## 3 Fundamentals of the ED Process  
According to Figure 1, which presents the main blocks of the MIMO-OFDM system employing the ED spectrum sensing realized by the SLC technique, the PU and SU are involved in the MIMO-OFDM transmission and reception processes. On the PU side, the signal is transmitted over an \(M\) Tx antenna(s) according to the principles of an OFDM transmission. The received signal on the SU side at each \(r\)-\(th\) Rx antenna is squared and combined using the SLC approach. The energy of the signal received is further exploited in the SS based on the principles of comparing the energy of received signal with the deterministic signal threshold (Figure 1). The PU is the licensed owner of the frequency band and has an advantage in terms of spectrum access, whereas the SU only has access to the spectrum when PU is not transmitting. Then, the SU can utilize the spectrum without interfering with the PU's operations. Table 1 lists all the parameters exploited in the presented analyses. Figure 1: Operational blocks of the MIMO-OFDM communication system employing ED spectrum sensing realized by the SLC technique. The PU signal is sent using \(m\) (\(m\) = 1,..., \(M\)) Tx antenna(s) in the analysed system and the transmitted PU signal is received using \(r\) (\(r\) = 1,..., \(R\)) Rx chains of the SU. The \(P_{m}\) denotes the PU Tx power of the signal that is transmitted by the \(m\)-\(th\) antenna. The total Tx power emitted by the PU over \(M\) Tx antennas is \(P=\sum_{m=1}^{M}P_{m}\). The complex signal sent by the \(m\)-\(th\) antenna is defined as \(\mathbf{s_{m}}=\mathbf{s_{m,r}}+\mathbf{j_{s_{m,i}}}\), where \(\mathbf{s_{m,i}}\) and \(\mathbf{s_{m,r}}\) represent an imaginary  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Symbol** & \multicolumn{1}{c}{**Meaning**} \\ \hline \(M\) & The PU’s total number of transmitting (Tx) antennas installed at the PU \\ \(R\) & The SU’s total number of receiving (Rx) antennas installed at the SU \\ \(m\) & The number of transmitting (Tx) antennas installed at the PU \\ \(r\) & The number of receive (Rx) antennas installed at the SU \\ \(N\) & Total number of samples utilized in the ED procedure without DDT and the NU variations \\ \(N^{NU}\) & Total number of samples utilized in the ED procedure with NU \\ \(N^{DDT}\) & Total number of samples utilized in the DDT-ED procedure \\ \(N^{NUDDT}\) & Total number of samples utilized in the DDT-ED procedure affected by NU \\ \(\mathbf{s}\) & A complex signal sent from the PU side using \(M\) Tx antennas \\ \(\mathbf{s_{m}}\) & A complex signal sent from the PU side using \(m\)-\(th\) antenna \\ \(P\) & Total PU power emitted via \(M\) Tx antennas \\ \(P_{m}\) & The power emitted via the \(m\)-\(th\) antenna at the PU side \\ \(\mathbf{Y}(n)\) & The overall received signal by all SUs \(R\) Rx antennas in the \(n\)-\(th\) SS period \\ \(\mathbf{h_{r}}(n)\) & Gain of the channel between the \(M\) Tx antenna and the \(r\)-\(th\) Rx branch in the \(n\)-\(th\) sensing interval \\ \(\mathbf{y_{r}}(n)\) & The received signal at the SUs \(r\)-\(th\) Rx antennas in the \(n\)-\(th\) SS interval \\ \(\mathbf{w_{r}}(n)\) & The noise of the signal received by SU via the \(r\)-\(th\) Rx antennas in the \(n\)-\(th\) SS interval \\ \(s_{r}(n)\) & Signal vector received at the \(r\)-\(th\) Tx branch within the \(n\)-\(th\) sensing interval \\ \(\sigma_{w}^{2}(n)\) & Received signal variance at the \(r\)-\(th\) Rx branch of the SUs in the \(n\)-\(th\) SS interval \\ \(\sigma_{w^{2}}^{2}(n)\) & Noise variance of the signal detected at the SUs \(r\)-\(th\) Rx antenna observed in the \(n\)-\(th\) SS interval \\ \(\sigma_{w^{2}}^{2}N\)\(N\  
and real component of the transmitted signal, respectively. As a result, the SU receives the signal via every of the _r-th_ Rx antennas and samples it using the \(N\) samples yielding the overall signal received by the SU which can be expressed as:  
\[\mathbf{y}_{\mathbf{r}}(n)=\left\{