Int. J. Electron. Commun. (AEÜ) 68 (2014) 79–83 Contents lists available at ScienceDirect International Journal of Electronics and Communications (AEÜ) jo ur nal ho me page: www.elsevier.com/locate/aeue Effects of spatial receiver distributions on the user capacity of broadcast channels Jalil Etminan, Hengameh Keshavarz ∗ Department of Communications Engineering, University of Sistan and Baluchestan, Iran a r t i c l e i n f o Article history: Received 7 April 2013 Accepted 12 September 2013 Keywords: User capacity Path loss Broadcast channels Power allocation Minimum-rate constraint a b s t r a c t In this paper, a broadcast channel is considered in which receivers are randomly distributed on the plane. It is assumed that the x and y coordinates of receivers positions are Gaussian-distributed ran- dom variables with the same variance. Hence, the distance between each transmitter–receiver pair and consequently, the path loss term is random. It is shown that as the total number of receivers, n, in the broadcast channel goes to infinity, the maximum number of active receivers (i.e. user capacity) scales with (˛/R min ) ln (b n) where b = (R min P 1/˛ )/(˛  2 ). Convergence of numerical results to the theoretical bounds in practical situations and the user capacity dependency on system parameters are shown in simulations results. © 2013 Elsevier GmbH. All rights reserved. 1. Introduction In wireless networks, nodes are usually mobile and conse- quently, the distance between any transmitter–receiver pair and the path-loss term are time-varying. Due to the time-varying nature of fading channels, it is assumed that the users’ channels are ran- dom over different time periods. To analyze asymptotically the throughput and the user capacity (i.e. the maximum number of users that can be activated simultaneously), fading channels statis- tics are required. As the channel states become time-varying, opportunistic power allocation must optimally be performed to use system resources efficiently. In delay-sensitive applications, each user’s transmission rate cannot be less than a threshold. Hence, a power allocation scheme with a minimum-rate constraint is herein con- sidered for the receivers in the broadcast channel. As it is not always possible for all receivers to maintain this minimum rate, there is a trade-off between the total throughput and the maxi- mum number of receivers supporting the minimum rate. To achieve the maximum total throughput, transmit power is only allocated to the receiver with the best channel gain; however, to activate more receivers, transmit power is allocated to users that can sup- port the minimum rate and then, extra power is allocated to the receiver with the best channel gain in order to obtain a higher total throughput. ∗ Corresponding author. Tel.: +98 915 194 9957. E-mail addresses: keshavarz@ece.usb.ac.ir, hkeshavarz@ieee.org (H. Keshavarz). The user capacity of cellular networks in the uplink and down- link with different assumptions has been investigated in the literature. In [1], the uplink of a code-division multiple access (CDMA) cell implementing successive interference cancellation (SIC) receivers with soft decision is considered. Then, the capac- ity and the asymptotic user capacity (the limit when spreading gains tend to infinity with the constraint of finite system load) is obtained. In [2], the downlink user capacity of dirty paper coding (DPC) and time-division multiple access (TDMA) is compared in a single cell of a cellular network with single antennas at the trans- mitter and each of the receivers. Their results have been shown that TDMA may be an attractive alternative to DPC because of the complexity of the latter. In [3], the single-channel user-capacity is determined for infinite linear and planar arrays of microcells using a very idealized environment, then the best and worst capac- ities is computed as well as the capacity achieved by random channel placement. In [4], the user capacity of the uplink of a mul- tiple cell synchronous CDMA system is analyzed along with power and channel allocation. For the most part, attention is focused on the situation when the signature sequences are chosen from an orthogonal sequence set. In [5], the user capacity supportable on the uplink of a multiple-macrocell CDMA system with multiple “hotspot” micro-cells embedded within is studied. It is shown that the user capacity depends on how the users are distributed among cells, and that the maximum (called the attainable capacity) occurs when all cells serve roughly the same number of users. In [6], both the uplink and downlink of a synchronous CDMA (S-CDMA) system with single cell are considered and the user capacity of a single cell with the optimal linear receiver is characterized. Finally, a power allocation scheme has been proposed in [7,8] to maxi- mize the number of active users, for each of which, a minimum 1434-8411/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.aeue.2013.09.002