On the Capacity of Certain Space-Time Coding Schemes
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On the Capacity of Certain Space-Time Coding Schemes Constantinos B. Papadias Global Wireless Systems Research Department, Bell Laboratories, Lucent Technologies, 791 Holmdel-Keyport Road, Holmdel, NJ 07733, USA Email: [email protected]
Gerard J. Foschini Wireless Communications Research Department, Bell Laboratories, Lucent Technologies, 791 Holmdel-Keyport Road, Holmdel, NJ 07733, USA Email: [email protected] Received 30 May 2001 and in revised form 22 February 2002 We take a capacity view of a number of different space-time coding (STC) schemes. While the Shannon capacity of multipleinput multiple-output (MIMO) channels has been known for a number of years now, the attainment of these capacities remains a challenging issue in many cases. The introduction of space-time coding schemes in the last 2–3 years has, however, begun paving the way towards the attainment of the promised capacities. In this work we attempt to describe what are the attainable information rates of certain STC schemes, by quantifying their inherent capacity penalties. The obtained results, which are validated for a number of typical cases, cast some interesting light on the merits and tradeoffs of different techniques. Further, they point to future work needed in bridging the gap between the theoretically expected capacities and the performance of practical systems. Keywords and phrases: MIMO systems, space-time coding, Bell labs Layered Space Time (BLAST), space-time spreading (STS), channel capacity, space-time processing (STP), transmit diversity.
1.
INTRODUCTION
The combined use of antenna arrays and sophisticated multiple-input multiple-output (MIMO) transceiver techniques has boosted the anticipated spectral efficiencies of wireless links in the last five years or so. The MIMO channel capacity expressions derived in [1] indicate that the spectral efficiencies of MIMO channels can grow approximately linearly with the (minimum of the) number of antennas available on each side of the link. Similar to the case of single-input single-output (SISO) channels, the attainment of the theoretically promised capacities in practice, has to rely on strong encoding/decoding techniques. In the SISO case, it took about fifty years to approach closely (with the advent of Turbo codes [2]) the channel capacities predicted by Shannon [3]. In the MIMO case, an initial (the so-called D-BLAST) architectural superstructure was proposed in [1] that is theoretically capable of achieving the channel capacity. The quest for practical capacity-approaching STC techniques is however ongoing. Interestingly, it seems that some existing STC techniques [4, 5], already allow to approach closely the channel capacities in a number of cases [6, 7]. These quite rapid advancements are of course not unrelated to the mature state of SISO encoding/decoding techniques. At the same time, there still
exist many cases of interest, where more research is needed in order to approach the capacities of MIMO systems in practice. In this paper, we will attempt to quantify the performance of cert
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