Optimal Power Control, Scheduling, and Routing in UWB Networks

Abstract

Abstract-Ultra-Wide Band (UWB) is an emerging wireless physical layer technology that uses a very large bandwidth. We are interested in finding the design objectives of the medium access (MAC, namely, power control and scheduling) and routing protocols of a multi-hop, best-effort, UWB network. Our objective is to maximize flow rates (more precisely, log-utility of flow rates) given node power constraints. The specificity of UWB is expressed by the linear dependence between rate and signal-to-noise ratio at the receiver. It is known that, in wireless networks, different routing strategies can imply differences in MAC protocol design. Hence we search for the jointly optimal routing, scheduling and power control.We find that the optimal solution is characterized by the following. (1) When data is being sent over a link, it is optimal to have an exclusion region around the destination, in which all nodes remain silent during transmission, whereas nodes outside of this region can transmit in parallel, regardless of the interference they produce at the destination. Additionally, the source adapts its transmission rate according to the level of interference at the destination due to sources outside of the exclusion region.(2) The optimal size of this exclusion region depends only on the transmission power of the source of the link, and not on the length of the link nor on positions of nodes in its vicinity. (3) Each node in a given time slot either sends data at the maximum power, or does not send at all. As for the routing, we restrict ourselves to a subset of routes where on each successive hop we decrease the distance toward the destination, and we show that (4) relaying along a minimum energy and loss route is always better than using longer hops or sending directly, which is not obvious since we optimize rate and not power consumption. Finally (5), the design of the optimal MAC protocol is independent of the choice of the routing protocol. For narrow-band networks, (2), (4) and (5) do not hold, which shows that the design of an UWB network should be addressed in a different way than for narrow-band.Our technical approach is based on expressing the design requirements as a mathematical optimization problem. We solve it exactly for simple networks on a line and approximately on random topologies in a plane with up to 50 nodes with various power constraints, traffic matrices, and mobility parameters.

Complexity in geometric SINR

“…They show that in a generalized, non-geometric model, finding an optimal schedule is NP-complete, if no interference is tolerated. Other aspects of scheduling and power control using an arbitrary gain matrix are studied for instance in [3,4,6,28,29,30].…”

Cross-layer QoS-aware communication for ultra wide band wireless multimedia sensor networks

“…The problem of joint optimal power control, scheduling and routing in UWB networks is dealt with in [20], with the objective of maximizing the aggregate achievable data rate. The problem is formulated as an optimization problem, and is solved approximately for small topologies (up to 50 nodes).…”

Practical Scheduling Algorithms for Concurrent Transmissions in Rate-adaptive Wireless Networks

“…In [10], [11], based on the concept of "exclusive region" [12], several heuristic scheduling algorithms with polynomial time complexity were proposed. In their work, each receiver defines an exclusive region, and flows are scheduled to transmit concurrently only if the senders are outside the exclusive regions of other receivers.…”

“…As pointed out in [12], in terms of throughput, the benefit of power control in UWB wireless systems is marginal compared to that from scheduling. Thus we assume that each sender uses the maximum power level P t for transmission.…”