Interference diversity in frequency-hopped systems with soft decoding Kostas Stamatiou and John G. Proakis Department of Electrical & Computer Engineering University of California San Diego, La Jolla, CA 92093-0407 Email: kostas@ucsd.edu, jproakis@cwc.ucsd.edu Abstract—In this paper, we analyze the effect of interference diversity on the capacity of a cellular system that employs frequency hopping, power control and bit-interleaved coded modulation. Interference is created when the hopping patterns of adjacent cells intersect with the patterns of the cell of interest, with a probability that depends on the occupancy of each cell. However, due to frequency hopping and power control, the power of the interference varies randomly across the received symbols creating what is usually named in the literature as interference diversity. We explicitly take into account this randomness and, under a channel model that accounts for fading and path loss, analyze the performance of two receivers; a receiver that tracks the variations of the interference power across the received symbols and a receiver that remains oblivious to these variations. Our results demonstrate under what circumstances the additional complexity of tracking the interference power variations is justified. I. I NTRODUCTION Frequency hopping (FH) combined with coding is a widely used technique at the physical layer of cellular systems. Fre- quency diversity is attained, if the channel frequency response varies over the hopping distance. More importantly, the inter- cell interference is “spread over” different users and no user is subject to worst case interference conditions. This effect is usually called interference averaging (IA) and the variation of the interference power across the received coded symbols, interference diversity (ID). ID is the result of FH, since some time/frequency slots are interfered and some are not, depending on the system load. However, even in a fully loaded system, ID is present if the interfering users are power controlled. Knowledge of the interference power at each received symbol can improve the reliability of the respective decoder metric and thus the overall error performance. This is similar to exploiting channel state information in a single-user fading channel (coherent vs. non- coherent detection) or the knowledge of unreliable symbols in errors-and-erasures decoding of Reed-Solomon codes [1]. The effect of ID is qualitatively analyzed in [2]. A specific construction of patterns that achieves perfect IA is described in [3] and more recently in [4]. Other related work on the topic includes [5], [6]. This work was supported by Ericsson Grant 02-10109 and by UC Discovery Grant com04-10173. In this paper, we analyze the effect of ID on the capacity of a cellular system that employs FH, PC and bit-interleaved coded modulation (BICM). A channel model that includes the effects of fading and path-loss is assumed. The performance of two receivers is analytically evaluated; a receiver that tracks the interference power variations and one that doesn’t. Our main conclusion is that, under small long-term signal-to-interference (SIR) ratios, which correspond to the user being situated close to the boundary of its cell, increasing the decoding complexity albeit ignoring the interference variations results in a small performance improvement. In other words, trading decoding complexity with an interference tracking capability can be more beneficial in terms of the error rate performance. A variety of numerical results are presented which illustrate this point. The rest of the paper is structured as follows. In section II our system model is described. We proceed with the analysis in section III. Section IV includes the numerical results and section V concludes the paper. II. SYSTEM DESCRIPTION Consider the downlink of a synchronous cellular system which is slotted in time and frequency. For simplicity, assume there are only two circular cells with radius R 0 , a base-station B i ,i =0, 1, at their center and uniformly distributed users. A user in the cell of B 0 is taken as a reference (user of interest, UI), thus the signals transmitted by B 1 generate interference to the link B 0 -UI. The selection of the downlink direction for the evaluation of the performance is arbitrary. The analysis can also be carried out in the uplink, with the proper modifications in the distributions of the random variables involved. The bandwidth is divided into N flat-fading frequency bands or subcarriers (the term subcarriers is more appropriate in the context of a FH-OFDMA system, see [4], [7].) Each user is assigned a hopping pattern, which chooses a subcarrier in each time slot. We assume that the patterns within a cell are orthogonal, so that there is no intra-cell interference. However, if N 1 users are present in cell 1, then there is a probability of interference of any hopping pattern in that cell with the pattern assigned to UI, equal to p = N 1 /N . It is also assumed that, within the span of the error events in the decoder of UI, the interference is due to different users. In other words, we are studying a scenario of complete interference randomization. A