Online algorithms for maximizing quality of link transmissions over a jammed wireless channel

Abstract

We consider the problem of a transmitter transmitting to its receiver over a wireless link subject to jamming and develop two online power control algorithms for maximizing wireless link quality (transmission rate). We assume that the transmitter transmits and the jammer interferes over a period of M time slots. The impact of the jammer is to deteriorate the quality of the wireless channel during time slots in which it is present. We assume a powerful random jammer with the ability to arbitrarily decrease the channel quality and affect any (unknown) number of time slots. Since the presence of the jammer is arbitrary, the complete jamming pattern (channel quality) over the given time period is unknown apriori. The current channel quality is revealed to the transmitter at the start of the current time slot while future channel quality remains unknown. The transmitter must then allocate power optimally to maximize the total transmission rate over M slots given only its knowledge of the current channel quality, thus giving rise to an online power control problem. We develop two online power control algorithms for maximizing the wireless link quality (transmission rate). The first algorithm is based on constant power scaling and has O(1) competitive ratio when the average received power quality over M time slots (h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">circ</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> /M) is either very small or very large. However when h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">circ</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> = O(M), this algorithm has an upper bound on its competitive ratio of O(log M/log log M). This upper bound is tight. The second online algorithm based on constant rate scaling has a worst case competitive ratio of O(1+ log log M/ 1+hgPT/M). By judiciously choosing which algorithm to use based on the offline available parameter of average received power, we can assure an almost constant competitive ratio for maximizing link quality under all cases.