If a, b, andN are finite, the series is called doubly finite. Since in any physically realizable system, the output can only depend on previous values of the input, the kernels tn) will be zero, if any of the variables t1, t2, tn are negative. The integrals may then be written over the half range from zero to infinity. Therefore, if the operator is causal a > 0. 376 Chapter 3 thermal noise which is typically generated by RF components. Using the estimated linear wireless channel, this method can mitigate transmitter impairments. Unlike other SIC meth- ods, the distortion of the transmitter signal by PA nonlinearity or by I/Q imbalance is obtained directly by the auxiliary receive chain. The specifications of a full-duplex system can be classified into three categories: main specifications, ADC specifications, and self-interference specifications. While the residual self-interference power PRSI is higher than the receiver noise floor level, the signal to self- interference plus noise ratio in a full-duplex system is lower than the SNR of a half-duplex system receiver. This means that the maximum efficiency of full-duplex cannot be achieved. In general, self-interference cancellation solutions are a combination of several techniques to help meet the system requirements. Fig. 3.39 provides an example, showing the average performance value achieved in each domain. In case of a shared transmit/receive antenna system, the suppression is performed using a three-port RF circulator. The ferrite within the device can be considered as a propagation domain. Achievable isolation by the circulator is between 15 and 30 dB, and in the case of wideband operation, the maximum value would decrease. In a separate-antenna system, sev- eral self-interference cancellation techniques can be used. The two transmit antennas can be placed at distances d and d + X/2 away from the receive antenna. Separating the two trans- mitters by half a wavelength causes their signals to cancel one another. For narrowband sig- nals, this technique is exp