Study of Broadband Postbeamformer Interference Canceler Antenna Array Processor using Orthogonal Interference Beamformer Lal C. Godara and Presila Israt The School of Information Technology and Electrical Engineering, The University of New South Wales, Australian Defence Force Academy, Canberra ACT 2600, Australia

Outline Introduction Preliminary Review Proposed Method Examples and Discussion Conclusion

Introduction Processing of narrowband signals induced on an array of sensors is normally carried out by multiplying these signals by complex weights and summing to produce the array output.

Postbeamformer Interference Canceller structure PIC Processor is a two channel processor which cancels directional interference by forming two beams using an antenna array.

Two Beam Processor

PIC Output –One beam referred to as the signal beam is steered in the signal direction, –the second beam referred to as the interference beam is steered away from the signal direction and –the weighted output of the second beam is subtracted from the first beam to form the output of the processor.

Narrowband Signals In the case of narrowband signals the beam steering is achieved by complex weighting and no physical delays are required. This scheme of complex weighting to steer beams is not possible to process broadband directional signals.

Broadband Signals For this case a processor normally requires a tapped delay line filter (TDL) and physical delays between the TDL filter and the sensors are used to steer a beam. These delays are not only cumbersome and expensive to use but also deteriorate the array performance due to implementation errors.

Aim of this paper This paper presents a technique to process broadband signals without using steering delays and studies the performance of PIC processor using this method in the presence of broadband directional signals.

Preliminary Review Consider an array of L elements in the presence of two uncorrelated broadband directional sources and uncorrelated noise. One source is a signal source and the other one is an unwanted interference.

Array Signals Let the induced voltage on the array elements be sampled at a sampling frequency f s and an NL dimensional vector X(t) denotes the N samples, that is,

Correlation matrix Define an NL × NL dimensional matrix R as

Fourier transform Define a correlation matrix at the k th bin as

Proposed Method

PIC at kth bin Figure shows the structure of the PIC processor at the k th bin. The output q(k) is given by

Output Power

Optimal weights The optimal weight which minimizes P(k) is given by

Signal and Interference Beams Signal Beam Interference Beam

Steering Vector Where P(k) is a projection matrix and is given by The steering vector in direction θ is defined as

Algorithm summary The following summarizes the algorithm to process broadband signals assuming that the frequency bin k = k1, k1 + 1,..., k2 corresponding to the desired frequency band.

Algorithm Estimate R using Calculate R(k) using Select V(k) and U(k) using Calculate the optimal weight using

Power The mean output power at each bin is given by

Signal to Noise ratio (SNR) Substituting () the correlation matrix for signal and noise, the expressions for the output signal power and the noise power can be obtained. Then the output SNR() is given by

Theoretical Results Let Ω() denote the output SNR at the centre frequency of the k ℎ bin. From the analysis of narrowband PIC it follows that

Theoretical Result When the interference beam is formed with () = (), then 0 () = () and Ω(k) becomes

Value of ρ for 4 element array with N=125

Comments One observes from figure that when θ s is close to θ I, ρ(k) is very small. As θ s moves away from θ I, ρ(k) varies monotonically with k whereas when θ s is far away from θ I, ρ(k) is between about 0.9 and 1.0 and variation with k is not monotonical. Ω(k) depends on ρ(k) which in turn depends on array geometry and relative positions of the two directions. For example when interference is about 140 0, ρ(k) increases monotonically between 0.5 to 0.95 whereas when interference is at about 60 0 the increase with bins is not monotonical and the variation between about 0.92 and 1.0. This variation reflects on Ω(k).

Example A linear array of 4 elements Number of samples N = 125 Desired normalised frequency 0.22 to 0.42 Interference direction variable Signal direction =110 degree Signal power =1 Interference power =1 Noise =1

Output SNR (Theory vs. Simulation)

Comments One observes from Figure that SNR() and Ω() in all cases are almost the same. Furthermore for interference source, making angles of and 95 0 with the line of the array, both SNR() and Ω() increase with similar to the increase in () whereas for interference angle of 70 0, the signal to noise ratio increases with first and then drops after reaching to a maximum as expected from the variation in () shown in previous Figure. Thus confirming the analytical study that the output SNR varies with k and the variation depends upon the relative positions of signal and interference sources.

Signal to noise ratios (effect of large no. of samples)

Comments Figure shows the same results for = 1000 to show that as increases SNR() approaches Ω().

Output signal to noise ratios (for low noise)

Comments Figure shows the effect of low background noise 0.01 and 100 respectively. One notes that for a very low noise Ω() ∝ () which is evident from the figure. One also observe from the figure that the effect of finite bandwidth is clearly evident in this case. For the case of high noise, it follows that SNR is very small in all cases which is evident from the next figure.

Example(s): Signal to noise ratios (for large noise)

Example(s): Output interference Power

Comments Figure shows the variation in () as a function of. One observes from the figure that the process cancels less interference when the interference is closer to the signal source.

Conclusion We proposed OIB method for PIC processor which effectively cancels interference without suppressing the signal. Analytical expression for SNR was derived to study the performance of OIB method. Analytical results show that the output SNR depends on the relative positions of the sources, input signal power, input interference power and background noise. Simulation results were presented to support the analytical expression.

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