This paper presents another look at the problem of energy detection of unknown signals over different fading channels. We start with the no diversity case and present some alternative closed-form expressions for the probability of detection (P d ) to those recently reported in [1]. We then investigate the system performance when different diversity schemes are employed. It is shown that there is not much improvement in the probability of detection when either the probability of false alarm (P f ) exceeds 0.1 or the average signal-to-noise ratio (SNR) exceeds 20 dB. In addition, receiver operating characteristic (ROC) curves comparing the performance of equalgain combining (EGC), selection combining (SC), and switch and stay combining (SSC) are presented. As an example, EGC introduces a gain of two orders of magnitude from the probability of miss perspective compared to the no diversity case while both SC and SSC introduce a gain of about one order of magnitude.
Emerging applications involving low-cost wireless sensor networks motivate well optimization of multi-user orthogonal frequency-division multiple access (OFDMA) in the power-limited regime. In this context, the present paper relies on limited-rate feedback (LRF) sent from the access point to terminals to minimize the total average transmit-power under individual average rate and error probability constraints. Along with the characterization of optimal bit, power and subcarrier allocation policies based on LRF, suboptimal yet simple schemes are developed for channel quantization. The novel algorithms proceed in two phases: (i) an off-line phase to construct the channel quantizer as well as the rate and power codebooks with moderate complexity; and (ii) an on-line phase to obtain, based on quantized channel state information, the optimum, rate, power and user-subcarrier allocation with linear complexity. Numerical examples corroborate the analytical claims and reveal that significant power savings result even with suboptimal schemes based on practically affordable LRF.
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