Exact Average OFDM Subcarrier SINR Analysis Under Joint Transmit–Receive I/Q Imbalance

The subcarrier signal-to-interference-plus-noise ratio (SINR) expression for orthogonal frequency-division multiplexing (OFDM) systems impaired by in-phase/quadrature (I/Q) imbalance is a ratio of correlated random variables. In its original form, a quadruple integral is required to evaluate the exact average subcarrier SINR, which is cumbersome to compute numerically. We show that the quadruple integral can be reduced to a single integral, which can be easily evaluated numerically. Furthermore, closed-form expressions are derived for several important special cases, including transmit (TX)-only I/Q imbalance, receive (RX)-only I/Q imbalance, and joint TX/RX I/Q imbalance with equal levels of I/Q imbalance at the transmitter and at the receiver. In addition, we derive high-input-SNR approximations that provide valuable insights on how the average SINR is affected by the I/Q imbalance levels at the transmitter and the receiver and by the channel correlation between the image OFDM subcarriers. For example, we show that at high input SNR, TX-only I/Q imbalance is more harmful, in terms of average subcarrier SINR, than RX-only I/Q imbalance. Furthermore, we show that an approximate OFDM subcarrier SINR expression, commonly used in the literature, is not accurate when RX I/Q imbalance is present.