{'fraction_non_alphanumeric': 0.011579818031430935, 'fraction_numerical': 0.0, 'mean_word_length': 5.1421319796954315, '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}}
On the throughput of proportional fair scheduling with opportunistic beamforming for continuous fading states [cellular wireless systems]

We examine the throughput of an opportunistic beamforming system with proportional fair scheduling and show for normally distributed channel fading states that for large numbers of users the average throughput of each user multiplied by the number of users approaches the maximum possible throughput of this user achievable by coherent beamforming, if round robin scheduling was used. Thus, we extend a proof by Viswanath et al. who showed this for discrete fading states. We give the average SNR of the scheduled user (averaged across the fading states) in closed form and the average throughput in the form of an integral as a function of the number of transmit antennas and users. Simulations of this system confirm the analytical results. Finally, we show that for a large number of transmit antennas, the probability density function of the SNR of the scheduled user and therefore also the throughput asymptotically approach those of a system with a max SNR scheduler that always transmits to the user having the largest SNR and thus maximizes the total throughput.