International Journal on Communications Antenna and Propagation (IRECAP), Vol., N.4 August 2 A Comparative Study on and Structures for Wideband Antenna Array Beamforming Shahriar Shirvani-Moghaddam, Nasrollah Solgi 2 Abstract In addition to a brief review on wideband digital beamforming, main purpose of this article is to evaluate and compare performance of two reference-based wideband beamforming structures, tapped delay-lines (s) and sensor delay-lines (s). To adaptively adjust array weights and beam pattern, normalized least mean squares (NLMS) algorithm that considers temporal sequence as reference signal is used. In order to compare and structures, 5 wideband signals are considered that one of m is desired source and or ones are interference signals. Besides absolute value of array factor (AF) for total bandwidth of signals and different angles, two well-known performance metrics, normalized mean square error () and signal to interference plus noise (SINR) are evaluated. Numerical results for both correlated and uncorrelated cases and also different bandwidths and number of branches as well as SNRs, show that higher performance can be achieved by compared to. Keywords: Digital adaptive array, Normalized least mean squares (NLMS), Sensor delay-line (), Tapped delay-line (), Wideband beamforming. Nomenclatures ) Input signal ) Weighted sum of received array signal ) Reference signal θ Signal angle of arrival φ Elevation angle Number of sensors in structure Number of sensors in structure Number of delays in structure Weight vector Delay between adjacent taps Angular frequency Spatial propagation delay Inter-element spacing Velocity of light, Inter-element spacing in structure Mean output power of desired signal Mean output power of noise Correlation matrix of signal Correlation matrix of interference Correlation matrix of noise, ) Array factor ) First order auto-recursive process I. Introduction Smart antenna is a multi-element antenna where signals received at each antenna element are intelligently combined to improve performance of wireless system [], [2]. These antennas can increase signal range, suppress interfering signals, combat signal fading, and increase capacity of wireless systems [3]. Furrmore, smart antenna system combines antenna array with digital signal processing capability to transmit and receive in an adaptive and spatially sensitive manner. Such a system automatically changes directivity of its radiation pattern in response to signal environment [4]. The main objective of a smart antenna is to implement an adaptive algorithm to dynamically achieve optimal weights of antenna elements that called beamforming [5]. Beamforming is an array signal processing technique to form beams in order to receive signals of interest (SOIs) from specific directions and attenuate interfering signals or signals not of interest (SNOIs) from or directions [6]. On or hand, smart antenna dynamically adjusts antenna array beam pattern, and can improve interference rejection. Thus beamforming by using sensor array is an effective method for suppressing interference whose angles of arrivals are different from looking direction [7],[8]. Beamformers can be categorized in different aspects. Foremost beamformers can be grouped according to bandwidths of signal environment. This can be eir narrowband or wideband (broadband). A beamformer for narrowband applications, that its signal bandwidth relative to its center frequency Manuscript received and revised xx 2, accepted xx 2 Copyright 2 Praise Worthy Prize S.r.l. - All rights reserved
is less than %, can be implemented using a linear array. In this scenario, we can steer its main beam to a desired direction by adding appropriate steering delays or phase shifts. Fig. shows a linear array configuration with M sensors that ) is input signal from direction, where array output ) is a weighted sum of received array signals. Narrowband beamforming is generally less complex and differ to broadband beamforming [9], []. Fig.. A general linear array structure considering weighting process. In a busy communication channel, signals can be eir narrowband or wideband. The wideband signal has a large bandwidth relativee to its center frequency up to 5%. One of major problems of future mobile communication systems is rapid increase in demand for different broadband services and applications same as third and fourth generations (3G and 4G) of mobile systems and broadband wireless systems such as WiMAX []-[3]. Use of frequency independent antennas becomes important in field of transmitting or receiving spread spectrum and wideband signals. The main requirement of wideband beamformer is, main beam pattern should be constant even re is a change in input signal frequency [4]. However, when bandwidth of signal is increased, structure in Fig. that works well for narrowband signals become less effective and beam pattern will change for different frequency components of communication wave without a suitable compensation technique [5]. Moreover, if signals are wideband, phase shifting networks may not be sufficient to provide desired output. This is because complex envelope of signal changes significantly across extent of array [6]. Recently broadband beamforming has found many applications in various areas rangingg from sonar and radar to wireless communications, and n we need use suitable structures for this case of beamformers [7]. Generally, we will need a series of tapped delay-lines (s) or finite impulse response (FIR) or infinite impulse response (IIR) filters in its discrete form to process each of received signals which can form a frequency dependent response for each of received broadband sensor signals to compensate phase difference for different frequency components [8]. In structure, delays between taps are being smaller and smaller with increasing signal bandwidth which leads to employ a very high speed circuit. For example, consider a general ultra-wideband (UWB) system with frequency range from to 6. If we perform beamforming in digital form, n, sampling rate should be at least 2. However, such a highh speed circuit cannot be efficiently implemented with current technologies. One possible solution is to replacee s by spatial propagation delays whichh are obtained by using more sensors behind original array. This structure is called sensor delay-lines (s) [8]-[2]. The rest of this paper is organized as follows. The broadband beamforming structures, s and s are reviewed in section II with more details. Comparative study based on numerical results of this investigation for uncorrelated broadband signals are reported in section III. Section IV shows and illustrates simulation results for correlated broadband signals. All simulation results of schemes in sections III and IV are compared based on two well-known performancee criteria, normalized mean square error () and signal to interference plus noise ratio (SINR). Finally, section V concludes this paper. II. Description of and Structures In structure, received signals are processed in temporal domain considering delays, which is equivalent to applying a FIR filter to each of received signals. Then, array can form a frequency dependent response for each of received broadbandd signals to compensate phase differencee for different frequency components. Fig. 2 shows general structure for broadband beamforming, in which is number of delay elements associated with each of sensor channels. The beamformer with such a structure sampless propagating wave field in both space and time domin [8], [9]. Fig.2. A general broadband beamforming structure by s [8]. Copyright 2 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol., N. 4
Then output ) can be written as: ) = ) () where =,,,, ) =,)..,)...,),) 2), and its response or array factor (AF) can be expressed as a function of signal angular frequency and direction of arrival angle, ) =, where is delay between adjacent taps of s and is spatial propagation delay between sensor and a reference point. For a uniform linear array (ULA) with an inter-element spacing, spatial propagation delay is given by: =, considering that first sensor position is phase reference point. structure can be applied to any kind of array especially for original linear array. This structure is a rectangular array system without s, since it is a broadband beamforming structure with spatial-onlin Fig. 3, which is information. Such a structure is shown an equally spaced rectangular array with sensors with an inter-element spacing of and, respectively. A complicated wideband beamforming system is able to be implemented by simple analogue circuits if we consider structure. This is especially useful when signal frequency and its bandwidth are very highh and a digital implementation becomes extremely difficult or even not viable at all (as mentioned in ). can also effectively avoid beam widening effect at high off-boresight angels. For example, for traditional structure, beamwidth will increase significantly when a broadside main beam is steered to an angle close to 9. However, in corresponding structure, we can rotate set of coefficients by 9 to form a main beam pointing to direction =9. Therefore, new beam will have same beamwidth and it has a full coverage over 36 azimuth range [ 9]-[23]. In this case, () and (2) are correct, but, (3) should be changed as follows:, ) =, ) ) 3) In above formulations, all signals are supposed to come from direction φ=. This means all signals are on same plane like rectangular array, i.e. elevation angle φ =. (4) Fig.3. A general broadband beamforming structure by s [8]. The coefficients (weights) for and structuress can be determined in different ways, depending on specific situation. We use case for which a referencee signal ) is available and weights are adjusted to minimize mean square error between beamformerr output ) and reference signal ) (Fig. 4). It is a classical adaptive filtering problem and can be solved by some existing adaptive algorithms such as least mean squares (LMS) or recursive least squares (RLS) algorithms. In our simulations, we use normalized least mean squares (NLMS) algorithm. The and SINR versus for and structures are presented in each simulation. Fig. 4. Reference signal-based beamformer. The formulation of SINR that used is as follow: = where is mean outputt power due to desiredd signal and is mean output power of array contributed by random noise and interferences that is: = = = = where, and are array correlation matrices due to signal source, unwanted interference, and (5) (6) 7) Copyright 2 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol., N. 4
random noise, respectively. Then SINR formulation can be written as:.9 = (8).8.7.6 III. Simulation Results for Uncorrelated Signals In this section, structure ( ==) is compared with structure ( = = ). The SOI comes from broadside and four SNOIs come from directions = [ 6, 3, 2, 4 ]. All signals have a bandwidth of [.4]. The signal to interference ratio (SIR) is about 2 and signal to noise ratio (SNR) is about 2. NLMS step size is.3. Fig. 5 and Fig. 6 show absolute value of AF for and structures, respectively. In wideband beamforming, AF is a function of two variables, frequency and angular location. Fig. 7. The learning curves of and structures..5.4.3.2. 5 5 2 25 3 - -2-3 5 5 2 25 3 Fig. 8. SINRs in different s for and structures. - AF[dB] -2 III.. The effect of bandwidth -3-4.4.6.8 Bandwidth 5 DOA(degree) - As shown in Fig. 9, increasing bandwidth is reason to increase in steady state of as well as. As expected, according to Fig., SINR is increased while signal bandwidth is decreased. This is same for and structures..9.8 [. ] [.5 ] [.9 ] Fig. 5. The Normalized AF for structure..7.6.5.4.3 AF[dB] - -2-3 -4.4.6.8 Bandwidth 8 6 4-2 2 DOA(degree) Fig. 6. The Normalized AF for structure. The (learning curve) and SINR criteria in different s are shown in Fig. 7 and Fig. 8, respectively. As depicted in se figures, convergence rate of learning curve of structure is lower than structure but its SINR is higher. -4-6 -8.2. 5 5 2 25 3.9.8.7.6.5.4.3.2. [. ] [.5 ] [.9 ] 5 5 2 25 3 Fig. 9. The for different normalized bandwidths. Copyright 2 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol., N. 4
5 - - [. ] [.5 ] [.9 ] -2 SNR= db SNR=- db -2 SNR=-2 db -3-3 5 5 2 25 3 5 5 2 25 3 - - [. ] [.5 ] [.9 ] -2 SNR= db SNR=- db SNR=-2 db -2-3 -3 5 5 2 25 3 Fig.. The SINR for different normalized bandwidths. III.2. The effect of signal to noise ratio The learning curves (s) and SINRs for different signal to noise ratios are shown in Fig., 2, respectively..9.8.7.6.5.4.3.2 SNR= db SNR=- db SNR=-2 db Fig. 2. The SINR for different SNRs. III.3. The effect of number of branches The and SINR versus number of s for different signal to noise ratios in both and structures are shown in Fig. 3, 4, respectively. 5 5 2 25 3.9.8.7.6.5.4.3.2. N=5 N= N=5 N=2. 5 5 2 25 3.9.8.7.6.5.4.3.2. SNR= db SNR=- db SNR=-2 db 5 5 2 25 3.9.8.7.6.5.4.3.2. N=5 N= N=5 N=2 5 5 2 25 3 Fig.. The for different SNRs. 5 5 2 25 3 Fig. 3. The for different number of branches. Copyright 2 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol., N. 4
5-2 - -2-3 N=5 N= N=5 N=2-3 correlated signal in teta=2 correlated signal in teta=-6-4 5 5 2 25 3-4 2 4 6 8 2 4 6 8 2-6 -8 - -2-22 -2-3 N=5 N= N=5 N=2-24 -26-28 -3-32 correlated signal in teta=2 correlated signal in teta=-6 5 5 2 25 3 Fig. 4. The SINR for different number of branches. -34-36 2 4 6 8 2 4 6 8 2 Fig. 6. The SINR in different s considering correlated signal. IV. Simulation Results for Correlated Signals Suppose that one of interference signals is correlated with desired signal by an AR() process with correlation coefficient =.5. Two cases are considered.9.8.7.6.5.4.3.2. correlated signal in teta=2 correlated signal in teta=-6 2 4 6 8 2 4 6 8 2.9.8.7.6.5.4.3.2. correlated signal in teta=2 correlated signal in teta=-6 2 4 6 8 2 4 6 8 2 Fig. 5. The in different s considering correlated signal. in this paper. First, nearest interference signal, located in =2, is correlated with desired signal and second case is that farst interference signal, located in = 6, is correlated with desired one. The simulation results for se cases are shown in Fig. 5, 6. It can be seen that performance of and structures is decreased with respect to uncorrelated cases. Obviously, while correlated interference signal is located in = 6, beamforming system offers a higher performance rar than or case. Correlation between desired signal and interference caused by multipath or jamming, limits applicability of weight estimation scheme. It means that beamforming algorithm fails. One of popular techniques to cancel an interference source that is correlated with signal is spatial smoothing. This preprocessing technique, also known as subarray averaging method, is employed in this investigation in order to build up rank of signal covariance matrix. The spatial smoothing method estimates weights of an -element antenna array system using an augmented array of more than elements, and is suitable for a uniform linear array [6, 24]. Fig. 7, 8 show effectiveness of spatial smoothing on performance, and SINR, of and structures, respectively. As depicted in se figures, is decreased and SINR is increased for smood signals with respect to correlated case. Copyright 2 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol., N. 4
Fig. 7. The in different s considering correlated signal and spatial smoothing..9.8.7.6.5.4.3.2. 2 4 6 8 2 4 6 8 2.9.8.7.6.5.4.3.2. correlated signal in teta=2 correlated signal in teta=-6 decorrelated signal in teta=2 decorrelated signal in teta=-6 2 4 6 8 2 4 6 8 2 - -2-3 correlated signal in teta=2 correlated signal in teta=-6 decorrelated signal in teta=2 decorrelated signal in teta=-6-4 2 4 6 8 2 4 6 8 2 - -2-3 correlated signal in teta=2 correlated signal in teta=-6 decorrelated signal in teta=2 decorrelated signal in teta=-6 correlated signal in teta=2 correlated signal in teta=-6 decorrelated signal in teta=2 decorrelated signal in teta=-6 2 4 6 8 2 4 6 8 2 Fig. 8. The SINR in different s considering correlated signal and spatial smoothing. V. Conclusions Recently, adaptive array antenna has been widely considered to improve quality of wireless radio signals and also to manage radio resources. In this paper, we focused on two and beamforming structures, appropriate for wideband radio signals. First, we evaluated performance of and structures based on and SINR criteria in case of uncorrelated sources. Also, effect of bandwidth, SNR and number of branches were investigated. It is shown that structure offers higher performance, lower and higher SINR, than structure in similar conditions. Simulations show following results: By increasing SNR, will be decreased and SINR will be converged faster. Increasing bandwidth is reason to decrease performance. Increasing number of or branches will increase performance, but, system will be more complicated. The number of s and s has an optimum amount that in our simulations optimum number is N=. In second part of simulations, we considered correlated signals and performance metrics were evaluated. Correlated signals degrade system performance in both and structures. This problem can be solved by using spatial smoothing to change correlated signals to uncorrelated ones. Simulation results of this investigation show that using spatial smoothing, performance will be improved. Acknowledgement We would like to thank Mr. Mahyar Shirvani- Moghaddam (University of Sydney) for great help he provided. References [] M.A. Doron, A. Nevet, Robust wave field interpolation for adaptive wideband beamforming, Elsevier Signal Processing, Volume 88 (Issue 6), June 28, Pages 57994. [2] V.K. Garg, S.R. Laxpati, D. Wang, Use of smart antenna system in universal mobile communications systems (UMTS), IEEE Antennas and Wireless Propagation Letters, Volume 3 (Issue ), December 24, Pages 66-7. [3] J.G. Stark, H.Y. Yang, Wide-band smart antenna design using vector space projection methods, IEEE Transactions on Antennas and Propagation, Volume 52 (Issue 2), December 24, Pages 3228-3236. [4] T. Do-Hong, P. Russer, Signal processing for wideband smart antenna array applications, IEEE Microwave Magazine, Volume 5 (Issue ), March 24, Pages 57-67. [5] J.H. Winters, Smart antenna techniques and ir application to wireless ad hoc networks, IEEE Wireless Communications, Volume 3 (Issue 4), August 26, Pages 77-83. Copyright 2 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol., N. 4
[6] L.C. Godara, Smart Antennas (CRC Press, 24). [7] K. Slavakis, I. Yamada, Robust wideband beamforming by hybrid steepest descent method, IEEE Transactions on Signal Processing, Volume 55 (Issue 9), September 27, Pages 45-4522. [8] A. Rawat, R..N. Yadav, S.C. Shrivastava, Design of dynamic phased array smart antenna using Fourierr series method, International Journal on Communications Antenna and Propagation (IRECAP), Volume (Issue ) ), February 2, Pages 3-6. [9] C.L. Koh, Broadband adaptive beamforming with low complexity and frequency invariant response, Ph.D. dissertation, Dept. of Electronics and Computer Science, Faculty of Engineering, University of Southampton, Southampton SO7 BJ, United Kingdom, October 29. [] W. Liu, S. Weiss, Beam steering for wideband arrays, Elsevier Signal Processing, Volume 89 (Issue 5), May 29, Pages 94-945. [] M. Ghavami, Wideband smart antenna ory using rectangular array structures, IEEE Transactions on Signal Processing, Volume 5 (Issue 9), September 22, Pages 243. [2] S. Shirvani-Moghaddam, M. Shirvani-Moghaddam, A comprehensive survey on antenna array signal processing, Journal of Trends in Applied Sciences Research, Volume 2, 2, Pages - 3. [3] S. Shirvani-Moghaddam, F. Akbari, A novel ULA-based geometry for improving AOA estimation, EURASIP Journal on Advances in Signal Processing, Volume 2 (39), August 2. [4] A.S. Srinivasa Rao, P. Mallikarjuna Rao, Design and analysis of non-uniform spacing broad-band antenna arrays using fractional Fourier transform, International Journal on Communications Antenna and Propagation (IRECAP), Volume (Issue ), February 2, Pages -7. [5] R.A. Monzingo, T.W. Miller, Introductionn to Adaptive Arrays (SciTech Publishing, 24). [6] S. Chandran, Wideband adaptive beamforming array with improved radiation characteristics, IEEE Transactions on Wireless Communications, Volume 4 (Issue 5), September 25, Pages 969-973. [7] L. Huang, B. Shen, M. Li, Z. Liu, An efficient subband method for wideband adaptive beamforming, The th International Conference on Advancedd Communicationn Technology (ICACT28), pp. 489-492, Gangwon-Do, China, February 7-2, 28. [8] Y. Zhao, W. Liu, R.J. Langley, Efficient design of frequency invariant beamformers with sensor delay-lines, The 5 th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM28), pp. 335-339, Darmstadt, 2-23 July 28. [9] Y. Zhao, W. Liu, R. Langley, An eigenfilter approach to design of frequency invariant beamformers, International ITG Workshop on Smart Antennas (WSA29), pp. -6, Berlin, Germany, February 6-8, 29. [2] W. Liu, Adaptive wideband beamforming with sensor delay-lines, Elsevier Signal Processing, Volume 89 (Issue 5), May 29, Pages 876-882. [2] N. Lin, W. Liu, R.J. Langley, Performance analysis of an adaptive broadband beamformer based on a two-element linear array with sensor delay-line processing, Elsevier Signal Processing, Volume 9 (Issue ), January 2, Pages 269-28. [22] W. Liu, Design of rectangular frequency invariant beamformerr with a full azimuth angle coverage, The 7 th European Signal Processing Conference (EUSIPCO29), pp. 57982, Glasgow, Scotland, August 24-28, 29. [23] Y. Zhao, W. Liu, Richard Langley, A least squares approach to design of frequency invariant beamformers, The 7 th European Signal Processing Conference (EUSIPCO29), pp. 844-848, Glasgow, Scotland, August 24-28, 29. [24] S. Chandran, Advances in Direction of arrival estimation (Artech House, 25) ). Authors information (Corresponding Author): Digital Communications Signal Processing (DCSP) Research Lab., Faculty of Electrical and Computer Engineering, Shahid Rajaee Teacher Training University (SRTTU), Lavizan, 67888, Tehran, Iran. Tel/Fax: +98 2 22976. Email: sh_shirvani@srttu.edu 2 Dig gital Communications Signal Processing (DCSP) Research Lab., Faculty of Electrical and Computer Engineering, Shahid Rajaeee Teacher Training University (SRTTU), Lavizan, 67888, Tehran, Iran. Shahriar Shirvani Moghaddam received B.Sc. degree from Iran University of Sciencee and Technology (IUST), Tehran, Iran and M.Sc.. degree from Higher Education Faculty of Tehran, Iran, both in Electricall Engineering, in 992 and 995, respectively. Also he received Ph.D. degree in Electrical Engineering from Iran University of Science and Technology (IUST), Tehran, Iran, in 2. He has more than 6 refereed international scientific journal and conference papers, 2 textt books on digital communications and one book chapter on MIMO systems. Since 23, he has been with Faculty of Electrical and Computer Engineering, Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran. He was nominated as best researcher and best teacher in SRTTU University in 2 and 2, respectively. Currently, he is an assistant professor in Digital Communications Signal Processing (DCSP) research laboratory of SRTTU. His research interests include digital signal processing, adaptive antenna beamforming, direction of arrival (DOA) estimation, and channel estimation of MIMO systems. Nasrollah Solgi received B.Sc. degree from Razi University of Kermanshah, Kermanshah, Iran, in 24, in Electrical Engineering. He is currently working toward M.Sc. degree at Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran. His current research interestss include wideband beamforming in adaptive antenna arrays. Copyright 2 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol., N. 4