{'fraction_non_alphanumeric': 0.02110022607385079, 'fraction_numerical': 0.0, 'mean_word_length': 5.541871921182266, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Enhanced Partial Update Beamforming for Closed Loop MIMO Systems

This work proposes a novel adaptive transmit beamforming algorithm, suitable for single-beam multiple-input multiple-output (MIMO) systems employing closed-loop feedback channels with low rate. A low computational complexity solution is achieved by means of a partial update strategy, in which only one of the complex baseband weights of the transmit antenna array is modified at each instance. The new algorithm can operate sequentially over the antennas, or employ a signal-dependent criterion that determines which antenna coefficient to update. The solution for the weight under consideration maximizes the signal-to-noise ratio at the receiver, given the current channel state and beamforming weights. Simulations show that the proposed algorithm reaches near optimal bit error probability (BEP) performance in low mobility scenarios, and offers advantages over non-recursive codebook solutions on a wide range of fading rates. The formulas presented in this paper specialize to a new solution in the single receive antenna multiple-input single-output (MISO) case, which allows an intuitive geometrical interpretation. The new MISO formulation is shown to outperform a recently proposed partial update beamforming scheme for single receive antenna systems