Diversity-Multiplexing Tradeoff in MIMO Systems Dan J. Dechene, Student Member, IEEE Department of Electrical and Computer Engineering The University of Western Ontario London, Ontario, N6A 5B9, Canada Email: ddechene@uwo.ca Abstract—It is well known that there exists a tradeoff between the diversity gain and the multiplexing gain achievable by a particular MIMO coding scheme. In this report we first look at the optimal trade-off in the infinite signal-to-noise (SNR) regime of both Rayleigh independent and identically distributed (i.i.d.) channels and a more general MIMO channel model. We then look at the tradeoff of both Space-Time Block Codes (such as Alamouti code) and BLAST Detection schemes. The effect of non-identically distributed and correlated channels is also briefly discussed. Finally, the diversity multiplexing (DIV-MUX) tradeoff is presented under the finite SNR regime. Index Terms—Diversity, Multiplexing, Space-Time Codes, MIMO, BLAST, Aloumouti I. I NTRODUCTION I N recent years, Multiple-Input, Multiple Output (MIMO) antenna systems have generated a great deal of attention from both the research and industry commu- nities. These systems have been shown [1] that they can improve system performance quite dramatically. To date researchers have utilized MIMO for both diversity ap- proaches to improve error performance [2] or to increase spectral efficiency via spatial multiplexing [3]. In initial research into MIMO systems, these schools of thought were segmented whereas a given scheme would attempt to either improve diversity or increase multiplexing but not both. In more recent works, researchers have focused examining the tradeoffs associated with diversity and multiplexing. The major pioneering work that studied these tradeoffs was by Zheng et. al [4] where the optimal diversity tradeoff in Rayleigh i.i.d. channels was studied. In this work we look at recent developments in the understanding of the diversity-multiplexing (DIV-MUX) tradeoff with a focus on the initial work by Zheng [4]. The remainder of this project is divided as follows. In the next section we describe a general MIMO system and define diversity gain and multiplexing gain in the context of MIMO systems. In Section III, we examine the optimal trade-off in both Rayleigh and more general 0 5 10 15 20 0 5 10 15 20 25 SNR (dB) Capacity (bps/Hz) Ergodic Capacity vs. SNR 1x1 SISO 2x2 MIMO 2x4 MIMO 4x2 MIMO 4x4 MIMO 8x8 MIMO Fig. 1: Ergodic Capacity of MIMO Channel without CSI, Rayleigh i.i.d. MIMO channels. In Section IV explores the DIV-MUX tradeoff achieved in real schemes as well as relaxing the high SNR assumption in Section V. Finally we draw some conclusions on the DIV-MUX tradeoffs and pro- pose some future directions for this work in Section VI. II. MIMO In general, we can represent a flat-fading multiple- input, multiple output (MIMO) antenna system with M T transmitter antennas and M R receiver antennas can be represented as [1] r(t)= H(t)s(t)+ n(t) (1) where r(t) is the M R × 1 receive vector, s(t) is the M T × 1 transmitter vector, H(t) is the M R × M T channel transfer matrix with entries h i,j (t) representing the transfer function from the j th transmitter antenna to the i th receiver antenna and n(t) as the M R × 1 additive noise vector with i.i.d. entries such that n(t) ∼ CN (0,N 0 I MR ). The strength of MIMO lies in the methods of pre and post-processing the transmitted and received vectors