{'fraction_non_alphanumeric': 0.016556291390728478, 'fraction_numerical': 0.0, 'mean_word_length': 5.128378378378378, '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}}
Max-min optimization of transmission powers in the two-way cognitive radio network assisted by orthogonally signaling relays

We study a cognitive radio network in which two sources communicate with each other through multiple relays operating in non-overlapping frequency bands in the radio spectrum. We consider the problem of optimizing the transmission powers of the sources and relays so that the minimum of the two sources' transmission capacities is maximized. Thanks to the non-overlapping nature of the relays' signals, the problem can be represented as a constrained optimization over two variables, but that formulation still results in a non-convex optimization. We show that an optimal solution occurs on the upper boundary of the feasible set. We further show that the objective function is unimodal on the boundary. We suggests a simple method of optimization that utilizes these properties.