## 4 Results
### Calculation of C-PCL System Performance
The C-PCL system may detect the reference channel receiver or the receivers in the main antenna array. The detection distance is denoted as L. The PCL system, taken for further calculations, had one equivalent receiving antenna with a gain \(\rm G_{\rm PCL-R}\) for signals reception and \(\rm G_{\rm PCL-T}\) for transmission of IMD products. For purposes of simplicity, it was assumed that the sounding frequencies and IMD products are so closely spaced that the radio link loss due to frequency had approximately the same value. The bandwidth of the IMD receiver is denoted as B. The analysis of the C-PCL performance uses formulas for radio link losses; however, here it was rearranged with respect to the received IMD signal power in the C-PCL receiver (see Figure 8). The bandwidth of the IMD receiver is denoted as B, and it allows the noise power to be calculated. \[\rm P_{N}[dBm]=-174+10\log_{10}(1000\cdot B[kHz]), \tag{2}\]  
Then, one may define the signal-to-noise ratio (SNR) that is sufficient to decide that the IMD signal (with the power \(\rm P_{R}\)) is detected with a sufficiently high probability. In this calculation, the SNR was assumed to be equal to 10 dB. \[\rm P_{R}[dBm]=P_{N}[dBm]+SNR[dB] \tag{3}\]  
The power of the IMD signal equal to \(\rm P_{R}\) appears at the input of the C-PCL receiver, after transmission through a radio link from the PCL antenna. Therefore, one may write:  
\[\rm P_{T-IMD}[dBm]=P_{R}[dBm]+LL_{UP}[dB], \tag{4}\]  
where:  
* \(\rm P_{T-IMD}\)--power of the IMD product generated at the amplifier's input;
* \(\rm LL_{UP}\)--link loss for uplink, i.e., from the PCL to the C-PCL. The uplink loss (i.e., from the C-PCL transmitter to the PCL receiver) was calculated according to the known formula:  
\[\rm LL_{UP}[dB]=FSL[dB]-G_{R}[dB]-G_{T-PCL}[dB], \tag{5}\]  
where:  
Figure 9: Diagram of C-PCL system considered for calculation of performance. * G\({}_{\text{T-PCL}}\) is the PCL antenna gain when the transmission of the IMD signals is considered;
* G\({}_{\text{R}}\) is the C-PCL receiver antenna gain;
* FSL is a free-space loss defined as: \[\text{FSL}[\text{dB}]=20\log_{10}(\text{L}[\text{km}])+20\log_{10}(\text{f}[ \text{MHz}])+32.44.\] (6) The power of the IMD products may be derived from: \[\text{P}_{\text{T-IMD}}[\text{dBm}]=\text{P}_{\text{R-PCL}}[\text{dBm}]~{}-~{} \text{CL}[\text{dB}],\] (7) where \(\text{P}_{\text{R-PCL}}\) denotes power of the sounding signals received by the PCL. The process of the IMD generation in the PCL low-noise amplifier is described by the frequency conversion loss (CL). This value was calculated from the measurement results. Then, the sounding power at the LNA input is given by: \[\text{P}_{\text{R-PCL}}[\text{dBm}]=\text{P}_{\text{T}}[\text{dBm}]~{}-~{} \text{LL}_{\text{DOWN}}[\text{dB}].\] (8)  
The downlink loss (i.e., from the C-PCL transmitting antenna to the PCL receiver) was calculated as in the case of uplink:  
\[\text{LL}_{\text{DOWN}}[\text{dB}]=\text{FSL}[\text{dB}]~{}-~{}\text{G}_{\text {T}}[\text{dB}]~{}-~{}\text{G}_{\text{R-PCL}}[\text{dB}] \tag{9}\]  
where \(\text{G}_{\text{R-PCL}}\) is the PCL antenna gain for the reception of sounding signals. The methodology presented above describes the relation between the sounding signals power \(\text{G}_{\text{T}}\) and the detection distance L for a given C-PCL receiver bandwidth B and SNR. The other variables are the gains of antennas and IMD generation efficiency (CL, conversion loss).