Frequency-Offset Sensitivity of Resilient Microwave Links Applying the Alamouti Scheme

Space-time codes were designed for fading environments in order to improve system capacity and/or to achieve a diversity gain. In this paper, a novel possible application of the Alamouti space-time block code (STBC) for two transmit antennas is investigated, to provide a switchless alternative in current resilient microwave radio links. Resilient means that transmitter (Tx) and receiver (Rx) are each equipped with two complete, independent, parallel Tx/Rx chains and particularly with two antennas. Conventionally, only one Tx/Rx chain is active, while the other one is kept in a ‘hot-stand-by’ mode. In the proposed alternative system design based on the Alamouti STBC, both Tx antennas are utilized at the same time. Since the Alamouti STBC is backward compatible with the single transmit antenna system, one Tx chain may fail without causing a rate loss. However, a resilient Tx/Rx structure implies that two independent local oscillators are employed for up-conversion as well as for down-conversion, i.e., the local oscillators at each antenna may independently differ from the nominal carrier frequency. It is shown here that in this case the orthogonality of the Alamouti STBC is lost, even if the frequency offsets are perfectly known at the receiver. Analytical expressions for the bit error probability as a function of the frequency offsets are derived, and the performance loss occurring in the case of perfect and non-perfect knowledge of the frequency offsets at the receiver is illustrated on the basis of simulation results.