Energy is a basic resource in digital transmission links. Physically, radio channels correspond to passive circuits and most of the transmitted energy is lost in the channel. Two alternative approaches are used for performance measurements in terms of energy. Either the average transmitted or received energy per bit is used, both usually normalized by the receiver noise spectral density. This leads to the average transmitted or received signal-to-noise ratio (SNR) per bit, respectively. However, the transmitted energy is the basic system resource. The average energy gain of a channel depends on the transmitted signal. For convenience, the transmitted SNR referred to the receiver is defined to be the product of the transmitted SNR and the representative energy gain, which is defined as the average energy gain of a signal that is uniformly distributed in all dimensions: time, frequency and space. An explicit relationship between the transmitted and received SNR's using the covariance concept is derived. Limitations of the use of different SNR definitions are summarized

Pilot-symbol-assisted modulation system using feedback minimum mean-square error (MMSE) power control in subject to an unavoidable feedback delay, and in conjunction with diversity, is considered over a slow Rayleigh fading channel. Feedback MMSE power control is defined as a power-control function, with feedback MMSE predictions of the current channel fading gains as input that minimizes the system-error probability. The use of feedback requires causality, and an MMSE predictor has to be employed for the purpose of power control. Previously, in the literature, the predictor was used also in detection. The pilot-symbol system with MMSE power control is shown to achieve a clear performance improvement by employing a smoother, instead of the predictor, in detection. Furthermore, the performance loss caused by a feedback delay of 10%-20% from the channel coherence time appeared to be minor with reasonable bit-error rate levels. Finally, additional performance improvement using low-order diversity was shown to be considerable.

The pilot symbol system with feedback MMSE power control over a slowly Rayleigh fading channel was previously considered in the literature. A feedback link was noiseless and delayless, and an MMSE predictor was used to estimate the channel state in both power control and detection. In this paper the feedback is noiseless and an MMSE smoother is used in detection. The effects of more accurate channel state estimates in detection and an unavoidable feedback delay on the system performance are derived.

A pilot symbol assisted modulation system with feedback MMSE power control over a slowly Rayleigh fading channel was previously considered in the literature. The MMSE predictor was used in power control and the MMSE smoother in detection, respectively, to estimate the complex fading gains. In this paper the additional effect of diversity on the system performance is derived. Furthermore, the coded bit error performance for the pilot symbol system using MMSE power control and diversity is arrived at through analytical bounds.