| We provide a general theory for the effect of transmission power on the optimal performance of ad hoc wireless networks: An ad hoc wireless network with n nodes and m source-destination pairs, using a scheduling based medium access control (MAC) and a routing mechanism that may be unicast or multicast based, is considered. Let S( P) denote the set of all achievable source-destination throughput vectors lambda = (lambda1,···,lambda m) under power vector P = (P1,···, Pn), 0 ≤ Pi ≤ Pmax, i = 1,···, n. We analyze and investigate the effect of nodal transmit power vector P on the supremum level of a general (real-valued) function of the source-destination throughput levels O(lambda 1,...,lambdam) levels subject to lambda ∈ S(P). We represent the latter supreme level attained under power vector P by O*(P). Assuming that O(lambda1,...,lambdam) is not directly a function of P (i.e., O is affected by P only through S(P)), we prove that, independent of nodal distribution, traffic pattern, and offered traffic load, O*(P) is maximized (over the set of all nodal power vectors P) by properly increasing the nodal transmit power levels. Under the special case of our analysis for which the transmission power levels of all nodes are assumed to be identical (yet programmable), we prove that the power vector P = (P 1 = Pmax,···, Pn = Pmax) maximizes O*( P), independent of nodal distribution, traffic pattern, and offered traffic load.; For the latter special case, when the objective function O(lambda 1,...,lambdam) is defined properly, so that O*(P) represents the throughput capacity under power vector P, our results imply that P = (P1 = Pmax,···, Pn = Pmax) maximizes the throughput capacity, independent of nodal distribution, traffic pattern, and offered traffic load. This result stands in sharp contrast with previous results that appeared in the literature for networks with random nodal distribution and traffic pattern, which suggest the use of minimal common transmission power that maintains connectivity in the network maximizes the throughput capacity. We derive a linear programming (LP) formulation for obtaining the exact solution to the optimization problem that yields the throughput capacity of finite ad hoc wireless networks. Our LP based performance evaluation results identify the magnitude of capacity upgrade that can be realized for networks with random and uniform topologies and traffic patterns.; We also develop medium access control (MAC) protocols and algorithms for TDMA type scheduling schemes in ad hoc wireless networks, using power control and spatial-reuse features to attain high throughput levels. We provide extensive evaluations of the performance of these schemes. |
