# Semi-Coprime Array with Staggered Beam-Steering of Sub-Arrays
## 3 Simulations and Results
### Scass-C  
SCASS-C with Chebyshev weights has been simulated for \(L=14\), steered towards different angles with suitably selected values of \(\Delta\). Employing Chebychev weights in linear arrays is a conventional technique to suppress side lobes of the beam pattern, consequently improving the PSLR. Although this benefit is accompanied with increased HPBW, in SCASS-C, this drawback is alleviated by adjusting the value of \(\Delta\). In this way, despite the power loss, PSLR is improved without compromising the HPBW. This is in contrast with existing linear arrays in which the HPBW is compromised when the PSLR is improved and vice versa. Chebyshev weights are calculated for a given side lobe attenuation (SLA) [35]; therefore, in the results shown here, the SLA values are also mentioned. Figure 3 shows the absolute and normalized beam pattern of the SCASS-C with 14 elements. Here, the adjustable parameters are set as \(\Delta=0.2^{\circ}\), \(0.9^{\circ}\) and SLA = 22.1 dB, 22.5 dB for \(\theta_{0}=0^{\circ}\), \(60^{\circ}\), respectively. Note that the peak side lobe level of the absolute beam pattern is the same as the given SLA, but the beam pattern peak is lower than 0 dB. For instance, for \(\theta_{0}=60^{\circ}\), the peak side lobe level is \(-22.5\) dB while the beam pattern peaks at \(-0.5\) dB. Hence the PSLR becomes 22 dB. As shown in the figure, when the beam pattern is normalized, its peak and side lobes increase identically. Consequently, its PSLR remains the same in the absolute and  
\(60^{\circ}\), respectively. Therefore, despite the power loss, the SCASS-C gives a PSLR of 22 dB for the two steering angles. If the SLA is set to 22.1 dB or 22.5 dB for the SCA-C too, its HPBW degrades further which is already worse than both the SCA-U and SCASS-C. Hence, the SCASS-C outperforms the SCA-U and SCA-C in terms of the HPBW for a given PSLR. In the second step, the proposed array is compared with other existing arrays. Figure 5 shows the beam pattern of the SCASS-C compared against different existing ULAs, NULAs and SAAs, namely: (i) CSA with a novel processor (CSA-N) [30]; (ii) ECSA with Chebyshev weights (ECSA-C) [18]; (iii) SULA with IWO-optimized weights (SULA-IWO) [3]; (iv) NULA with GO-optimized spacing (NULA-GO) [17]; (v) NULA with GA-optimized spacing (NULA-GA) [8]; (vi) NULA with spacing and weights found using parabolic relations (NULA-P) [13]; and (vii) SULA with PSO-optimized weights (SULA-PSO) [10]. For simulation of the existing arrays, their weights, spacings and other parameters were taken as proposed originally. However, for the ECSA-C, we took \(M=3\), \(N=4\) and the extension factor = 3. It is obvious from these figures that all the arrays suffer degradation either in the HPBW, PSLR or both when they are beam-steered away from the broadside. In contrast, the HPBW of SCASS-C degrades minimally among them while its PSLR remains constant when steered away from the broadside. Figure 5: _Cont._  
The performance metrics of these arrays are shown in Table 1. This table shows that the SCASS-C, with suitably selected \(\Delta\) and SLA, offers the minimum HPBW among them, except for CSA-N [30] which offers an HPBW 0.02\({}^{\circ}\) smaller than the SCASS-C in the broadside direction. However, as soon as it is beam-steered away from the broadside its main lobe becomes wider than the SCASS-C. Moreover, its PSLR is inferior to that of the SCASS-C for all steering angles. Although some arrays are superior to the SCASS-C in terms of the PSLR for \(\theta_{0}=0^{\circ}\), when they are beam-steered away from the broadside, not only do their HPBW worsen further but their PSLR also drop below that of the SCASS-C. It is also noteworthy that the SCASS-C has been simulated for 14 sensors, while the other arrays have been simulated for a larger number of sensors, except CSA-N. Even then, the SCASS-C outperforms the other arrays in terms of its HPBW and directivity for the angles away from the broadside direction. The only array with a directivity higher than the SCASS-C is the CSA-N.