UC San Diego

Power control has become an important aspect of any communication system such as cellular networks, wireless LANs and DSL modems. Power control offers many benefits: optimizing the SNR in the link, conserving the battery life and minimizing the interference between the transmitter terminals. Power control is recognized as adaptive control. Here, we consider solely the optimization of the battery life and assessing the total energy cost in power control. The power control problem is formulated in a communication link with a static complex gain and a single transmitter, corrupted by complex normal noise. The channel estimate is computed by least squares using pilot tones. Then the signal power and noise power estimates are calculated, and ultimately the SNR estimate and its statistical properties. Based on this SNR estimate, an appropriate power level can be chosen for data transmission. The total energy cost of the power control process is formulated with aid of the statistics of SNR estimate. The cost is found to exhibit a pathological behavior, where a transmitter should send an infinite number of pilot tones at zero transmitted power to minimize the non-zero total energy cost of power control. When the transmitter is moving, however, this pathological behavior disappears. Next we look at the power control problem from the perspective of ODAC. The dual feature of the problem is that to probe the link effectively, the transmitter must use a large power level, but this affects the control process negatively as it increases the overall energy cost. A balance between the two aspects must be obtained. Assuming some a priori information about the fade is known, we use SDP, with aid of the information state that describes the evolution of the fade's statistics as measurements are obtained and controls applied, thus acquiring ODAC solutions to the power control problem. The solutions are found to depend greatly on what we know beforehand about the channel, a feature that is not present in current power control algorithms. We also develop heuristics that help reduce the computational demand due to SDP algorithm