Joint Time and Frequency Synchronization in Halved Phase-Only MIMO

Halved phase-only multiple input multiple output (HPOMIMO) completes wireless transmission based on π-periodic phase measurements, which are directly acquired by phase detectors at the base station. However, existing synchronization algorithms for MIMO can no longer be applied into HPO-MIMO, because they work under complete measurements with both magnitude and phase information but HPO-MIMO loses magnitude information completely. This correspondence paper proposes a joint time and frequency synchronization algorithm for HPO-MIMO, which exploits the repeatability of a pilot preamble. Starting-time and carrier frequency offset (CFO) are jointly estimated under a grid-searching manner. At first, continuous starting-time and CFO estimation are uniformly sampled from their potential value ranges. On all potential startingtime points, the received phase measurements are uniformly sliced according to the repetition structure of the preamble, and then the phase rotations due to CFO are removed based on each potential CFO value. The shifted phase measurements would show strong similarities if CFO is successfully compensated. The similarities among these sliced phase sequences are characterized by a metric named phase sequence distance (PSD). They are summed up as a final PSD, whose minimum value corresponds to the estimated starting time and CFO. Simulation results validate the effectiveness of the synchronization algorithm under different signalto-noise ratios and lengths of preamble. HPO-MIMO with our synchronization algorithm can even perform similarly as its perfect-synchronized correspondence.