Designing discrete-time amplitude limited signals for maximum
amplitude separation
Designing discrete-time amplitude limited signals for maximum
amplitude separation
M. L. Honig, K. Steiglitz, V. Balakrishnan, and E. Rantapaa
IEEE Trans. Information Theory, 41(1):164--170, January 1995
Abstract: Given a discrete-time, linear, shift-invariant
channel with finite impulse response, the problem of designing
finite-length input signals with bounded amplitude (l_infinity norm)
such that the corresponding output signals are maximally separated in
amplitude (l_infinity sense) is considered. In general, this is a
nonconvex optimization problem, and appears to be computationally
difficult. An optimization algorithm that seems to perform well is
described. Optimized signal sets and associated minimum distances
(minimum l_infinity separation between two distinct channel ouputs)
are presented for some example impulse responses. A conjectured upper
bound on the minimum distance is given that is easily computed given
the impulse response of the channel, the number of inputs, and the
input length. This upper bound is shown to be valid for a limited
class of impulse response functions.
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