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In this paper, we derive an exact closed-form expression for the ergodic capacity of an i.i.d. Rayleigh fading MIMO channels when the transmitter has no channel knowledge (no CSIT) and when transmitter has channel distribution side information (CDIT). This new expression is in terms of the sum of two polynomials that one of them is multiplied by the exponential integral. The coefficients of these polynomials are characterized and recursive formulas are derived to evaluate them. Additionally, by placing an additional antenna at either transmitter or receiver, the achieved ergodic capacity is analytically and asymptoticly compared, and accordingly the antenna allocation that maximizes the ergodic capacity is determined.