Equalization and Decoding for Multiple-Input Multiple-Output Wireless Channels
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Equalization and Decoding for Multiple-Input Multiple-Output Wireless Channels Bjørn A. Bjerke Qualcomm, Inc., 9 Damonmill Square, Suite 2A, Concord, MA 01742, USA Email: [email protected]
John G. Proakis Department of Electrical and Computer Engineering, Northeastern University, 360 Huntington Avenue, Boston, MA 02115, USA Email: [email protected] Received 31 May 2001 and in revised form 11 January 2002 We consider multiple-input multiple-output (MIMO) wireless communication systems that employ multiple transmit and receive antennas to increase the data rate and achieve diversity in fading multipath channels. We begin by focusing on an uncoded system and define optimal and suboptimal receiver structures for this system in Rayleigh fading with and without intersymbol interference. Next, we consider coded MIMO systems. We view the coded system as a serially concatenated convolutional code (SCCC) in which the code and the multipath channel take on the roles of constituent codes. This enables us to analyze the performance using the same performance analysis tools as developed previously for SCCCs. Finally, we present an iterative (“turbo”) MAPbased equalization and decoding scheme and evaluate its performance when applied to a system with N transmit antennas and M receive antennas. We show that by performing recursive precoding prior to transmission, significant interleaving gains can be realized compared to systems without precoding. Keywords and phrases: MIMO systems, multiple antennas, fading channels, MLSE, linear equalization, DFE, MRC, union bound, turbo equalization.
1.
INTRODUCTION
Recently, multiple-input multiple-output (MIMO) wireless systems have attracted considerable attention in the communications community. Such systems employ multiple antennas, or antenna arrays, at both the transmitter and the receiver to enable spatial multiplexing of data and, thus, increased data rates. Traditionally, multiple antennas have been used at the receiver to provide spatial diversity and mitigate the effects of signal fading due to multipath propagation in the channel. However, recent developments in information theory have shown that by using multiple transmit and receive antennas, signal fading can in fact be turned into an advantage. With multiple antennas at both the transmitter and the receiver, spatially distributed channels can be supported simultaneously in the same frequency band, and by transmitting data in parallel through these channels the data rate can be increased. When deployed in a rich scattering environment, such systems are capable of greatly increasing the spectral efficiency over traditional single channel systems. Foschini and Gans [1] showed that the capacity of the flat MIMO Rayleigh fading channel associated with a system
with N transmit antennas and M ≥ N receive antennas is given as
C = log2 det IM + ρHH
bit/s/Hz,
(1)
where IM is the M × M identity matrix, ρ is the signal-to-noise ratio (SNR), and H is the M ×N matrix whose elements {hnm } represent the channel gains between pa
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