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An adaptive generalised selection-combining (GSC) receiver is proposed for time-varying frequency selective fading channel. The receiver adaptively selects and combines a subset of diversity branches out of the available branches and discards the others. This is performed by comparing the maximum likelihood (ML) metric of each diversity branch with a threshold. The branches that are lower than the threshold are selected and combined using maximal ratio combiner. The proposed adaptive GSC receiver dynamically adjusts the threshold value according to the time variations of the channel. Equalisation and data detection are performed after combining using ML sequence estimation implemented by Viterbi algorithm. The minimum survivor technique is employed to reduce the complexity of the receiver. An upper bound for the probability of error of the proposed receiver is derived. The performance of the proposed adaptive GSC receiver is compared with the performance of different threshold GSC receivers.