88 IEEE COMMUNICATIONS LETTERS, VOL. 3, NO. 4, APRIL 1999 Performance of Multi-Beam CDMA-Based LEO Satellite Systems in a Rice-Lognormal Channel Hongyi Fu, Guoan Bi, Member, IEEE, and K. Arichandran, Senior Member, IEEE Abstract— The performance of multi-beam code-division multiple-access (CDMA)-based low earth orbit (LEO) systems with convolutional coding and soft decision Viterbi decoding is analyzed. The multiple access interference due to all visible interferers of the given satellite is taken into account. The results show that the interference coming from the users located outside the footprint but still seen by the given satellite has a nontrivial effect on the system capacity. The multiple access interference, though, can be reduced by increasing the elevation restraint of each satellite footprint. Estimates on this reduction are given. Index Terms— Bit error rate, code-division multiple access, multiple-access interference, satellite communication. I. INTRODUCTION I N CODE-DIVISION multiple-access (CDMA) based low earth orbit (LEO) satellite systems for provision of personal communication services (PCN’s), the uplink performance is mainly limited by multiple access interference (MAI). It becomes essential to include all possible MAI in the system performance analysis. However, only part of all possible MAI was taken into account in previous studies to analyze the bit error rate (BER) of the CDMA system in a satellite channel. The case of a single spot beam was analyzed by Monk and Milstein [1] and the MAI due to all interferers within a satellite’s footprint was given consideration by Vojcic et al. [2]. For a realistic system, in order to get a satisfactory link performance, the elevation restraint, i.e., the minimum elevation angle of the service area, of a satellite is usually greater than 0 . Some users located outside the footprint are still visible to the given satellite. Such users contribute to the MAI and this causes additional degradation of the system performance. Although in [3] a stochastic model for the location of users as to whether they were either inside or outside the footprint of the given satellite was proposed, the emphasis was put on the effect of traffic nonuniformity on the throughput performance of a single-beam LEO system. Also the impact of the variability of the satellite antenna radiation pattern on MAI was not considered in the above studies. In this paper, a practical satellite antenna radiation pattern is taken into account. We calculate the effect of MAI from interferers both inside and outside the footprint of a satellite Manuscript received February 5, 1998. The associate editor coordinating the review of this letter and approving it for publication was Prof. A. K. Elhakeem. H. Fu is with the Center for Wireless Communications, National University of Singapore, Singapore Science Park II, Singapore 117674. G. Bi and K. Arichandran are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798. Publisher Item Identifier S 1089-7798(99)04258-1. Fig. 1. Coverage area of the given satellite. and analyze the BER with convolutional coding and soft decision Viterbi decoding of a DS-CDMA system with BPSK modulation over a Rice-Lognormal (RLN) channel. II. SYSTEM MODEL We divide the coverage area of the given satellite into three parts, as shown in Fig. 1. The first part is the region denoting the desired spot beam. The second part is the region inside the footprint but outside the desired spot beam. The third part is the region outside the footprint but still seen by the given satellite. The users in and are accessible by the given satellite. While a user in will be served by an adjacent satellite with the highest elevation angle relative to the user. The RLN channel model can be interpreted as the product of independent Rice fast fading and Lognormal shadowing [4]. We assume that each satellite provides perfect power control to the users located within its footprint and the power control algorithm is fast enough to track power variations associated with path loss and shadowing. Then, taking account of the interference from all visible users, the test statistic for user #1 at the given satellite is (1) where is the unfaded amplitude of the received signal, denotes the independent Rice fading, is the bit duration, is the current data bit detected, denotes the random 1089–7798/99$10.00  1999 IEEE