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In this paper, linear combining receivers with deterministic weights are considered for a communication system employing receive diversity in flat Rician fading. We propose two receiver structures: (1) a modified maximum likelihood (ML) receiver in which detection is performed by maximizing the likelihood function of the combined received signal, (2) a deterministic maximal-ratio combining (MRC) receiver which uses the same structure as that of an MRC receiver but with deterministic weights. The deterministic weight vector is chosen such that it minimizes the union bound on the symbol error probability. Methods of computing this deterministic weight vector are presented. The error performance of the receivers is numerically compared with that of the square-law combining receiver and the equal-gain combining (EGC) receiver (which requires more complex phase estimation rather than using fixed, deterministic weights). Numerical results show that in the case of phase-shift keying, the EGC receiver performs better than the modified ML receiver (which has the same performance as that of the deterministic MRC receiver), but the performance gap decreases with increase of the Rician K-factor. It is also seen that in the case of orthogonal frequency-shift keying, the modified ML and deterministic MRC receivers outperform the square-law combining receiver.