Spatial Block Codes Based on Unitary Transformations Derived from Orthonormal Polynomial Sets
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Spatial Block Codes Based on Unitary Transformations Derived from Orthonormal Polynomial Sets Giridhar D. Mandyam Nokia Research Center, 6000 Connection Drive, Irving, TX 75039, USA Email: [email protected] Received 1 September 2001 and in revised form 15 March 2002 Recent work in the development of diversity transformations for wireless systems has produced a theoretical framework for spacetime block codes. Such codes are beneficial in that they may be easily concatenated with interleaved d trellis codes and yet still may be decoded separately. In this paper, a theoretical framework is provided for the generation of spatial block codes of arbitrary dimensionality through the use of orthonormal polynomial sets. While these codes cannot maximize theoretical diversity performance for given dimensionality, they still provide performance improvements over the single-antenna case. In particular, their application to closed-loop transmit diversity systems is proposed, as the bandwidth necessary for feedback using these types of codes is fixed regardless of the number of antennas used. Simulation data is provided demonstrating these types of codes’ performance under this implementation as compared not only to the single-antenna case but also to the two-antenna code derived from the Radon-Hurwitz construction. Keywords and phrases: spatial block codes, closed-loop transmit diversity, space-time codes.
1. INTRODUCTION In wireless communications systems, fading transmission channels are problematic due to the fact that fading channels are nonstationary, and therefore the design of effective channel codes based on assumed channel statistics becomes difficult. As a result, diversity is essential for addressing the problem of fading in wireless channels. Diversity essentially entails receiving several replicas of the same signal over independently fading channels [1]. Diversity may take many approaches. For instance, frequency diversity methods employ transmission of multiple symbol replicas over multiple carriers, each of the carriers separated in frequency by a sufficiently large amount to ensure independent fading. This approach is accompanied with the additional cost of increased complexity at the transmitter and receiver, along with the fact that it may be difficult to implement in bandwidthlimited systems (such as common public wireless systems that must conform to electromagnetic compatibility requirements). Temporal diversity entails transmission of signal replicas in different time slots, each slot sufficiently spaced in time to ensure independent fading. This approach suffers from reduced throughput due to multiple transmissions of the same symbol over time. Another instance of temporal diversity may be achieved in multipath channels where the signal bandwidth is larger than the coherence time of the channel; in this case the multipaths are resolvable and may be recovered by a rake receiver.
However, flat fading channels are troublesome for bandwidth-limited systems where neither frequency nor temporal diversity is poss
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