# Energy Efficiency Analysis of MIMO Wideband RF Front-End Receivers
## 4 Results and Discussions  
In this section we provide a few numerical results with the two considered RF front-end architectures. The system parameters are listed in Table 2. In addition, we consider nodes from a wireless sensor network with the same number of antennas to transmit and receive, \(N_{\text{t}}=N_{\text{r}}\). The transmission system is evaluated using the closed-form expressions for the outage probabilities. In other words, given the target outage probability \(\mathcal{O}^{\star}\) we find the required transmission power for each scheme, using (10), (12) and (14), respectively for the SISO, AS and SVD schemes. In addition, these expressions also depend on the noise figure of the receiver, so that each RF front end architecture \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline \(B\) & Channel bandwidth & 20 MHz \\ \hline \(M_{1}\) & Link margin & 20 dB \\ \hline \(G_{\text{a}}\) & Total antenna gain & 5 dBi \\ \hline \(f_{\text{c}}\) & Carrier frequency & 2.4 GHz \\ \hline \(N_{0}\) & Noise PSD & \(-174\ dBm/\text{Hz}\) \\ \hline \(\alpha\) & Path loss exponent & 2.5 \\ \hline \(\mathcal{O}^{\star}\) & Target outage probability & \(10^{-3}\) \\ \hline \(R\) & Spectral efficiency & 1 bit/s/Hz \\ \hline \(P_{\text{Rx}}\) & Power consumption at the TX & 97.9 mW [27] \\ \hline \(P_{\text{Rx}}\) & Power consumption at the RX & 92.2 mW [27] \\ \hline \(\eta\) & Drain efficiency of the PA & 0.35\% [27] \\ \hline \(m\) & Nakagami-\(m\) fading parameter & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. impacts the required minimum transmission power. With that in hand, the energy efficiency of each scheme is computed using (16). Table 3 shows the energy efficiency of the LNA designs, selected from [10; 11; 12], as a function of the transmission distance. Then, for each LNA we consider SISO, AS and SVD schemes, with the architecture that yields the best performance highlighted in orange, cyan and green shadings, respectively. Please note that the front-end designs with the lowest power consumption are not necessarily the ones with the best energy efficiency. The association of low noise figure and low power consumption clearly plays a very important role in designing an energy efficient system. Then, in Table 3 we observe that the LNA in [12] yields the highest energy efficiency for SISO, AS and SVD. Next, Table 4 considers the LNTA designs selected from [14; 17; 18]. As we observe, the LNTA in [14] yields the highest energy efficiency for SISO when \(d=50\) m, being outperformed by the LNTA in [17] when \(d\geq 100\) m. Using the AS scheme, the LNTA in [18] performs best when \(d=50\) m, the LNTA in [14] performs best when \(d\in\{100,150\}\) m and the LNTA in [17] performs best when \(d\geq 200\) m. Therefore, the blue shading shows the highest energy efficiency across architectures. Finally, the SVD scheme follows the same idea, so that the best architecture starts with the LNTA in [18] when \(d\leq 150\) m, shifting to the LNTA in [14] when \(200\) m \(\leq d\leq 350\) m and to the LNTA in [17] when \(d\geq 400\) m. As a consequence, in the sequel we pick the LNA/LNTA architectures with the best performance among their counterparts. According to Table 3, the LNA in [12] is the best choice, while the LNTA in [17] outperforms the other LNTAs most of the time according to Table 4.  
\(N_{\rm t}=N_{\rm r}=2\) antennas. As we can observe, the LNTA architecture at the receiver usually achieves higher energy efficiency, except for short transmission ranges with the MIMO schemes. In this example, the LNA outperforms the LNTA in terms of EE with AS when \(d\leq 150\) m, while this distance increases up to \(d\leq 220\) m with the SVD scheme.