Adaptive Beamforming for Efficient Interference ...

Adaptive Beamforming for Efficient Interference Suppression Using Minimum Variance Distortionless Response

Kaushik Jyoti Das & Kandarpa Kumar Sarma Department of Electronics and Communication Engineering, Gauhati University, Guwahati-781014 Assam, India E-mail Id: kaushikjyotidas@gmail.& [email protected] Abstract – Adaptive Beamforming approach have provided significant amount of contribution in mitigating interference in wireless communication. This paper presents an Adaptive Beamforming approach using MVDR (Minimum Variance Distortionless Response) for interference suppression and to form beam in the estimated direction. Non-Blind algorithm with MVDR beamforming approach have been proposed in this paper. Simulated results show that the proposed method provides better performance with narrower beamwidth and higher gain. Keywords: Adaptive Beamforming, MVDR(Minimum Variance Distortionless Response), LMS(Least Mean Square), DOA(Direction of Arrival).

I.

INTRODUCTION

Organization of the paper is as follows: Section II provides the background principles related to the working of the proposed model. All experimental results and related discussion are included in Section III. The paper is concluded by summing up the work in Section IV.

Potential jamming in signal processing and telecommunication applications has been a major concern for system designers. And usual filtering techniques are not helpful as the jamming signal and desired signal are of same frequency. Various methods have been adopted to avoid jamming, including frequency hopping but it requires excessive bandwidth. Spatial filtering can solve the problem without the need of additional bandwidth as signals are filtered on basis of their direction of arrival(DOA). Smart antennas possess the capability of suppressing jamming signal, so they can improve signal to interference plus noise ratio (SINR). Array processing utilizes information regarding locations of signal to aid in interference suppression and signal enhancement and is considered promising technology for anti-jamming. This paper presents a comparative performance of Adaptive Beamforming technique in wireless communication. A comparative analysis of Non-Blind algorithms are studied and implemented. Non-blind algorithms as discussed in this work require the information of desired signal but cannot estimate the Direction of Arrival (DOA) of the source signal. Hence we have implemented Minimum Variance Distortionless Response beamformer which can estimate the Direction of Arrival and then this direction information can be utilized in Non-Blind beamforming algorithms to form beam in the estimated direction. LMS algorithm is known for its simplicity and robustness. Experimental results shows better performance when MVDR approach is utilized along with the LMS algorithm.

Figure 1: Block diagram of Adaptive Beamforming. II. THEORETICAL CONSIDERATIONS AND PROPOSED MODEL The purpose of beamforming is to form multiple beams towards desired users while nulling to the interferers at the same time, through the adjustment of the beamformer’s weight vectors. Figure 1 shows a generic adaptive beamforming system which requires a reference signal. The signal x(n) received by multiple antenna elements is multiplied with the coefficients in a weight vector w (series of amplitude and phase coefficients) which adjust the phase and amplitude of the incoming signal accordingly. This weighted signal is summed up, resulting in the array output, y(n). An

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‫ ׎‬represents the phase shift from element to element

adaptive algorithm is then employed to minimize the error e(n) between a desired signal d(n) and the array output y(n). For the beamformer, the output at time n, y(n) is given by a linear combination of the data at the K sensors and can be expressed as:

along the array and is defined by

φ=

y(n)=w Hx(n) ……………………………..(1)

2π

d cos θ ………………....(4)

λ

where d is the element spacing and λ is the wavelength of the received signal. The signal vector x(t) can be written as

where w=[w1 … wK] and x(n)=[x1(n) … xK(n)], H denotes Hermitian (complex conjugate) transpose. The weight vector w is a complex vector. The process of weighting these complex weights w1, …, wK adjusted their amplitudes and phases so that when added together they form the desired beam. Typically, the adaptive beamformer weights are computed in order to optimize the performance in terms of a certain criterion [4]. NonBlind algorithm: LMS have been taken into consideration for this work.

x(t ) = A.s (t ) …………………(5) The array output consists of the signal plus noise components, and it can be defined as

u (t ) = x(t ) + w(t ) ………………..(6) The spatial correlation matrix R of the observed signal vector u(t) can be defined as

In this paper we formulate a methodology of nulling interference using MVDR beamformer. Here, we generate the magnitude response and beam pattern of the signal using Adaptive Beamforming algorithm with MVDR beamformer. A block diagram of the proposed work is shown in Figure 2. The proposed model is equipped with five sensors with half wavelength spacing.

R = E u (t ).u (t ) H ………………(7) where E[ ] and H are the expectation and conjugate transpose operators, respectively. Substituting (4.5) into (4.6), the spatial correlation matrix R can now be expressed as

R = E A.s(t ).s (t ) H . AH + E w(t ).w(t ) H ….(8) With the implementation of MVDR beamformer ,this technique minimizes the contribution of the undesired interferences by minimizing the output power while maintaining the gain along the look direction to be constant, usually unity.

min E[ y (θ ) ] = min wH Ruu w, wH A(θ o ) = 1 (9) 2

Using Lagrange multiplier, the weight vector that solves equation (4.1) can be shown to be

w=

Ruu −1 A(θ ) ……………(10) AH (θ ) Ruu −1 A(θ )

Now the magnitude response of the array as a function of the DOA estimation, using MVDR beamforming method [14], is given by MVDR spatial spectrum as

Figure 2: Block diagram of the proposed system The array output will consist of the signal plus noise components. The signal vector x(t) can be defined as

dB =

x(t ) = ∑ a(θ m ).sm (t ) ………………..(2)

1 ……….(11) A (θ ) Ruu −1 A(θ ) H

2.1 Non-Blind Algorithm In a non-blind adaptive algorithm, a training signal, d(t), which is known to both the transmitter and receiver, is sent from the transmitter to the receiver during the training period [4]. The beamformer in the receiver uses the information of the training signal to

The array response to that source or array steering vector for that direction is given by

a (θ ) = [ e− jφ .....e− j ( N −1)φ ] …………….(3)


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variation of magnitude at different beamforming angles. The proposed approaches nearly provide similar results and track the variations properly. We also generated polar plots of received signals with MVDR approach, with with beamforming using LMS algorithm and without beamforming. Figure 4.4 shows that with the proposed beamforming method, the directive of the receiver antenna improves considerably .

compute the optimal weight vector. After the training period, data is sent and the beamformer uses the weight vector computed previously to process the received signal. Typical non-blind algorithms used are Wiener Solution, Method of Steepest-Descent, Least-MeanSquare (LMS), Normalized LMS (NLMS), Recursive Least-Square (RLS) algorithms, etc. [5]. 2.2 LMS algorithm

Comparing to the case when no beamforming is used (Figure 4), the proposed approach reduces power distribution along the side lobes as seen in Figure 8. Thus, from magnitude response and polar plot the proposed approach provides considerable improvement and is suitable for communication systems.

Because of its simplicity and robustness, the LMS algorithm has become one of the most popular adaptive signal processing techniques adopted in many applications including antenna array beamforming. Moreover, there is always a trade off between the speed of convergence of the LMS algorithm and its residual error when a given adaptation step size is used. The LMS algorithm is a popular solution used in beamforming technique. This algorithm is easy to implement with low computation and performs pretty well [2]. The basic LMS algorithm is expressed as

Table 1. Parameters used for the work

w(n+1)=w(n)+2µx(n)e(n)..……………….(12)

Desired Signal Angle

200

Interference Signal Angle

600

LMS Step-size Parameter

0.05

III. RESULTS AND DISCUSSION Matlab is used as the simulation tool. In this paper we considered MVDR beamformer consisting of a linear array of five uniformly spaced sensors. The spacing d between adjacent elements of the array equals one half of the received wavelength so as to avoid the appearance of grating lobes. The beamformer operates in an environment that consist of two components: a target(desired) signal impinging on the array along a direction of interest, and a source of interference. It is further assumed that these two components originate from independent sources and that the received signal consist of additive white gaussian noise. For our simulation we have taken the direction of interest to be at 20o and that for the interference signal to be directed at 60o respectively. The array response is taken in the direction of the desired signal.

Figure 3: Magnitude response without beamforming technique.

The spatial co-rrelation matrix R is calculated considering both the desired signal and interference components. Finally the weights are updated using the LMS algorithm. MVDR beamformer is utilized along with LMS algorithm as this technique is used to minimize the unwanted interference signal by minimizing the output power while maintaining the gain in the look direction at unity (as formulated in eq.9). We compared the magnitude response of the proposed method with that generated using LMS adaptive beamforming. Results show that main beams of both the responses are directed along the desired angle but the proposed method shows a better performance with narrower beamwidth and higher gain. Table 2 shows

Figure 4: Radiation pattern without beamforming.


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Figure 8: Radiation pattern with LMS Adaptive Beamforming using MVDR.

Figure 5: Magnitude response with LMS Adaptive Beamforming

Table 2: Magnitude vs angle response. Angle

Theory (dB)

LMS

-15.296

-13.76

-0.17

0

-0.60

-0.34

-0.26

0

-2.26

-1.26

-2.7

0

-20.01

-10.83

-10.54

0

-12.93

-36.47

-39.88

0

0 15 30 45 60

(dB)

Proposed (dB)

We compared the magnitude response when no beamforming, LMS Adaptive Beamforming and Adaptive Beamforming using MVDR appproach are used. Results show that main beams are directed along the desired angle but MVDR approach shows a better performance with narrower beamwidth and higher gain as shown in Figure 7. Table 2 shows variation of magnitude at different beamforming angles. The proposed approaches nearly provide similar results and track the variations properly. We also generated polar plots of received signals with and without beamforming. Figure 7 shows that with the proposed beamforming method, the directive of the receiver antenna improves considerably (around 200). Comparing to the case when no beamforming is used (Figure 4), the proposed approach reduces power distribution along the side lobes as seen in Figure8. Thus, from the magnitude response and polar plot the proposed approach provides considerable improvement.

Figure 6: Radiation pattern with LMS Adaptive Beamforming.

Figure 7: Magnitude response with LMS Adaptive Beamforming using MVDR.


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IV. CONCLUSION In this paper, we compared the magnitude response and beam pattern when no beamforming is used and when adaptive beamforming using MVDR is implemented. We have proposed the MVDR beamforming approach which helps to nullify interference and ensures that the signal passes through the beamformer undistorted. LMS algorithm is applied to MVDR application for better performance. Results show that when the proposed method is used the radiation pattern is better and more directed.

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