In this paper we derive exact expressions for the mutual information (MI) probability density function and the MI cumulative distribution function of dual-branch multipleinput multiple-output (MIMO) systems (either two transmit (Tx) or two receive (Rx) antennas) communicating over a Ricean channel with no constraint on the rank of the line-of-sight (LOS) channel matrix. This is done both for the case where the channel is only known at the Rx, and for the case where the channel is known both at the Tx and the Rx. As an example, to evaluate the expressions, we employ uniform linear arrays and give expressions for the eigenvalues of the LOS channel matrix for the dual-branch case.

The memoryless noncoherent single-input-single-output (SISO) Rayleigh-fading channel is considered. Closed-form expressions are derived for the mutual information between the output and the input of this channel when the input magnitude distribution is discrete and is restricted to having two mass points. It is subsequently shown how these expressions can be used to obtain closed-form expressions for the capacity of this channel for signal to noise ratio (SNR) values of up to approximately 0 dB, and a tight capacity lower bound for SNR values between 0 dB and 10 dB. The expressions for the channel capacity and its lower bound are given as functions of a parameter which can be obtained via numerical root-finding algorithms.

The power adaptation strategy which maximises the average information rate that can be reliably transmitted over average and peak power constrained block-fading single-user discrete-time channels, in which perfect transmitter and receiver channel state information (CSI) are available and in which any transmitted codeword spans a single fading block, is characterised by means of a theorem and subsequently computed numerically in different scenarios. The results reveal striking differences between the well known water-pouring power adaptation strategy which is optimal from a capacity point of view in the case of stationary and ergodic fading channels where the input is subject to an average power constraint only, and the rate-optimal power adaptation strategy of the average and peak power constrained block-fading channels studied in this document.

The energy-efficient design of short-distance wireless communication systems requires the inclusion of circuit energy consumption in the system's total energy budget. We consider the design of link adaptation schemes in which circuit energy consumption is included in the total energy budget, in which a set of signal constellations of constant peak-to-average power ratio (PAPR) is used, and in which the transmitted power is kept constant whatever be the particular signal constellation in use. We show how the dimensionality of the associated non-linear optimisation problem can be reduced from N + 1 to one, where N denotes the number of available transmission schemes. These principles are then applied to a design example.