Performance Evaluation of the Discrete Fourier Transform Based Beamformers Under Block and Sliding Window Processing Modes

The techniques that are used to make an array of sensors directive are known as beamforming techniques. Beamformers (BFs) have been designed to function as spatial-temporal filters. In this thesis, Capon’s beamforming technique has been studied under both narrowband and broadband scenarios. To compensate for the propagation time of the signals to other antenna elements (under narrowband scenario) Minimum Variance BF (MVB) would apply a simple phase shift to each signal. This phase-shift corresponds to a correct time delay for one particular frequency only and can’t be applied under the broadband scenario where multiple frequencies exist. To achieve high spectral and spatial resolution over wideband channels a large number of sensors or tapped-delay-line elements would be required and this would inevitable cause an increase in computational complexity. Fortunately, this high computational complexity can be reduced by applying a transformation at TDL elements of each sensor. In this thesis we have used the Discrete Fourier Transform (DFT) to generate various frequency bins and have applied narrowband beamforming for each different bin. Frequency bins in the DFT-based broadband BF are created using Block Processing (BP) and Sliding Window processing (SW). To evaluate the performance of the DFT-based BF, Ensemble Mean Squared Error (EMSE) and the Signal to Interference plus Noise Ratio (SINR) have been used. In addition, the thesis provides a comparison for the computational complexity of DFTbased BF under BP and SW modes. The complexity has been assessed in terms of the Multiply-ACcumulate (MAC) operations. For simulations MATLAB platform has used. Three broadband incoming signals each with bandwidth 𝐵����� = 50𝑀�����𝐻�����𝑧�����, central frequencies of 150 𝑀�����𝐻�����𝑧����� and DOAs of 𝜃�����1 = 20° , 𝜃�����2 = 40° and 𝜃�����3 = −20° were assumed. The signal with direction 𝜃�����1 = 20°was marked as the desired signal and power of the three sources were respectively set to 𝑃�����𝑠�����𝑑����� = 5,10,10(𝑑�����𝐵�����𝑊�����/𝑀�����𝐻�����𝑧�����) . Each sensor’s output was sampled at Nyquist rate of 1/2𝐵�����. For a fair comparison between the DFT based BF using BP and the DFT based BF using SW processing, the length of the signals were fixed to 𝑁����� = 1000 samples. Simulation results show that the DFT-based BF under BP has higher proficiency in handling wideband signal sources. The SINRs at the output of the DFT-based BF was seen to be time varying (in fact periodic). On the other hand, the DFT-based BF utilizing SW processing would take one new snapshot under each iteration, and generate one sample at its output and would suffer from highly correlated inputs. DFTbased BF under SW processing would deliver lower SINRs in comparison to a DFTbased BF under BP when the window size and the block size are same. Finally, the number of blocks or slides are the main factor in adjusting the computational complexities and accuracy of the estimated correlation matrices. Therefore, the size of blocks/slides should be selected carefully to meet certain criteria. Keywords: Tapped Delay Line, DFT-based Beamformer, Block or Sliding Window Processing, SINR, Multiply-Accumulate Operations