Space-Time Codes for Wireless Optical Communications
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Space-Time Codes for Wireless Optical Communications Shane M. Haas Laboratory for Information and Decisions Systems, and Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA Email: [email protected]
Jeffrey H. Shapiro Laboratory for Information and Decisions Systems, and Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA Email: [email protected]
Vahid Tarokh Laboratory for Information and Decisions Systems, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA Email: [email protected] Received 1 June 2001 A space-time channel coding technique is presented for overcoming turbulence-induced fading in an atmospheric optical heterodyne communication system that uses multiple transmit and receive apertures. In particular, a design criterion for minimizing the pairwise probability of codeword error in a space-time code (STC) is developed from a central limit theorem approximation. This design criterion maximizes the mean-to-standard-deviation ratio of the received energy difference between codewords. It leads to STCs that are a subset of the previously reported STCs for Rayleigh channels, namely those created from orthogonal designs. This approach also extends to other fading channels with independent, zero-mean path gains. Consequently, for large numbers of transmit and receive antennas, STCs created from orthogonal designs minimize the pairwise codeword error probability for this larger class of fading channels. Keywords and phrases: space-time codes, optical communication, orthogonal designs.
1.
INTRODUCTION
In atmospheric optical communication, lognormal fading arising from refractive-index turbulence can make the recovery of a transmitted signal extremely difficult at the receiver. As a result, the receiver must have a redundant replica of the transmitted signal for reliable communication. Space-time codes (STCs) provide both spatial and temporal redundancy, or diversity, by using multiple apertures (antennas) over several time-slots. Tarokh et al., in [1], established space-time code design criteria for Rayleigh and Ricean fading channels. These design criteria specify the pairwise properties of codewords from the STC. In this paper, we derive a similar design criterion for the lognormal fading channel based on a central limit theorem approximation. Our criterion leads to STCs created from orthogonal designs, a subset of the previously reported STCs for Rayleigh channels. Tarokh et al., in [2], showed that such codes have a decoding algorithm requiring only linear processing at the receiver. We show that these STCs also maximize the mean-to-standard-deviation ratio of
the received energy difference between codewords, a result analogous to maximal ratio combining. Our derivation extends to other fading channels with independent, zero-mean path gains. In other words, we show that for large numbers of transmit and receive antennas, STCs created from orth
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