Miso Time Reversal and Time Compression

This paper illustrates that the application of the time reversal technique in multiple inputsingle output (MISO) communications systems can effectively limit the perceived delay spread of the channel. Fixed wireless access channels in the 5GHz band have been measured with 8 element uniform linear antenna arrays at both ends, thus providing an 8x8 MIMO configuration. The measurements were performed at 3 different locations in downtown Toronto. The measurements show that the application of the time reversal technique can reduce the delay spread of the channel impulse response by a factor of 2. INTRODUCTION Fixed wireless access (FWA) is an alternative to cable connections in places where fiber has not yet been deployed, or where very fast deployment or capacity upgrade is desired. Wireless optics provides coverage in line-of-sight (LOS) conditions, but in the more obstructed non-LOS case wireless radio connections have to be employed. In North America the UNII band is license free for FWA applications. The modem designs that are suitable for secure and reliable high data rate operation depend on the characteristics of the radio channel. The delay spread of the channel limits the allowable data rates, as has been shown in Chuang [1]. OFDM and equalization techniques have been proposed as strong contenders to counteract the effects of frequency selective fading. However such advanced modulation/ demodulation schemes come at the cost of hardware design and power consumption, and require accuracy in the knowledge of the channel and the operation of the local oscillators. It would be desirable to build a system that is less sensitive to such effects, while keeping the cost of the receiver units low. In this paper we present a scheme that is based on the concept of time-reversal. While operable in wideband environments, this technique removes the complexity from the receiver and requires only a more complicated transmitter instead. TIME REVERSAL PRINCIPLES Throughout this paper we discuss the complex base-band representation of the signals and assume that perfect sampling, filtering and down-conversion have been performed. For the purpose of our analysis we neglect the time variation of the channel. This simplification is reasonable fixed wireless access (FWA) situations, where the channel stays relatively constant. If the channel impulse response between the transmitter and the receiver is a function h( ) of the delay , the delay spread is given as the second moment of the average power delay profile pdph (averaged over the channel realizations) d pdp pdp d pdp pdp h pdp h h h h h h 2 2 2 2 2 2 2 1 , 1 , E ) ( (1) where 2 denotes the Frobenius norm of the argument (in our case d 2 2 ). The configuration of the proposed MISO system is shown in Fig. 1, where there are M transmit antennas and the intended receiver has one receive antenna. Let x(t) represent the data stream destined for intended user. If the signal x(t) goes through a filter gm(t) before it gets transmitted from antenna m, the signal sm(t) that is transmitted from antenna m can be written as t x t g t s m m . Let the filter gm be given by the time reversed version of the channel impulse response between antenna m and the intended receiver hm, i.e. let t h A t g m m m * , as in Fink [2]. This technique has also been proposed in the context of CDMA systems, where it is referred to as a pre-rake combiner (Choi et al [3] among others). The scaling factor Am describes various power allocation situations. The implicit assumption is that the transmitters have channel state information (CSI). This can be obtained via channel estimation on the uplink, or feedback of CSI from the intended receiver. The performance of such systems is inherently limited by the rate of change of the channel. For the purpose of demonstration of