimization Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Joint optimization of FIR prefilter and channel estimate for sequence estimation

Olivier

Xiao²

2002

IEEE Trans. Commun.

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“…A mathematical "experiment" was made to test the restoring action of the dynamic represented by (10). The mathematical tools in Ref.…”

Section: Analysis Of a Related One-dimensional Evolutionmentioning

confidence: 99%

Equalizing Without Altering or Detecting Data

Foschini

1985

At&T Technical Journal

154

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For terrestrial digital radio systems that use Quadrature Amplitude Modulation, the idea of adapting equalizers to multipath distortion, without relying on accurate data estimates, is attractive. Prompt adaptation following a severe fade, when accurate data estimates are unavailable, is useful for reducing outage time. To avoid processing and administrative overhead, the adaptation method should not involve violating the transmitted signal with the insertion of equalizer training signals. We approach this kind of equalization by building on an algorithm of D. Godard (IEEE Transactions on Communications, November 1980)1 that was devised for voiceband polling networks. The method involves a very simple tap update procedure. However, the technique lacks the foundation of the years of analysis and experimentation that underlie least‐mean‐square adaptation algorithms. The main purpose of this paper is to present new findings, including (1) a proof that the algorithm, thought to require special equalizer initialization, converges regardless of initialization (this offers useful flexibility in digital radio systems, since, after a severe fade, the algorithm could start with any tap misalignment); (2) a preliminary look at convergence speed suggesting the possibility of significant outage reduction; (3) an algorithm that provides phase coherence (the original algorithm requires a follow‐on phase‐locked loop); and (4) an algorithm for cross‐polarization cancellation as well as equalization.

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“…The more serious problem in applications is the complexity of error estimation . Recently, Feichtinger and Grochenig [4] designed a new iterative algorithm to recover a band-limited signal, which uses only the function values on a sequence and thus can be thought of as a sampling theorem.…”

Section: A Introductionmentioning

confidence: 99%

Some counterexamples in the theory of Weyl-Heisenberg frames

Janssen

1996

IEEE Trans. Inform. Theory

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We consider the causal channel g always generates a Weyl-Heisenberg frame gna+b, n,m E Z, when a , b > 0, ab < 1. Here g Z I Y ( t ) = exp (-nizy + 27riyt) g ( t -z), t E wWe truncate the channel response so that N , = 0 and AT, = 20.As before, the channel input is an i.i.d. sequence, and the noise is stationary and white with SNR,h,, =20 dB. We assume the number of feedforward taps is fixed at q = 10. Fig. 3 shows the optimal decision delay (defined as thlat which maximizes SNRDFE) versus the number of feedback taps. 'When the number of feedback taps is small, the optimal feedforward filter is two-sided; that is, it contains both causal and anticausal taps. As expected, however, the optimal A converges to q -1 as the number of feedback taps get large. Note that when A = q-1, the feedforward filter is anticausal; that is, {~k } = { w -~, . . . ,WO}. REFERENCES Some Counterexamples in the Theory of Weyl-Heisenberg Frames A. J. E. M. JanssenAbstruct-We present an example of a positive function g with a positive Fourier transform g and reasonable smoothness and decay properties such that (-lInm exp (zitm) g(t -n ) , n, m E Z does not constitute a frame for L2(W). We also give counterexamples for the statement that one can tell (in)definiteness of a Weyl-Heisenberg frame operator from @)definiteness of its Weyl symbol.

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Design of Transmitter and Receiver Filters for Decision Feedback Equalization

Cited by 13 publications

References 3 publications

Joint optimization of FIR prefilter and channel estimate for sequence estimation

Joint optimization of FIR prefilter and channel estimate for sequence estimation

Equalizing Without Altering or Detecting Data

Some counterexamples in the theory of Weyl-Heisenberg frames

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