79,444 research outputs found
Error Rate Analysis of Cognitive Radio Transmissions with Imperfect Channel Sensing
This paper studies the symbol error rate performance of cognitive radio
transmissions in the presence of imperfect sensing decisions. Two different
transmission schemes, namely sensing-based spectrum sharing (SSS) and
opportunistic spectrum access (OSA), are considered. In both schemes, secondary
users first perform channel sensing, albeit with possible errors. In SSS,
depending on the sensing decisions, they adapt the transmission power level and
coexist with primary users in the channel. On the other hand, in OSA, secondary
users are allowed to transmit only when the primary user activity is not
detected. Initially, for both transmission schemes, general formulations for
the optimal decision rule and error probabilities are provided for arbitrary
modulation schemes under the assumptions that the receiver is equipped with the
sensing decision and perfect knowledge of the channel fading, and the primary
user's received faded signals at the secondary receiver has a Gaussian mixture
distribution. Subsequently, the general approach is specialized to rectangular
quadrature amplitude modulation (QAM). More specifically, optimal decision rule
is characterized for rectangular QAM, and closed-form expressions for the
average symbol error probability attained with the optimal detector are derived
under both transmit power and interference constraints. The effects of
imperfect channel sensing decisions, interference from the primary user and its
Gaussian mixture model, and the transmit power and interference constraints on
the error rate performance of cognitive transmissions are analyzed
Estimating Mixture Entropy with Pairwise Distances
Mixture distributions arise in many parametric and non-parametric settings --
for example, in Gaussian mixture models and in non-parametric estimation. It is
often necessary to compute the entropy of a mixture, but, in most cases, this
quantity has no closed-form expression, making some form of approximation
necessary. We propose a family of estimators based on a pairwise distance
function between mixture components, and show that this estimator class has
many attractive properties. For many distributions of interest, the proposed
estimators are efficient to compute, differentiable in the mixture parameters,
and become exact when the mixture components are clustered. We prove this
family includes lower and upper bounds on the mixture entropy. The Chernoff
-divergence gives a lower bound when chosen as the distance function,
with the Bhattacharyya distance providing the tightest lower bound for
components that are symmetric and members of a location family. The
Kullback-Leibler divergence gives an upper bound when used as the distance
function. We provide closed-form expressions of these bounds for mixtures of
Gaussians, and discuss their applications to the estimation of mutual
information. We then demonstrate that our bounds are significantly tighter than
well-known existing bounds using numeric simulations. This estimator class is
very useful in optimization problems involving maximization/minimization of
entropy and mutual information, such as MaxEnt and rate distortion problems.Comment: Corrects several errata in published version, in particular in
Section V (bounds on mutual information
Symbol Error Rate Performance of Box-relaxation Decoders in Massive MIMO
The maximum-likelihood (ML) decoder for symbol detection in large
multiple-input multiple-output wireless communication systems is typically
computationally prohibitive. In this paper, we study a popular and practical
alternative, namely the Box-relaxation optimization (BRO) decoder, which is a
natural convex relaxation of the ML. For iid real Gaussian channels with
additive Gaussian noise, we obtain exact asymptotic expressions for the symbol
error rate (SER) of the BRO. The formulas are particularly simple, they yield
useful insights, and they allow accurate comparisons to the matched-filter
bound (MFB) and to the zero-forcing decoder. For BPSK signals the SER
performance of the BRO is within 3dB of the MFB for square systems, and it
approaches the MFB as the number of receive antennas grows large compared to
the number of transmit antennas. Our analysis further characterizes the
empirical density function of the solution of the BRO, and shows that error
events for any fixed number of symbols are asymptotically independent. The
fundamental tool behind the analysis is the convex Gaussian min-max theorem
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