Low-Complexity Multi-Stream Space-Time Codes—Part I: Direct-Sum Codes and Design Criteria

Multi-stream codes are used in wireless broadcast services where two or more priority classes of data are transmitted simultaneously, and a receiving terminal may decode one or more of the streams as a function of its receive signal to noise ratio. Present-day commercial cellular-based broadcast services generally utilize hierarchical modulation, a clever technique for embedding high and low-priority streams in a single modulated quadrature symbol. With many cellular standards moving to multiple-transmit antenna configurations, there are opportunities for designing new multi-stream encoding techniques that exploit these antennas. We examine the design of space-time codes that allow simple encoding and decoding of high and low-priority streams of data. A desirable multi-stream space-time code has a combination of good performance and low complexity. Performance is generally measured as coded bit-error rate, assuming max-log maximum aposteriori decoding. Complexity is measured as the effort needed to compute the aposteriori probabilities for either stream. Hierarchical modulation, for single-antenna transmissions, allows each stream to be decoded simply and independently. The paper comprises two parts. In this first part, we establish a general performance criterion for two-stream space-time codes and derive a formula for the complexity of max-log maximum aposteriori decoding of either stream. We also show how existing space-time codes may be combined with hierarchical modulation in a "direct sum". The direct-sum codes have low complexity, but we show in the second part of this paper that these codes can be significantly outperformed by non-direct-sum codes. One of our proposed two-stream codes performs 4 dB better than the Alamouti direct-sum code; it also has the benefit of decoding complexity in one stream that is a bounded function of the rate of the other.