Stability and Control of Mobile Communications Systems With Time Varying Channels

Consider the forward link of a mobile communications system with a single transmitter and rather arbitrary randomly time varying channels connecting the base to the mobiles. Data arrives at the base in some random way (and might have a bursty character) and is queued according to the destination until transmitted. The main issues are the allocation of transmitter power and time to the various queues in a queueand channelstate dependent way to assure stability and good operation. The control decisions are made at the beginning of the (small) scheduling intervals. Stability methods are used to allocate time and power. Many schemes of current interest can be handled: For example, CDMA with control over the bit interval and power per bit, TDMA with control over the time allocated, power per bit, and bit interval, as well as arbitrary combinations. There might be random errors in transmission which require retransmission. The channel-state process might be known or only partially known. The details of the scheme are not directly involved; all essential factors are incorporated into a “rate” and “error” function. The system and channel process are scaled by speed. Under a stability assumption on a model obtained from the “mean drift,” and some other natural conditions, it is shown that the scaled physical system can be controlled to be stable, uniformly in the speed, for fast enough speeds. Owing to the non-Markov nature of the problem, we use the perturbed Liapunov function method, which is very useful for the analysis of non-Markovian systems. Finally, the stability method is used to actually choose the power and time allocations. The allocation will depend on the Liapunov function. But each such function corresponds loosely to an optimization problem for some performance criterion. Since there is a choice of Liapunov functions, various performance criteria can be taken into account in the allocations. The resulting controls are quite reasonable. The power of the method is due to the rather general conditions under which it works and the reasonableness of the controls. Both authors were partially supported by Army Research Office Contract DAAD19-00-10549 and National Science Foundation Grant ECS 9979250.