# Physical Layer Security for Military IoT Links Using MIMO-Beamforming at 60 GHz
## 3 Results and Discussions  
As an illustration of the challenges involved in the design of this circuit, we conducted some MATLAB simulations. Directional beams simulated at 60 GHz mmWave bands using Uniform Linear Arrays (ULA) are shown in Figures 3-7. Assuming an array with a physical size of 5 cm \(\times\) 5 cm, \(\lambda/2\)--spacing implies array elements up to \(N\) = 400 at 60 GHz for this array size. Military devices have a fixed physical area, regardless of the frequency of operation. This allows for more array elements at higher frequencies, thus increasing the directivity and security of the communication link. However, the beamforming weights computed at a particular sub-band must be reoptimized for use in another sub-band, in order to minimize energies in the sidelobes. Sidelobes result in signal leakage to unintended receivers, and thus, compromises secrecy. For the simulations in Figures 3-7, we observed the effects of steering vector \(A\) on the resulting beam. For the results shown in Figure 3, an 8-element array is used with the steering vector \(A\) = [4 3 2 1 1 2 3 4]. This steering vector is not optimized, hence significant sidelobes are generated in addition to the main beam. For the results in Figure 4, an 8-element array is used with the steering vector \(A\) = [1 1 1 1 1 1 1 1]. The steering vector is optimized in this case. An optimum beamformer allocates equal power to all the array elements (as performed in this figure), in the absence of channel state information at the transmitter. Hence, the resulting sidelobes are very small, but still noticeable. For the results in Figure 5, a 12-element array is used with the steering vector \(A\) = [1 1 1 1 1 1 1 1 1 1 1]. The steering vector is also optimized in this case, and a narrower beam is also generated due to the increase in the number of array elements. This produces a more secure radio link for IoT systems. For the increased secrecy and link privacy required for military use, we further increase the array element to \(N\) = 40 and \(N\) = 400. The maximum number of array elements, \(N\), possible while still maintaining \(\lambda/2\)--spacing in an array sized 5 cm \(\times\) 5 cm is \(N\) = 400 at 60 GHz. Figure 6 displays the resulting pencil beam generated for \(N\) = 40, while Figure 7 displays the corresponding results for the case \(N\) = 400. There is virtually no sidelobe generated at \(N\) = 400, but beams produced from \(N\) = 40 up to \(N\) = 400 will all be highly directional as illustrated in these two figures. Such beams ensure that the TX-RX communication link is highly secure and private. Figure 4: Directional beams produced by uniform linear arrays (ULA) operating at 60 GHz; 8 array elements with \(\lambda/2\)-spacing; steering vector \(A=[1\;1\;1\;1\;1\;1\;1\;1\;1]\). Figure 5: Directional beams produced by uniform linear arrays (ULA) operating at 60 GHz; 12 array elements with \(\lambda/2\)-spacing; steering vector \(A=[1\;1\;1\;1\;1\;1\;1\;1\;1\;1\;1\;1]\). Figure 3: Directional beams produced by Uniform Linear arrays (ULA) operating at 60 GHz; 8 array elements with \(\lambda/2\)-spacing; steering vector \(A=[4\;3\;2\;1\;1\;2\;3\;4]\). Figure 6: Directional beams produced by uniform linear arrays (ULA) operating at 60 GHz; 40 array elements with \(\lambda/2\)-spacing; 40 \(\times\) 1 steering vector \(A=[1\;1\;1\;\ldots\;1]\). The problem of optimum beamforming weighting vectors that maximize radio capacity in the OFDM-SDMA system was addressed in [16], where an adaptive algorithm was developed for computing the optimum beamforming weights, \(w\), that maximizes channel capacity in a multi-user OFDM-SDMA system using gradient descent method. The performance of the channel capacity-aware beamforming algorithm was shown to achieve substantially higher system capacity compared to the eigen-beamforming design. This is due to the fact that the algorithm directly maximizes the channel capacity criterion for each user iteratively.