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In this paper, via the exact closed-form expressions, we statistically investigate the symbol-error-rate performance of the limited feedback-based adaptive threshold-based relay selection (ATRS) scheme under multiple type II relay environments. Our analytical results are thoroughly validated by cross-checking them against the results obtained via the Monte Carlo simulations. Some selected results show that the performance degradation caused by minimizing the feedback can be compensated by refining the feedback information, specifically by applying a 1-bit increase in terms of the feedback data rate and an additional single-comparison process in terms of complexity. Note that our derived results are valid for both symmetric and asymmetric link conditions. Additionally, the analytical results can be easily evaluated numerically with the standard mathematical packages. Furthermore, the analytical framework and the derived results can be applied for the expansion of the  $n$ -bit feedback-based ATRS scheme. Finally, for practical consideration, we provide useful discussion on the plausibility that the extended scheme can be implemented with only a 1-bit feedback.

SER Analysis of Adaptive Threshold-Based Relay Selection With Limited Feedback for Type II Relay