## 2 System Architecture and Requirements
### Receive Chain  
#### 2.1.1 Requirements for FDD  
In a dual antenna mobile terminal, the isolation between TX and RX antennas can be around 20 dB to 30 dB [17]. Here, we assume 25 dB TX-RX antenna isolation as a typical value. For the FDD scenario, we consider as a reference 4G LTE band 2 with 20 MHz channel bandwidth [26]. With the maximum TX power of 23 dBm, the maximum TX leakage signal arriving at the RX antenna is \(-\)2 dBm. Removing external filters in front of the receiver, OOB blockers as high as \(-\)15 dBm may be present at the receiver input together with the \(-\)2 dBm TX leakage. This can cause strong in-band intermodulation if the receiver IIP3 is not sufficiently high. In the presence of a strong OOB blocker, the receiver sensitivity of \(-\)92 dBm (for QPSK modulated wanted signals) can be degraded by 9 dB for 20 MHz channel bandwidth [26]. Considering a signal-to-noise ratio of \(-\)1 dB for QPSK, the maximum noise + distortion level is \(-\)82 dBm. Assuming, pessimistically, that the receiver has the maximum allowed noise figure of 9.8 dB, which barely meets the sensitivity requirement, the maximum third-order intermodulation level is \(-\)82.6 dBm. Hence, in the worst case, i.e., when the OOB blocker appears at a frequency offset from the receiver that is exactly twice the TX-RX frequency spacing, the effective receiver IIP3 (as defined in [18]) should be larger than \(-\)2 dBm + \((-15+82.6)/2=31.8\) dBm. Such a high value is nearly impossible to achieve using standard LNA design techniques and represents a challenging target even for SIC FDD receiver architectures. Assuming an RF SIC of 20 dB in front of the receiver, the receiver IIP3 requirement is decreased by the same amount to a more feasible value of 11.8 dBm. Nonetheless, the nonlinearities of the canceller are also very important and can easily become the bottleneck for the entire receiver. To illustrate this issue, we refer to Figure 2.  
The canceler sees the large TX signal at the input (V\({}_{\text{TX}}\)) and a large blocker signal (V\({}_{\text{BK}}\)) at the output. This causes two types of nonlinearities. First, due to the nonlinear canceler gain, the TX signal generates intermodulation products in the vicinity of the TX band. In FD mode, since TX and RX bands coincide, this is the main nonlinearity mechanism affecting the receiver effective IIP3. Second, due to the canceler limited reverse isolation, its output signals, including its nonlinear products, are modulated by the blocker at the canceler output (i.e., at the receiver input). This creates cross-modulation products between the TX signal and the blocker, that degrades the SIC receiver effective IIP3 in FDD mode. We express the canceler characteristic using a Taylor series expansion as follows:  
\[\text{V}_{\text{o}}=\Big{(}\alpha_{1}\text{V}_{\text{TX}}+\alpha_{2}\text{V} _{\text{TX}}^{2}+\alpha_{3}\text{V}_{\text{TX}}^{3}\Big{)}(1+\lambda\text{V }_{\text{B}}) \tag{1}\]  
and we assume that the TX signal is given by two tones (V\({}_{\text{TX}}=\text{V}_{\text{A}}\cos(\omega_{1}\text{t})+\text{V}_{\text{A}} \cos(\omega_{2}\text{t})\)) and the blocker is CW (V\({}_{\text{BK}}=\text{V}_{\text{B}}\cos(\omega_{\text{B}}\text{t})\)). The two nonlinear mechanisms described above generate two  
Figure 2: Canceler feedback linearization. distinct 3 rd order nonlinear products: the intermodulation between the TX input tones (V\({}_{\text{o,IM3}}\)) and the cross-modulation between the TX tones and the blocker (V\({}_{\text{o,XM3}}\)).