MIMO Decorrelating Discrete-Time RAKE Receiver Tunc ¸er Baykas ¸ School of Information Technology and Engineering University of Ottawa Ottawa, Canada tbaykas@site.uottawa.ca Mohamed Siala SUP’COM Cit´ e Technologique des Communications Ariana, Tunisia mohamed.siala@supcom.rnu.tn Abbas Yongac ¸o¯ glu School of Information Technology and Engineering University of Ottawa Ottawa, Canada yongacog@site.uottawa.ca Abstract—In this paper, we introduce a decorrelating discrete- time RAKE receiver for MIMO systems. Conventional RAKE receivers require acquisition and tracking systems to detect new paths and to follow them. To avoid this requirement a discrete- time RAKE receiver (DTR) has been proposed, which is obtained by sampling the received signal at twice the chip rate. The DTR works well in both specular and diffuse multipath channels. A drawback of the DTR is its sensitivity to channel estimation errors. To eliminate this weakness an optimum combining tech- nique has been introduced, called the decorrelating discrete-time RAKE receiver (D-DTR). The D-DTR exploits the covariance matrix of the discrete-time channel for a better robustness against channel estimation errors. In this paper, we extend this system to the MIMO case. Our simulations show that gains up to 2 dB are available in 2 transmit 2 receive antenna and 3 transmit 3 receive antenna systems at a bit error rate of 10 -2 . I. I NTRODUCTION Conventional RAKE receivers are used in DS-CDMA sys- tems to collect energy from multipath channels. A RAKE receiver can be seen as a filter matched to the spreading code, pulse shaping filter and multipath channel. A conventional RAKE receiver is a combination of a specified number of elementary receivers called RAKE fingers. Each finger is associated with one of the multipath signals. The outputs of the RAKE fingers are combined to detect the transmitted symbols. A RAKE receiver uses an acquisition system (or searcher) to detect new paths with significant power, and a tracking system to follow the continuously time-varying delays of the existing paths [1], [2]. The acquisition and tracking systems have two main weaknesses. First, the assumption that the multipaths are discernable is often unrealistic [2]. Additionally, the acquisition and tracking systems can neither distinguish nor follow paths separated less then a chip period apart [3], [4]. A RAKE reception system, the discrete-time RAKE receiver (DTR), without complex acquisition and tracking devices is obtained by sampling a transmit filtered version of the channel impulse response, has been proposed in [5]. The main weakness of the DTR is its sensitivity to channel estimation errors. Furthermore some paths taken into consideration are mainly due to noise and they reduce the overall performance of the DTR. Several intuitive methods have been presented in [5] to overcome these flaws. Whereas the derivation of an optimum structure for the discrete-time RAKE receiver, complying with the maximum a posteriori (MAP) criterion, has been made in [2]. The decorrelating discrete-time RAKE (D-DTR) exploits the covariance matrix of the channel values at the RAKE fingers to decorrelate channels and to find the optimum combining weights. From this point on we will refer to the conventional DTR as C-DTR to emphasize the distinction between the receivers. MIMO (multi input multi output) systems, which employ more than 1 transmit and 1 receive antennas, have become popular in wireless communication standards because of their high capacity. In this work, we extend the decorrelating discrete-time RAKE to MIMO systems. The simulations show that gains up to 2 dB are available in 2 transmit 2 receive antenna and 3 transmit 3 receive antenna systems at a bit error rate of 10 -2 . The outline of the paper is as follows. In the next section we explain the system model and the C-DTR and the D-DTR for single antenna systems. Afterwards we show how to extend the D-DTR to the MIMO D-DTR. Section 4 presents the simulation results. We finish the paper with the conclusions and comments on future research. II. SYSTEM MODEL AND DISCRETE-TIME RAKE RECEIVERS In this section we explain the C-DTR and the D-DTR using a basic DS-CDMA transmitter model as shown in Figure 1. The symbol s k is spread using a long spreading code c k . We assume that the code c k has the perfect correlation property to eliminate the interchip interference. The spread symbol is convolved with a pulse shaping filter with impulse response g(τ ) and transmitted through the channel. Throughout this paper we assume that the modulation scheme is BPSK. The channel is a quasi-static diffuse multipath Rayleigh fading channel. The channel impulse response changes inde- pendently from one realization to another, but the multipath intensity profile of the channel does not change. Assuming the impulse response of the channel to be h(τ ), the received signal r(t) for the symbol s k can be written as 0-7803-8887-9/05/$20.00 (c)2005 IEEE