Figure 6.48 Measured FLOPS as a function of the number of elements (SNR = 10 dB, trials = 50, two uncorrelated signals at (θ1, φ1) = (−20°, −15°) and (θ2, φ2) = (20°, 15°)).

6.3 Comparative Analysis

In the previous sections, analysis of the ESPRIT-based algorithms for DOA estimation is presented. As discussed before, the unitary ESPRIT reduces the computational complexity by doing all mathematical computations in real numbers than in complex numbers as compared to standard ESPRIT. In this section, the performance comparison between the standard ESPRIT and the unitary ESPRIT is presented with a six-element one-dimensional ULA.

Again the RMS error in the DOA estimation is used as the metric of performance. Fifty trials are run, with each trial involving 250 snapshots. These simulation parameters are maintained throughout the simulations unless otherwise mentioned. Two equal power uncorrelated signals at 5° and 10° are impinging on the array.

Figures 6.51 and 6.52 show the performance with respect to the number of snapshots. In Figure 6.51, the SNR is kept at 5 dB. In Figure 6.52, the SNR is kept at 15 dB. It is observed that the unitary ESPRIT achieves a better performance than the standard ESPRIT in both cases. The unitary ESPRIT has an error of about 8% less than standard

ESPRIT at the SNR of 5 dB, and it has about 15% less at the higher SNR of 15 dB.

Figures 6.53 and 6.54 show the performance with respect to the SNR. In Figure 6.53, the SNR is varied from −5 dB to 5 dB, and 250 snapshots of data are taken. In Figure 6.54, 500 snapshots of data are taken with the same variation in the SNR. Again, the unitary ESPRIT outperforms the standard ESPRIT even at low SNR conditions. At −5 dB and with 500 snapshots of data available, it can be seen that the RMS error with the unitary ESPRIT is about 33% less than that with the standard ESPRIT.

The estimation errors of the standard ESPRIT and unitary ESPRIT versus the number of signals are also compared. Figures 6.55 and 6.56 show the results. A 10-element array is taken and nine signals are made impinging on the array. Two simulations are conducted with 500 snapshots per trial at an SNR of 5 dB and 10 dB, respectively. As can be seen from Figures 6.55 and 6.56, both the standard ESPRIT and the unitary ESPRIT perform similarly in picking up the maximum number of the signals with the acceptable errors.

Figure 6.51 RMS error in a DOA estimation as a function of the snapshots (SNR = 5 dB, six-element ULA, trials = 50, two uncorrelated signals at 5° and 10°).

Figure 6.56 RMS error in a DOA estimation as a function of the signals (SNR = 15 dB, 25-element ULA, trials = 50, two uncorrelated signals at 5° and 10°).

The performance of the standard ESPRIT is compared to that of the unitary ESPRIT with respect to the number of elements in the array. The results are shown in Figures 6.57 and 6.58. The number of antenna elements is varied from 4 to 10 and two SNR scenarios of 5 dB and 10 dB are simulated. To estimate the DOA, 250 snapshots are taken. Overall, the unitary ESPRIT shows the errors that are about 10% smaller than those of the standard ESPRIT as the number of elements are increased.

The performance of standard ESPRIT and unitary ESPRIT with respect to power level of the received signal is shown in Figures 6.59 and 6.60 with a 10-element antenna array. Simulations are performed with a signal that is arriving at 5° as the strong signal, and the power of the signals arriving at 10° is varied from −20 dB to −5 dB less than the power of the strong signal. Simulations were conducted in two different SNR scenarios with 5 dB and 10 dB. The results show an error with unitary ESPRIT about 40% smaller than those with the standard ESPRIT at large power differences. However, at low power level differences, both the algorithms perform similarly.

The resolution capabilities of the standard ESPRIT and unitary ESPRIT are compared and presented in Figures 6.61 and 6.62. Here