{'fraction_non_alphanumeric': 0.025518341307814992, 'fraction_numerical': 0.0, 'mean_word_length': 5.469072164948454, '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}}
Optimization of Power Allocation and Relay Placement for Decode-and-Forward ARQ Relaying

In this letter, we investigate the power allocation and relay placement for decode-and-forward (DF) automatic repeat request (ARQ) relaying over fast Rayleigh fading channels, where the channel gains are constant during each ARQ transmission round and change independently from round to round. Specifically, when the relay decodes correctly, the source and the relay send the Alamouti space-time block coded (STBC) signals to the destination. The maximum number of ARQ rounds is represented by L, and an outage event occurs when the destination decodes the packet unsuccessfully after L ARQ rounds. Based on these assumptions, we derive the asymptotically tight approximation of outage probability in the high signal-to-noise ratio (SNR) regime. Furthermore, three optimization problems are formulated to minimize the obtained asymptotic outage probability, namely, optimization of the power allocation at the source and the relay with fixed relay placement, optimization of the relay placement with fixed power allocation, and joint optimization of the power allocation and relay placement. It is shown that joint optimization obtains the best outage performance.