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The performance analysis of dual (two-branch) MRC under imperfect weight is derived. The weight of the perfect MRC is the conjugate of the channel gain normalized to the noise variance of each branch. On the other hand, the imperfect MRC in this paper means the case that the weight is only the conjugate of the channel gain, not being normalized to the noise variance. Considering the system (or channel) conditions that the noise level of each branch is different, we present the accurate performance analysis of imperfect dual MRC in terms of average combined signal-to-noise ratio (SNR), outage probability and average symbol error rate for arbitrary modulations in closed-form and compare them with the performance of the perfect MRC and the selection combining (SC). The interesting statistical results such as probability density function, cumulative distribution function, and moment generating function of the combined output SNR, which follows the ratio distribution of the square of the sum of the exponential random variables (RVs) to the weighted sum of the exponential RVs are derived. From the performance results we provide the criterion in choosing the imperfect MRC, perfect MRC, or SC depending on the degree of the difference of the noise level between branches.