Noncoherent Decorrelative Multiuser
Detection for Nonlinear Nonorthogonal Modulation
M. K. Varanasi and A. Russ, Proc of the 1997 IEEE Intl Conf Communications, Montreal,
Quebec, Canada, June 1997.
Coherent multiuser detection for linear modulation has been the subject of intense
research in the past decade. Noncoherent detection for linear differentially phase shift
keyed modulation has also received much attention in the last few years. This paper
considers for the first time the problem of noncoherent detection for M-ary nonlinear
nonorthogonal modulation in the Gaussian correlated-waveform multiple-access channel.
A key idea proposed here is that of a noncoherent decorrelative front end for nonlinear
modulation. Like its counterpart in linear modulation, that front-end eliminates multiuser
interference (at the price of noise enhancement) and reduces the multiuser detection
problem into that of single-user detection over an equivalent (noise-enhanced) single-user
channel.
However, the M effective signals of the equivalent single-user channel are correlated
and of unequal energy. Noncoherent detection even in this effective single-user channel
has been an open problem to date. We derive the optimum detector for this channel. It is
unfortunately too complicated to implement or analyze. Two suboptimal detectors are
proposed as a result depending on whether knowledge of the energies of the M signals are
known or unknown at the receiver. For unknown energies, the generalized likelihood ratio
test leads to a detector which is easy to implement. Error probability bounds are obtained
for this detector. It is shown to be near-far resistant (in contrast to the conventional
detector). For known energies, an asymptotic series expansion of a special function
involved in the optimum noncoherent decision rule leads to the other suboptimum detector.
Its analysis is more difficult but we nevertheless obtain exact expressions for error
probability for binary modulation and bounds on error probability in the M-ary case. This
detector can outperform the GLRT detector by a significant margin. Both detectors far
outperform the conventional single-user detector.
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