2005 Conference on Information Sciences and Systems, The Johns Hopkins University, March 16–18, 2005 Greedy Interference Avoidance in Non-Collaborative Multi-Base Wireless Systems Otilia Popescu WINLAB Rutgers University 73 Brett Road Piscataway, NJ 08854-8060 otilia@winlab.rutgers.edu Dimitrie C. Popescu Dept. of Electrical Engineering University of Texas at San Antonio 6900 N Loop 1604 W San Antonio, TX 78249-0669 dimitrie.popescu@utsa.edu Christopher Rose WINLAB Rutgers University 73 Brett Road Piscataway, NJ 08854-8060 crose@winlab.rutgers.edu Abstract — In this paper we present application of greedy interference avoidance to wireless systems with multiple bases which do not collaborate or ex- change information. We start with a simple system consisting of two users and two base stations for which we formally state a greedy interference avoidance al- gorithm and show that its application converges to a simultaneous water filling solution which is also a Nash equilibrium point for the system. We discuss generalization of the algorithm to systems with more than two user-base pairs which do not collaborate, and present also numerical results obtained from sim- ulations. I. Introduction Interference avoidance has emerged in the literature as a method for distributed codeword adaptation in CDMA sys- tems. Introduced originally in the context of a single cell CDMA system with MMSE receivers [2, 27] MMSE interfer- ence avoidance was followed by greedy interference avoidance which uses matched filter receivers and a minimum eigenvec- tor approach [21, 22]. For a single cell system interference avoidance was subsequently extended to incorporate non-ideal channels between users and the base station [6, 12, 13]. In a single cell system all users communicate with a sin- gle base station which knows codewords for all users in the system and uses them to decode the transmitted information symbols. In general, wireless systems consist of a collection of users and base stations dispersed over a given geographical area, in which individual users are interested in sending infor- mation only to a particular base station and each base cares only about decoding the users assigned to it. For wireless sys- tems with multiple base stations interference avoidance was also applied in a collaborative scenario which assumes that information received at all bases is collectively available for decoding [15–17]. Under this scenario the system under con- sideration can be regarded as a system with multiple inputs and multiple outputs (MIMO), and application of greedy in- terference avoidance in this scenario leads to a social optimum corresponding to maximum sum capacity. When no collaboration among base stations operation is as- sumed, a given user is decoded at its associated base under in- terference from transmissions by other users intended for other bases. In the most general case, with Gaussian channels and multiple transmitters and receivers such systems are instances This work was supported in part by NSF grants CCR-0205362 and CCR-0312323. of the general interference channel, which is still an open re- search problem [8, p. 382]. We note that the interference channel problem was formulated originally by Shannon [26] and main results on capacity for the interference channel were established by Ahlswede [1], Carleial [3–5], Sato [23–25], Han and Kobayashi [10], and Costa [7]. We also note that an infor- mation theoretic approach to the interference channel problem is beyond the scope of this paper, and we make no attempt to address capacity issues for the interference channel here. Rather, our work is along the line of more recent work by Yu [28] which proposes a distributed iterative algorithm for performance optimization in a Gaussian interference channel scenario, and in this paper we present application of greedy in- terference avoidance methods to non-collaborative multi-base wireless systems. We start with a simple system consisting of two bases, each base having only one user associated with it, which is depicted in Figure 1, and which is similar to the one considered by Yu [28]. However, unlike Yu [28] we explic- 1 1 B 2 B 1 U 1 U 2 g g 1 2 Figure 1: A system with two transmitters and two re- ceivers. itly assume that users transmit information using a multicode CDMA approach for which we plan to apply greedy interfer- ence avoidance to adaptation of user codewords. In this paper we present an iterative algorithm for codeword optimization for the two user-base system which is based on greedy inter- ference avoidance. We look at fixed-point properties of the proposed algorithm and discuss extensions to systems with more than two user-base pairs. II. System Description and the Greedy Interference Avoidance Algorithm For the non-collaborative system with two users and two base stations in Figure 1 we assume an arbitrary signal space repre- sentation 1 of dimension N , in which during each signaling in- terval users transmit frames of data using a multicode CDMA approach described schematically in Figure 2. Thus, each user 1 Implied by finite bandwidth and finite signaling interval con- straints [11].