## Signal and detector randomization for multiuser and multichannel communication systems

##### Author

Tutay, Mehmet Emin

##### Advisor

Gezici, Sinan

##### Date

2013##### Publisher

Bilkent University

##### Language

English

##### Type

Thesis##### Item Usage Stats

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Show full item record##### Abstract

Randomization can be considered as a possible approach to enhance error performance
of communication systems subject to average power constraints. In
the first part of this dissertation, we consider downlink of a multiuser communications
system subject to an average power constraint, where randomization
is employed at the transmitter and receiver sides by modeling signal levels as
random variables (stochastic signals) and employing different sets of detectors
via time-sharing (detector randomization), respectively. In the second part, we
consider single-user systems, where we assume that there exist multiple channels
between the transmitter and receiver with arbitrary noise distributions over each
of them and only one of the channels can be employed for transmission at any
given time. In this case, randomization is performed by choosing the channel
in use according to some probability mass function and employing stochastic
signaling at the transmitter.
First, the jointly optimal power control with signal constellation randomization
is proposed for the downlink of a multiuser communications system. Unlike
a conventional system in which a fixed signal constellation is employed for all the bits of a user (for given channel conditions and noise power), power control with
signal constellation randomization involves randomization/time-sharing among
different signal constellations for each user. A formulation is obtained for the
problem of optimal power control with signal constellation randomization, and
it is shown that the optimal solution can be represented by a randomization of
(K + 1) or fewer distinct signal constellations for each user, where K denotes the
number of users. In addition to the original nonconvex formulation, an approximate
solution based on convex relaxation is derived. Then, detailed performance
analysis is presented when the receivers employ symmetric signaling and sign detectors.
Specifically, the maximum asymptotical improvement ratio is shown to
be equal to the number of users, and the conditions under which the maximum
and minimum asymptotical improvement ratios are achieved are derived. In
the literature, it is known that employing different detectors with corresponding
deterministic signals via time-sharing may enhance error performance of communications
systems subject to average power constraints. Motivated by this
result, as a second approach, we study optimal detector randomization for the
downlink of a multiuser communications system. A formulation is provided to
obtain optimal signal amplitudes, detectors, and detector randomization factors.
It is shown that the solution of this joint optimization problem can be calculated
in two steps, resulting in significant reduction in computational complexity. It is
proved that the optimal solution is achieved via randomization among at most
min{K, Nd} detector sets, where K is the number of users and Nd is the number
of detectors at each receiver. Lower and upper bounds are derived on the performance
of optimal detector randomization, and it is proved that the optimal
detector randomization approach can reduce the worst-case average probability
of error of the optimal approach that employs a single detector for each user by
up to K times. Various sufficient conditions are obtained for the improvability
and nonimprovability via detector randomization. In the special case of equal crosscorrelations and noise powers, a simple solution is developed for the optimal
detector randomization problem, and necessary and sufficient conditions are
presented for the uniqueness of that solution.
Next, a single-user M−ary communication system is considered in which the
transmitter and the receiver are connected via multiple additive (possibly nonGaussian)
noise channels, any one of which can be utilized for a given symbol
transmission. Contrary to deterministic signaling (i.e., employing a fixed constellation),
a stochastic signaling approach is adopted by treating the signal values
transmitted for each information symbol over each channel as random variables.
In particular, the joint optimization of the channel switching (i.e., time-sharing
among different channels) strategy, stochastic signals, and decision rules at the receiver
is performed in order to minimize the average probability of error under an
average transmit power constraint. It is proved that the solution to this problem
involves either one of the following: (i) deterministic signaling over a single channel,
(ii) randomizing (time-sharing) between two different signal constellations
over a single channel, or (iii) switching (time-sharing) between two channels with
deterministic signaling over each channel. For all cases, the optimal strategies
are shown to employ corresponding maximum a posteriori probability (MAP)
decision rules at the receiver.

##### Keywords

MultiuserDownlink

Probability of Error

Minimax

Detection

Stochastic Signaling

Detector Randomization

Channel Switching

M-ary Communication

Gaussian Noise

Multimodal Noise

Power Constraint