Rake receiver performance for CDMA downlink

Abstract

This paper presents a closed-form expression of the average SIR of the optimum CDMA downlink Rake receiver (1) for identically independently distributed (iid) Raleigh fading and a tight bound for the non-iid case. It shows that the average SIR decreases as the number of multipaths, L, increases and achieves its minimum when the channel multipath intensity profile (MIP) is constant. This paper also proves, both in theory and with simulations that the BER increases as L increases, and that it is a convex function of the multipath channel gains and achieves its maximum when the channel MIP is constant. In addition, this paper derives a decision threshold for MRC, which results in a non-optimum Rake, to determine if a multipath is to be combined without loss of SIR. In summary, this paper proves, against conventional wisdom, that a Rake receiver for the CDMA downlink does not achieve the Lth order diversity gain. In fact, its performance varies inversely to an Lth order diversity system, such as CDMA uplink. L MPI's. In this paper, we derive a closed form expression for the average SIR of the IMOC for iid Raleigh fading channels. This average SIR is found to be monotonically decreasing as L increases. For the non-iid Raleigh fading channels, we derive a lower bound for the SIR and this bound is tight when applied to the SIR for the iid case. The bound is also proved to be minimized when the channel MIP is constant. The paper shows both in theory and in simulations that BERs of both the IMOC and MRC obtain their maximum when the channel MIP is constant and increase as L increases. Therefore, the BER of a Rake receiver with either IMOC or MRC in the presence of MPI behaves in an opposite way to the BER with a diversity gain of order L where the BER decreases as L increases and obtains its minimum when the channel MIP is constant.