Optimum Detection of Quantized PAM Data Signals

TLDR: Performance is evaluated under the assumption of high signal-to-noise ratio (SNR), and the resultant error probability is a good approximation for coarse quantization, and an upper bound for any degree of quantization is suggested.

Abstract: The degree of complexity of a digital signal processor is closely related to the precision with which samples of an incoming analog waveform are represented. There is considerable interest in determining how coarse this representation can be without seriously degrading performance from that of an ideal processor of unquantized samples. This question is examined for a receiver of noisy, linearly distorted pulse amplitude modulation (PAM) signals. An optimum [maximum likelihood (ML)] detector, analogous to the Viterbi detector for unquantized samples, is derived for the case of a quantized sample sequence. Performance is evaluated under the assumption of high signal-to-noise ratio (SNR), and the resultant error probability is a good approximation for coarse quantization, and an upper bound for any degree of quantization. For a specified error probability, the degree of quantization suggested by this approach is conservative. Since receiver complexity is closely associated with the length of the digital representation of an input sample, an upper bound on receiver complexity is also suggested. Numerical evaluation of the error probability is quite tedious for an arbitrary channel; however, system performance may be readily evaluated for partial-response (PR) signaling. For the PR channels

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Optimum Detection of Quantized PAM Data Signals
Item Type text; Proceedings
Authors Foschini, G. J.; Gitlin, R. D.; Weinstein, S. B.
Publisher International Foundation for Telemetering
Journal International Telemetering Conference Proceedings
Rights Copyright © International Foundation for Telemetering
Download date 10/08/2022 03:09:05
Link to Item http://hdl.handle.net/10150/609389

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The paper has been submitted to the IEEE Transaction on Communications.
OPTIMUM DETECTION OF QUANTIZED PAM DATA SIGNALS
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G. J. FOSCHINI, R. D. GITLIN and S. B. WEINSTEIN
Bell Telephone Laboratories
Holmdel, New Jersey 07733
ABSTRACT
The degree of complexity of a digital signal processor is closely related to the precision
with which samples of an incoming analog waveform are represented. There is
considerable interest in determining how coarse this representation can be without
seriously degrading performance from that of an ideal processor of unquantized samples.
This question is examined for a receiver of noisy, linearly-distorted PAM signals. An
optimum (maximum likelihood) detectors analogous to the Viterbi detector for unquantized
samples, is derived for the case of a quantized sample sequence. Performance is evaluated
under the assumption of high signal-to-noise ratio, and the resultant error probability is a
good approximation for coarse quantization, and an upper bound for any degree of
quantization. For a specified error probability, the degree of quantization suggested by this
approach is conservative. Since receiver complexity is closely associated with the length of
the digital representation of an input sample, an upper bound on receiver complexity is also
suggested.
Numerical evaluation of the error probability is quite tedious for an arbitrary Channel;
however, system performance may be readily evaluated for partial-response signaling. For
the partial-response channels(1,1) and (1,2,1), it is shown that five and six bit quantizers
provide, respectively, a degradation of less than 1 dB in SNR from the infinitely quantized
(Viterbi) receiver.

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This question is examined for a receiver of noisy, linearly-distorted PAM signals. For the partial-response channels ( 1,1 ) and ( 1,2,1 ), it is shown that five and six bit quantizers provide, respectively, a degradation of less than 1 dB in SNR from the infinitely quantized ( Viterbi ) receiver. For a specified error probability, the degree of quantization suggested by this approach is conservative. Since receiver complexity is closely associated with the length of the digital representation of an input sample, an upper bound on receiver complexity is also suggested.