In this paper, differential modulation and demodulation in a multiple relay system using either the decode-and-forward (DF) protocol or the selection relaying (SR) protocol, are investigated. For the DF protocol, the detectors at the destination take the average bit error probabilities (BEPs) of all the source-relay transmissions into account. For a DF single relay system, the exact BEP and its approximation at high signal-to-noise ratio (SNR) are obtained. The approximation of the BEP at high SNR shows explicitly the diversity order and the different effects of the source-relay link and the relay-destination link on the end-to-end error performance. For a DF multiple relay system, a Chernoff upper bound on the BEP and a high SNR approximation for the BEP are obtained. For the SR protocol, some computational complexity is shifted from the destination to all the relays. Each relay computes the instantaneous BEPs of the source-relay transmissions, and uses the instantaneous BEPs to decide whether to transmit or remain silent. The destination performs simple maximal ratio combining (MRC) reception whose error performance is analyzed at high SNR. It shows from an error probability perspective that the SR protocol offers a space diversity order equal to the number of all the potential cooperating nodes.

In a fading environment, the statistical distribution of the mutual information of a multiple-input multiple-output (MIMO) system depends on the joint distribution of the eigenvalues of a Wishart matrix, and is quite complex in general. We obtain here simple expressions for the distributions of the determinant and the trace of a Wishart matrix. Based on the obtained distributions, we derive some simple and tight bounds on the complementary cumulative distribution function (CCDF) of the mutual information of a MIMO system in Rician fading environments. The bounds obtained on the CCDF of mutual information provide further insights into the channel mutual information, and show the effects of the system parameters on the mutual information distribution explicitly. In addition, results for the Rayleigh channels are obtained as a special case.

We derive a decision-feedback channel estimation receiver for independent and non-identically distributed (i.n.d.) Rayleigh fading channels. The receiver has memory to store signals received over the past several symbol intervals, and then use them to adaptively estimate instantaneous channel gains. The receiver adapts its decision rule based on estimates of the varying channel gains, and hence it is partially coherent. We also obtain the bit error rate (BER) of the channel estimation receiver for binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK) modulations. The BER results are obtained in simple forms which explicitly show the effects of system parameters on the BER. In addition, our results are applicable to the cases where all the branches have arbitrary fade rates.

In this paper, a decode-and-forward (DF) single relay model in a Rayleigh fading environment is considered. The outage probability and ergodic rate for this model are derived. With the objective of either minimizing the outage probability or maximizing the ergodic rate, optimal and approximately optimal transmission strategies are developed through selecting appropriate transmit signaling and/or spatial power allocation. The derived transmission strategies only require the knowledge of the second-order statistics of the channels at the transmitters, which can be readily acquired in practice. Simulation results demonstrate that the optimal transmit signaling and/or spatial power allocation can offer considerable performance improvements over the equal power allocation strategy.

We consider about a multiple relay system operating under amplify-and-forward (AF) protocol and non-coherent modulation and demodulation. When the relays are under long-term power constraints, a near-maximum likelihood (ML) receiver and a diversity combining receiver are proposed. Both the near- ML receiver and the diversity combining receiver are expressed in simple closed forms and only rely on the second order statistics of the fading coefficients. Moreover, both of the proposed detectors outperform a non-cooperative system which only has a direct link with non-coherent ML detection in a Rayleigh fading environment. However, when the relay output is under a short-term power constraint, the ML detector derived here for the non-coherent AF relay performs the same as the non-cooperative system.

In this paper, we derive an optimal spatial power allocation strategy that maximizes the achievable rate of the decode-and-forward (DF) relay channels in a Rayleigh fading environment. Different from prior work, the derived strategy only requires the knowledge of the variances of the channels at the transmitters, which does not require frequent updates. Furthermore, we demonstrate that the optimal spatial power allocation strategy leads considerable performance improvements over the equal power allocation one.

The distribution of the capacity of multiple input multiple output (MIMO) fading depends on the joint distribution of the eigenvalues of a Wishart matrix, and is quite complex in general. We obtain here simple expressions for the distributions of the determinant of a Wishart matrix. Based on the distributions of the determinant and the trace of the Wishart matrix, we derive some simple and tight bounds on the complementary cumulative distribution function (CCDF) of the capacity of MIMO Rayleigh fading channels. The new bounds on capacity CCDF provide further insights into the channel capacity, and show the effects of the system parameters on the capacity distribution explicitly. These bounds can be used to evaluate the mean capacity as well.