Throughput improvement in ALOHA networks with power capture and a cheat-proof access control

In this paper, we consider the problem of power level selections under an average power constraint in slotted ALOHA networks. In the network, each node chooses a power level from a pre-determined power level set based on a probability for each access attempt. The derivation of the probability for maximizing the throughput is difficult. In addition, nodes may not always obey the given algorithm in a distributed network because a misbehaving node might gain better performance at the expense of the others. To prevent the potential of misbehavior, we derive a cheat-proof algorithm based on game theory, which will make no nodes in the network want to deviate from the algorithm. Further, we show the throughput loss of the cheat-proof algorithm compared to the optimal one, and show the occurrence of unjust situation if the property of cheat-proof is not taken into account.

I. Introduction

In this paper, we study improving the throughput of ALOHA networks [1] [2] by power capture. ALOHA networks and its variants have been well studied over more than thirty years, and many methods were proposed to improve the efficiency of ALOHA networks. The use of multiple power levels to artificially introduce power capture is a simple and effective method for increasing the throughput of ALOHA networks, and was first proposed and analyzed by Metzner [3]. It was shown that by simply dividing nodes into two classes with one transmitting at high power level and the other transmitting at low power level, the throughput of a slotted ALOHA can be increased from 0.368 to about 0.53. Later on, [5] [6] proposed to let each node transmit with different powers from a set of pre-selected power levels according to a given probability distribution, to avoid the unfair treatment in [3] of the class of nodes that were assigned lower power level. A detailed work in formulating the throughput optimization problem was done in [4]. The authors of [4] studied a finite number of nodes in a slotted ALOHA system, where each node randomly chooses one of the power levels during each access attempt. The optimal probability for choosing each power level was presented in a recursive form, and the values of power levels to maximize the throughput were also discussed. In addition, the maximum throughput derived under a saturation assumption (i.e., nodes always have packets whenever they take an access attempt) was shown to be the same as Metzner's result from a Poisson traffic model.