Spatial Multiplexing and Diversity Gain in OFDM-Based MIMO Systems Haideh M. Karkhanechi & Bernard C. Levy Dept. of Electrical and Computer Engineering University of California Davis Davis, CA. 95616 Abstract--- Multiple transmit and receive antennas can be used with orthogonal frequency division multiplexing to improve performance and transmission rate. In this paper we investigate trade offs between different techniques in broadband OFDM- based MIMO systems for achieving full diversity or maximum spatial multiplexing gain. The basic model of OFDM-based spa- tial multiplexer is very suitable for high data rate transmission, and if combined with other techniques such as channel coding or space time coding can provide desired diversity and spatial multiplexing gain. I. INTRODUCTION In broadband environment combined orthogonal frequency division multiplexing (OFDM) and space time processing is an effective method to combat fading and achieve high data rate communication. In OFDM, using IFFT at the transmitter and FFT at the receiver, transforms the broadband frequency selective channel into a set of ISI-free narrow-band subchan- nels, so that each subchannel can be easily equalized at the receiver. To avoid inter-symbol interference a cyclic prefix is added at the transmitter and removed at the receiver prior to detection. The main problem is that if a subcarrier falls in a deep fade or channel null, all the information carried by that subcarrier is affected and results in an error burst that greatly degrades the system performance. In order to deal with bad sub-carriers, techniques such as channel coding or changing subcarrier positions at the transmitter (requires CSI at the transmitter) can be used. Multicarrier space-time processing allows multi-transmit and multi-receive communication through multiple parallel sub-channels at high data rate that can provide diversity gain and spatial multiplexing gain. Space time block codes with two transmit antennas, or orthogonal codes for arbitrary num- ber of transmit antennas [1,2] achieve full diversity gain and linear low complexity decoding at the expense of lower transmission rate. Diversity gain is achieved by sending the same information through different paths, whereas spatial multiplexing gain is achieved when each transmit antenna, transmits different information that results in higher transmis- sion rate [4,6]. In a MIMO OFDM system, both diversity and spatial multiplexing gains can be achieved but a higher diver- sity gain is achievable at the expense of sacrificing the spatial multiplexing gain (lower transmission rate). In this paper we investigate different techniques for improving system per- formance that demonstrate trade-offs and differences between spatial-multiplexing gain and diversity gain. For simplicity simulations are done for (2,2) and (2,1) systems where the channel is assumed to be known at the receiver through OFDM training blocks [9]. II. OFDM-BASED MIMO SYSTEM WITH FULL SPATIAL MULTIPLEXING GAIN In this section we describe the system model of an OFDM based spatial multiplexer (OFDM-SM) for high data rate transmission, and deal with the problem of bad sub-carriers in order to improve system performance. A. SYSTEM MODEL We consider a (2,2) OFDM-SM, where each transmit an- tenna transmits different OFDM symbols. This system can achieve half diversity gain with full spatial multiplexing gain compared to SISO OFDM. The broadband fading channel is modeled as a tapped-delay-line (polynomial model) [8] be- tween transmit antenna i and receive antenna j with K taps, the channel impulse response can be written as: ∑ = - = K l s l ij ij T m t l t h 1 ) ( ) ( ) ( δ α (1) where ) (l ij α is the complex coefficient, with zero-mean Gaussian distribution, of the th l tap with integer delay l m and sampling period of T s . After matched filtering (raised- cosine) and sampling the channel is defined as sum of K con- volutions of the channel coefficients with the pulse shaping filter response: ∑ = - = K l s l ps ij ij T m n f l n g 1 ) ( ) ( ) ( α (2) At the transmitter the incoming bit-stream goes through a serial to parallel demux and is divided to M sub-streams. Each sub-stream goes through an OFDM modulator to make M OFDM symbols. In each sub-stream after mapping, modu- lating and taking N-point IFFT, a cyclic prefix is prepended (copy of at least K samples) to each OFDM symbol to avoid ISI due to channel delay spread. The received signal is the superposition of all M transmitted OFDM blocks going through channel plus noise. At the receiver detection is done after the OFDM demodulator removes the cyclic prefix and performs FFT. The detection is done at each subcarrier by a simple one-tap matrix equalizer. 0-7803-8197-1/03/$17.00 (c)2003 IEEE