Randomized Space-Time Block Coding for the Multiple-Relay Channel

In the last decade, cooperation among multiple terminals has been seen as one of the more promising strategies to improve transmission speed in wireless communications networks. Basically, the idea is to mimic an antenna array and apply distributed versions of well-known space-diversity techniques. In this context, the simplest cooperative scheme is the relay channel: all the terminals (relays) that overhear a point-to-point communication between a source and a destination may decide to aid the source by forwarding (relaying) its message. In a mobile system, it is common to assume that the relays do not have any information about the channel between them and the destination. Under this hypothesis, the best solution to exploit the diversity offered by multiple transmitting antennas is to use space-time coding (STC). However, classical STC’s are designed for systems with a fixed and usually low number of antennas. Thus, they are not suitable for relaying in most mobile communications systems where the number of terminals is potentially large and may vary as users join or leave the network. For each new configuration, a new code has to be chosen and notified to the relays, introducing a set-up overhead of signaling traffic. In this dissertation we will propose and analyze a randomized distributed linear-dispersion space-time block code (LD-STBC): each relay is assigned a specific matrix which linearly transforms (left-multiplies) the column vector of source symbols. Each matrix is independently generated and does not depend on the total number of transmitters, which can thus change without interrupting data transmission for a new code-relay assignment. The more intuitive way to build independent linear-dispersion matrices is to fill them with independent and identically distributed (i.i.d.) random variables. Therefore, we will first consider these i.i.d. codes and characterize the resulting spectral efficiency. In order to analyze the performance achieved by the system, we consider a large-system analysis based on random matrix theory. We will show that the random spectral efficiency (function of the random linear-dispersion matrices) converges almost surely to a deterministic quantity when the dimensions of the code grow indefinitely while keeping constant the coding rate. Since convergence is very fast, the random spectral efficiency will be approximated by the deterministic limit in the subsequent analysis. By comparison with the direct link, sufficient conditions are derived for the superiority of relaying. Next, we will analyze the outage probability of the system, that is the probability that the spectral efficiency falls below a given target rate due to channel fading. The main purpose of diversity techniques is to introduce alternative paths from the source to the destination, so that data transmission does not fail when the direct link undergoes deep fading. We will show that the diversity behavior of LD-STBC relaying mainly depends on both the coding rate and the relaying strategy (amplify and forward or decode and forward). It is then important to choose the coding rate that maximizes the diversity order without wasting too many resources. To conclude the dissertation, we will consider a different code based on independent isometric Haar-distributed random linear-dispersion matrices. The new code maintains the flexibility of the previous one with respect to variations in the number of relays. However, the more complex structure of the codes allows a noticeable reduction of the interference generated by the relays. Unfortunately, isometric codes also require more sophisticated mathematical tools for their asymptotic analysis. For this reason, we simply introduce the problem by showing that it is possible to have some spectral-efficiency gain with respect to i.i.d. codes. The outage-probability analysis requires a more thorough understanding and will be the subject of future work.