Robust Interference Suppression Using a New LMS-Based Adaptive Beamforming Algorithm

Ali Hakam1, Raed Shubair1,2, Shihab Jimaa1 , and Ehab Salahat1

1Electrical and Computer Engineering Department, Khalifa University, Sharjah, UAE 2Center for Intelligent Antennas and Radio Systems, University of Waterloo, Canada

E-mails: Ali.Hakam.A@ieee.org, rshubair@kustar.ac.ae, ehab.salahat@ieee.org, saj@kustar.ac.ae

Abstract— This paper introduces a robust variable step size NLMS algorithm to improve interference suppression in smart antenna system. This algorithm is able to resolve signals arriving from narrowband sources propagating plane waves close to the array endfire. The results of the fixed step size NLMS will result in a trade-off issue between convergence rate and steady-state MSE of NLMS algorithm. This issue is solved by changing the step size from constant to variable. The proposed VSSNLMS algorithm reduces the mean square error (MSE) and shows faster convergence rate when compared to the conventional NLMS. Moreover, the enhanced performance of the new VSSNLMS algorithm is validated from the output beam pattern which introduces deeper nulls to mitigate the effect of interfering signals.

Index Terms— Smart antenna, Beamforming, NLMS, MSE, VSSNLMS.

I. .INTRODUCTION MART antenna have many benefits and critical roles in improving the performance concerning both capacity and range. With the development of communication systems,

there is a very high demand for greater data rates in modern communication and mobile systems. Many applications now depend on smart antenna technology as a vital solution for many reasons. This emphasizes the necessity to enhance both the speed and range of wireless links and has also encouraged interest in the deployment of used technologies. Smart antennas proved themselves as one of the most popular and leading advanced innovations for obtaining networks with high efficiency where capacity, quality, and coverage are improved to the optimum. Moreover, they provide higher capacity and performance than conventional antennas due to their use in customizing and fine-tuning the coverage of antenna configurations to change radio frequency (RF) or traffic conditions in any wireless system [1-3]. A smart antenna which is held in the base station of a mobile system comprises of a uniform linear array (ULA) antenna where the amplitudes are accustomed by a group of complex weights using an adaptive beamforming algorithm. The adaptive beamforming algorithm improves the output of the array beam pattern in a way which it maximizes the radiated power where it will be produced in the directions of the desired mobile users. Moreover, deep nulls are produced in the directions of undesired signals which symbolize co-channel interference from mobile users in the adjacent cells. Before adaptive beamforming, direction of arrival estimation is used to

specify the main directions of users and interferers [4-5]. Many adaptive beamforming algorithms are based on the conventional quadratic cost function such as Least Mean Square (LMS). The normalized LMS (NLMS) outperforms conventional LMS due to its enhanced convergence characteristics. This is due to the fact that NLMS uses a variable step-size parameter. The variation in the step-size is accomplished because of the division process at each iteration of the fixed step size by the input power [6-7]. This paper demonstrates that the combination between beamforming and VSSNLMS leads to better results than NLMS and all other LMS-based algorithms (LMS and VSS-LMS) in terms of interference suppression. The remaining part of this paper is structured as follows: Section II presents the mathematical derivation and theory of the NLMS and VSS-NLMS algorithms for improved beamforming, whereas in section III, simulation results which present MSE and output beam pattern of the antenna array are illustrated and discussed. Finally, the paper findings are summarized in section IV.

Figure 1: A plane wave incident on ULA of different number of equi-spaced sensors.

S

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II. ADAPTIVE BEAMFORMING

A. NLMS Algorithm The functionality of Normalized Least Mean Square (NLMS) adaptive algorithm is presented in Fig. 2. Where x(k) is the input signal, whereas y(k) is the output signal that is subtracted from the desired signal d(k) to calculate the error signal e(k). x(k) and e(k) are both combined in the NLMS algorithm that controls the adaptive beamformer behavior to reduce the mean square error (MSE). This procedure is repeated for a number of times until the steady state is reached [8].

Figure 2: Block diagram of an NLMS algorithm.

To illustrate the NLMS as an equation, the w(k) is considered as old weight vector of the filter at iteration k and w(k+1) is its updated weight vector at iteration k+1. We may then formulate the criterion for designing the NLMS algorithm as that of constrained optimization: the input vector x(k) and desired response d(k) determine the updated tap-weight vector w(k+1) so as to minimize the squared Euclidean norm of the change as [9] δ 푤(푘 + 1) = 푤(푘 + 1) −푤(푘), (1)

subject to the constraint:

푑(푘) = 푤 (푘 + 1)푥(푘). (2)

The method of Lagrange multiplier is used to solve this issue as follows:

푤(푘 + 1) = 푤(푘) + 휆 ∗ 푥(푘). (3)

Substituting equation (3) into equation (2) to find unknown multiplier휆:

휆 = ( )‖ ( )‖

. (4)

The error signal is shown as follow:

푒(푘) = 푑(푘) −푤 (푘)푥(푘) (5)

Next, by combining equation (3) and (4), the optimal values of the incremental change, δ 푤(푘 + 1) . The new equation will be written as follow:

푤(푘 + 1) −푤(푘) = ( ) ( )‖ ( )‖

(6)

We can write it as follow: 푤(푘 + 1) = 푤(푘) + ( ) ( )

‖ ( )‖ (7)

Sometimes x(k) which is the input signal becomes very small which may cause 푤(푘 + 1) to be unbounded. However, to avoid this situation; 휎 which is a constant value is added to the denominator which made the NLMS algorithm be described as 푤(푘 + 1) = 푤(푘) + ( ) ( )

‖ ( )‖ (8)

B. VSSNLMS Algorithm

The main aim of the developed Variable Step Size (VSS) NLMS algorithm is to replace the fixed step size µ that is used in NLMS by a variable one. This is to avoid a trade-off issue between convergence rate and steady-state MSE. In this algorithm a large step size is used in the initial stages to speed the rate of convergence and a smaller step size is used near to the steady state of the Mean Square Error (MSE) to obtain an optimum value [9]. To achieve this, µ is multiplied by P(k) which is randomly chosen from the uniform distribution [0 1] and each time of the N iteration times. Then to control the variable step value, it is multiplied by a curve function that is as follows:

휻(푘) =푘 − + 0.0011 ≤ 푘 ≤

0.001 ≤ 푘 ≤ 푁

Where N is the input signal number.

Figure 3:Distribution of 휻 (k)

It shown that in the first part, the curve will be quickly decreased from 1 to 0.001 as shown in Fig. 3. In this stage, the system requires large values of step size. This is to make the system converge to the steady-state as fast as possible and requires small values of step size when reaching close to the steady state. Then, The slope of this curve must not be too steep; if not this will lead to small values of step size where as the system still requires large values. In the interval of steady state, the system requires the step size to preserve a small value but must not down to zero to reduce the steady-state MSE. For that reason, the curve is generated to preserve a small value (0.001) in a steady state. Next, by Multiplying equation (9) by the random numbers P(k) and the normalized step size parameter 휇, the variable step size develops to:

휇(푘) = 푃(푘)휻(푘)휇

Substituting the variable step size (10) to the conventional fixed step size NLMS algorithm (8), the proposed algorithm is shown as:

푤(푘 + 1) = 푤(푘) + ( ) ( ) ( )‖ ( )‖

Transversal Filter

NLMS Algorithm

Σ푥(푘)푦(푘)

푑(푘)

푒(푘)

−

+

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of Iterations

Val

ue

(9)

(11)

(10)

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III. SIMULATION RESULTS A. Comparison of MSE for NLMS and Proposed VSSNLMS

In VSSNLMS algorithm, the value of the step size changes with time, while in standard NLMS algorithm the value of the step size is fixed. Figures 4 and 5 show that the convergence is faster when the adaptive VSSNLMS algorithm is used rather than NLMS algorithm. However, as seen from Figure 5, VSSNLMS algorithm requires more processing time for updating the tap weights.

Figure 4: Error vs. iterations for NLMS algorithm.

Figure 5: Error vs. iterations for VSSNLMS.

Then, the obtained results by using a ULA which is the most simple antenna configuration with N = 5 elements. The inter-element spacing d =0.5λ. The maximum output radiation of source signal arriving at an angle θS = 0.the values of SNR (signal to noise ratio)= 20dB. The goal is to diminish an interference signal which is arriving at an angle θI = -60. The value of SIR = -10dB (signal-to-interference ratio). The Step size Parameter µ = 1. µ = 1 leads to the best performance by using NLMS algorithm and that shown in part B from this section and Also According to [8][9], it seems that µ = 1 gives the best results in equalization system for NLMS, No. of iteration = 3000. VSSNLMS algorithm was simulated with the same parameters that as used in NLMS algorithm, but with variable µ.

B. Beampattern Comparison for NLMS and proposed VSSNLMS

By comparing beampattern results in Figures 6 and 7 for the NLMS and proposed VSSNLMS, respectively, it is clearly shown that the proposed VSSNLMS outperforms NLMS. This takes the form of deeper nulls.

Figure 6: Array beam pattern using NLMS algorithm.

Figure 7: Array beam pattern using VSSNLMS algorithm

Both of the beampattens are simulated with same parameters which are used in the previous part. We can see that the normalized power at -60o is approximately -60 dB by using NLMS algorithm. When the proposed VSSNLMS is used we can see that the difference is around 30 dB and the normalized power is around -90 dB. This is an enhanced improvement which leads to deeper nulls towards interfering signals. These results explain that the VSSNLMS beamformer is capable of iteratively update the weight of array. This is to work on forcing a deeper null in which are in the direction of the interference signal -60o when compared with NLMS beamformer. Also, Figure 8 shows beam patterns of VSS-NLMS and different number of NLMS beam patterns with different µ. It shown that VSSNLMS leads to better interference suppression due to deeper nulls produced in the directions-of-interfering-signals.

0 500 1000 1500 2000 2500 3000-200

-150

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-50

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100Error vs. Iterations for NLMS

No.of Iterations

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r (dB

)

0 500 1000 1500 2000 2500 3000-200

-150

-100

-50

0

50

100Error vs. Iterations for VSSNLMS

No.of Iterations

Erro

r (dB

)

-80 -60 -40 -20 0 20 40 60 80-90

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Beampattern Using NLMS Adaptive Beamforming Algorithm

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Beampattern Using VSSNLMS Adaptive Beamforming Algorithm

Normalized Power = - 60 dB

Normalized Power = - 90 dB

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Figure 8: Beampattern using NLMS+VSSNLMS Adaptive Beamforming Algorithm to diminish interference signals at θI = -60, -20, 20, 60.

Also, we make the procedure here more complicated. We put the goal now is to diminish an interference signals which is arriving at an angle θI = -60o, -20o, 20o, 60o. We specify four interference signals and with the same parameters which are used before. It shown from Fig. 8 that VSSNLMS works on diminishing an interference signal which is arriving at an angles -60o, -20o, 20o, 60o.

TABLE 1: NORMALIZED POWER IN dB OF SELECTED NULLS.

Interference signal -60 o -20 o 20 o 60 o NLMS u=0.2 none -36.14 -43.25 none NLMS u=0.4 -38.11 -36.72 -39.97 -39.23 NLMS u=0.6 -44.02 -44.36 -44.77 -39.34 NLMS u=0.8 -48.93 -45.92 -46.32 -47.89 NLMS u=1.0 -55.04 -56.79 -54.66 -53.57 VSSNLMS -86.6 -80.0 -74.98 -79

The previous table has shown all the normalized power in dB by using VSSNLMS and different cases of NLMS. At least, there is 20 dB deference at any null. In Fig 9, the first null from Fig.8 is shown. It is clear that the VSSNLMS outperforms NLMS and leads to deeper nulls towards interfering signals.

Figure 9: Null towards interfering signal at θI = -60o

In general, the proposed VSSNLMS shows a great improvement in the case of single and multiple interference signals. Also, the VSSNLMS leads to better interference suppression when it is compared with different cases of using NLMS as a beamformer with different µ.

IV. CONCLUSION

The paper presented and analyzed the use of a new variable step size normalized least mean square VSSNLMS algorithm in the design of adaptive beamforming smart antenna system for interference suppression. The used VSSNLMS algorithm enhances the performance of the smart antenna by reducing the mean square error (MSE) which results in faster convergence rate when compared to NLMS algorithm. The robust performance of the developed VSSNLMS algorithm takes the form of better interference suppression due to deeper nulls produced in the directions of interfering signals.

REFERENCES [1] L. Haitao, S. Gao and T.-H. Loh, "Small Director Array for Low-Profile

Smart Antennas Achieving Higher Gain," IEEE Trans. on Antennas and Propagation, vol. 61, no. 1, pp. 162-168, Jan, 2013.

[2] T. S. Rappaport, Wireless Communications: Principles and Practice, NJ: Prentice-Hall, 1996, 1996.

[3] J. H. Winters, "Smart antenna techniques and their application to wirelessad-hoc networks," IEEE Trans. on Wireless Communications, vol. 13, no. 4, pp. 77-83, 2006.

[4] M. R. Yerena, "Adaptive wideband beamforming for smart antennas using only spatial signal processing," in 15th International Symposium on Antenna Technology and Applied Electromagnetics, Toulouse, France, June, 2012.

[5] A. Hakam, R. Shubair and E. Salahat, "Enhanced DOA Estimation Algorithms Using MVDR and MUSIC," in IEEE International Conference on Current Trends in Information Technology (CTIT'2013), Dubai, UAE, 2013.

[6] H. Takekawa, T. Shimamura and S. Jimaa, "An efficient and effective variable step size NLMS algorithm," in 42nd Asilomar Conference on Signals, Systems and Computers, October, 2008.

[7] S. Jo. and K. S. W. Kim, "Consistent normalized least mean square filtering with noisy data matrix," IEEE Trans. Signal Process, vol. 53, no. 6, p. 2112–2123, June, 2005.

[8] S. Haykin, Adaptive Filter Theory, Prentice-Hall, 2002. [9] T. Arnantapunpong, T. Shimamura and S. A. Jimaa, "A New Variable

Step Size for Normalized NLMS Algorithm," in Int. Workshop on Nonlinear Circuits Communications and Signal Processing, Hawaii, USA, March, 2010.

-80 -60 -40 -20 0 20 40 60 80-100

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NLMS u=0.2NLMS u=0.4NLMS u=0.6NLMS u=0.8NLMS u=1VSSNLMS

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NLMS u=0.2NLMS u=0.4NLMS u=0.6NLMS u=0.8NLMS u=1VSSNLMS

The difference is shown in figure 9.

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