06095424

7/30/2019 06095424

http://slidepdf.com/reader/full/06095424 1/5

MUSIC Algorithm for DOA Estimation

Using MIMO Arrays

Azardokht ZaherniaShiraz University of Technology

Shiraz, [email protected]

Mohammad Javad Dehghani Shiraz University of Technology


Reza Javidan

Shiraz University of Technology


Abstract—In this paper MUSIC algorithm by using of multi-

input multi-output (MIMO) arrays is investigated and itsperformance is compared with conventional arrays. The

parameters involved in this comparison are: the number of the

snapshots and array elements, and the SNR values. MIMO

configuration with spatially orthogonal signal transmission isequivalent to additional virtual sensors which extend the array

aperture with virtual spatial tapering. These virtual sensors canbe used to form narrower beams with lower sidelobes and,

therefore, provide higher performance in target detection,

angular resolution, and angular estimation accuracy. Simulation

results on prototype data showed the superiority of MUSICalgorithm performance; that is without requirement to increasethe SNR value or the elements and snapshots number, high

performance is simply possible by means of MIMO arrays.

Keywords- MIMO Array, MUSIC algorithm; DOA Estimation;

SNR Value, Snapshots number; Elements Number.

I. INTRODUCTION

Accurate estimation of signal direction-of-arrival (DOA) has received considerable attention in communication andradar systems of military and commercial applications.Mobile communication, radar, sonar, and seismology are afew examples of the many possible applications. Forexample, in defense application, it is important to determinethe direction of a possible threat. One example of commercialapplication is to localize the direction of an emergency phonecall to dispatch a rescue team to the proper location [1, 2].

Using a fixed antenna that refers to start of DOA estimationappearance had many limitations that explained in [3]. As aresult, utilization of an antenna array with innovative signalprocessing instead of using a single antenna has beenexpanded [4]. An array sensor system has multiple sensorsdistributed in space. This array configuration provides spatialsamplings of the received waveform. A sensor array hasbetter performance than the single sensor in signal reception,parameter estimation, and resolution of a signal DOA [4].

There are two basic antenna configurations: linear and

circular arrays [5]. In the former the elements are arrangedalong a straight line; in the latter the elements are placedcircularly [5]. From another viewpoint the arrays arecategorized to two set: active and passive arrays [6]. Activearrays transmit a directional beam, and the target echo signalis processed in the receive mode. In passive arrays targetdetection and localization is only performed by array

processing of the received signal without any signaltransmission to targets [6].

Antenna arrays with signal processing algorithms canaccurately estimate the DOA. There are many different superresolution algorithms including spectral estimation, modelbased, and eigen-analysis [7]. MUSIC (MUltiple SIgnalClassification) [8] and its variants are popular methods forDOA estimation. They are based on subspace analysis, andcan be applied even for mixed signals as long as there arefewer source signals than sensors.

In the last two decades, array processing of the receivedsignal has been greatly investigated (see, for example, [9]). If the transmitted signals are spatially coded, spatiallyorthogonal signals, array processing in both receive andtransmit modes is possible [10]; therefore digitally steeringthe beam pattern in the transmit mode in addition to receivedsignal is provided. This concept can be actualized by multipleinput-multiple output (MIMO) arrays [10]. It has beenrecently proved that multiple-input multiple-output (MIMO)antenna systems have the potential to dramatically improvethe performance of conventional antenna arrays [10-12]. Themain advantages of MIMO configuration are as follows [12]:

• Digital beamforming of the transmitted beams in

addition to the received beams, therefore preventing beam

shape loss;

• Extension of the array aperture by virtual sensors,

therefore acquiring narrower beams;

• Virtual spatial tapering of the extended array aperture,

therefore acquiring lower side lobes;

• Improvement of the angular resolution by using the

information in the transmit and the receive modes;

• Increasing the upper limit on the number of targets

which can be detected and localized by the array (this isassociated with the virtual sensors);

• Decreasing the spatial transmitted peak power density.

In this paper significant improvement of MUSICperformance by MIMO array has been demonstrated. In

many papers, MUSIC algorithm performance in terms of itsinput parameters such as SNR value and the number of thesnapshots or sensors has been comprehensively investigated(for example, see [13-14]). According to these papers theperformance of the algorithm can be enhanced by increasingof the SNR value or the number of the sensors or snapshots.As mentioned above MIMO arrays structure contains some

The 6th International Conference on Telecommunication Systems, Services, and Applications 2011

978-1-4577-1442-9/11/$26.00 ©2011 IEEE 149

7/30/2019 06095424


advantages that indirectly provide these options. In this paperMIMO array signal model is investigated and by simulationaccomplished in MATLAB, the performance enhancement of MUSIC algorithm by MIMO configuration is obviouslydemonstrated.

II. MIMO ARRAY SIGNAL MODEL

The signal vector received in MIMO array with M receiving

sensor and N transmitter sensor is obtained as follows [9]:

(1)

In the above equation denote the location of the

far-field targets with K being the number of the targets at a

particular range bin of interest; a(θ ) CM×1

and b(θ ) CN×1

are the steering vectors for the receiving and transmitting

sensors, respectively; ( )T

determines the vector or matrix

transpose; are the target complex amplitudes; s[l] is

the transmitted narrowband signal vector; w[l] is the noise

and interference term, which includes the response due to the

targets at other range bins; and l=1, …, L; where L is thesnapshot number. It is assumed that w[l] is independent and

identically distributed complex gaussian random vector with

mean zero and covariance . xrm=(x(1)

rm ,x(2)

rm)T

and xtn =(x(1)

tn , x(2)

tn)T

denote the locations of the mth receive

sensor and the nth transmit sensor, respectively (Fig.1[11]).

III. VIRTUAL APERTURE EXTENSION

Let τ rm identify the delay from the mth receiving sensor to

the target and τ tn from the target to the nth transmitting

sensor. The entire delay from the nth transmitting sensor to

the mth receiving sensor are τ rm+ τ tn, so, the delay vector for

all the combinations of the transmitting and receiving sensors

can be written as [11]:

(2)

The steering vector corresponding to the delay vector is:

(3)

Fig.1. MIMO array configuration [11].

The transmitting and receiving steering vectors are defined

respectively as:

(4)

(5)

v=a b (6)

where the is Kronecker product.

Since the combination number of all the receiving and

transmitting sensors is M×N , MIMO steering vector can be

considered as the spatial convolution of the receive and

transmit steering vectors providing an augmentation of the

conventional array steering vectors. The mnth element of the

MIMO array steering vector corresponding to the m×nth

delay combination can be written as:

(7)

and

(8)

where and λ stands for the signalwavelength. Thus, the MIMO array response consists of virtual sensors located at the combinations of xrm+ xtn.Therefore, the array aperture is virtually extended.

(a)

(b)

Fig.2. (a) Conventional array aperture M = 3, L = 1. (b) MIMO array

aperture for orthogonal signals M=N=3, L = 1; ×-points: actual sensors, o-

points: virtual sensors. Two sensors are located at points B, C, E [11].


978-1-4577-1442-9/11/$26.00 ©2011 IEEE 150

7/30/2019 06095424


The steering vector relation clearly shows that in practicethe MIMO array looks like a conventional array with M×N sensors at different locations corresponding to all possiblecombinations of xrm+ xtn.

In order to illustrate these advantages, in [12] an example

with three array elements ( M=3) which are placed at vertexes

of an equilateral triangle by one target ( L=1) was examined.

In Fig.2 [12] the equivalent array structure for conventional

and MIMO arrays is displayed, respectively. As mentioned

above, the equivalent array for MIMO includes all transmit–

receive combinations of xrm+xtn. This is equivalent to an

extended array, whose elements are located

at . Thus the equivalent array consists of

virtual sensors in addition to the actual sensors.According to (2), the total number of delays is nine,representing nine different virtual sensors. In thisconfiguration, we acquire three sensors at the actual sensorlocations (points A, B, C ), three virtual sensors at newlocations (points D, E, F ), and three additional virtual sensorsat other sensor locations (points B, C, E ). Finally, the virtualaperture of the MIMO array is produced by nine sensors (sixof them are at different locations), compared to three sensorsof the conventional array.

IV. SIMULATION RESULTS

To investigate practically the higher performance of MUSIC algorithm with MIMO array against conventionalmethod, simulation is performed using MATLAB software.The simulation is performed under these conditions:

A uniform linear array under frequency equal to 40kHz andthe inter-element spacing equal to λ /2= 0.04m is used toestimate the direction of a pair plane waves from narrowbandand farfield sources with input angle equal to (40°, 50°). TheSNR value, the elements and snapshots number are variedamong several different quantities. For each SNR, theelements and snapshots number the ULA is examined in thetwo forms: conventional and MIMO array; therefore these

two arrays in all parameters are identical. In conventionalconfiguration M transducer is used as receiving sensors; inMIMO structure those transducers are used as receiving andalso transmitting sensors, i.e. M=N . Orthogonal signalstransmit toward two aiming targets, and the target echo signalis processed in the receive mode.

The diagrams of Fig.3 which obtained from one timed

program running, intuitively show the considerable advantage

of MIMO configuration as compared to conventional one.

The failure of conventional array against of the success of

MIMO array can be clearly seen from these diagrams.Fig.3 (a) shows MUSIC spectrum in MIMO and

conventional array with a low SNR (equal to -20db). In spiteof the little amount of SNR, MUSIC algorithm in MIMO

configuration can exactly resolve the received angles withoutany problem whereas in conventional array, the spectrum isso smooth and there isn’t any sharp peak corresponding to theinput angles.

There is similar condition about the number of elementsand snapshots. Fig.3 (b) and (c) represent the MUSIC

spectrum in a few number of the elements and snapshot,( M=3, K=20). These figures obviously illustrate MIMO arrayeven by using of small number of elements or snapshots canaccurately detect and localize the received signals; whereas inconventional array, little number of elements or snapshotscause MUSIC algorithm to fail completely.

For more accurate analysis, the two above mentioned arraysare employed to estimate DOA in several different values of SNRs and the number of the elements and snapshots. The

angles of two target signals are equal to (40°, 50°). DOAestimation is repeated in the process of 100 independentMonte-Carlo examinations. The means, variances, errors(rms) and the resolution probabilities are measured. Theresults have been represented in the Tables I-VI. In Tables Iand II MUSIC performance in the two arrays is compared fordifferent SNR values. The minimum SNR value inconventional array is selected equal to 6; because in negativeSNRs the success percent is so low (nearly 0%). Tables IIIand IV compare the two arrays in different elements number;and Tables V and VI compare the two arrays in differentsnapshots number.

The means related to the tables of conventional array are farfrom the exact incoming values. Whereas the mean values of

MIMO array are so close to exact values. So if the SNR valueis low or only small number of the elements and snapshotsare available, precise DOA estimation is simply possible byusing of MIMO configuration.

-100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100-20

-15

-10

-5

0

MUSIC spectrum in conventional and MIMO array with SNR=-20

Angles(degree), target angles=(40,50)

M U S I C

s p e c t r u m ( d b )

Conventional Array Spectrum

MIMO Array Spectrum

(a)

-100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100-60

-50

-40

-30

-20

-10

0

MUSIC spectrum in conventional and MIMO array with M=3

Angles(degree),target angles=(40,50)

M U S I C s

p e c t r u m


MIMO Array Spectrum

(b)

-100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100-40

-30

-20

-10

0MUSIC spectrum in conventional and MIMO array with K=20

Angles(degree), target angles=(40,50)

M U S I C

s p e c t r u m


MIMO Array Spectrum

(c)

Fig.3. MUSIC performance in MIMO array in comparison withconventional one.


978-1-4577-1442-9/11/$26.00 ©2011 IEEE 151

7/30/2019 06095424


TABLE I. MUSIC PERFORMANCE IN CONVENTIONAL ARRAYWITH DIFFERENT SNR VALUES, (θ1,θ2)= (40°, 50°).

TABLE II. MUSIC PERFORMANCE IN MIMO ARRAY WITHDIFFERENT SNR VALUES, (θ1,θ2)= (40°, 50°).

TABLE III. MUSIC PERFORMANCE IN CONVENTIONAL ARRAYWITH DIFFERENT ELEMENTS NUMBER, (θ1,θ2)=(40°,50°).

TABLE IV. MUSIC PERFORMANCE IN MIMO ARRAY WITHDIFFERENT ELMENTS NUMBER, (θ1,θ2)=(40°,50°).

Elements

NumberMean Variances Error(rms) Success

Percent

340.0002

50.0002

0.2298×10-7

0.2298×10-7

0.4879×10-3

0.4879×10-3 100%

440.0003

50.0003

0.2041×10-7

0.2041×10-7

0.3174×10-3

0.3174×10-3 100%

540.0003

50.0003

0.2237×10-7

0.2237×10-7

0.2215×10-3

0.2215×10-3 100%

640.0002

50.0002

0.2429×10-7

0.2429×10-7

0.2689×10-3

0.2689×10-3

100%

740.0003

50.0003

0.1753×10-7

0.1753×10-7

0.1225×10-3

0.1225×10-3 100%

TABLE V. MUSIC PERFORMANCE IN CONVENTIONAL ARRAYWITH DIFFERENT SNAPSHOTS NUMBER, (θ1,θ2)=(40°,50°).

TABLE VI. MUSIC PERFORMANCE MIMO ARRAY WITHDIFFERENT SNAPSHOTS NUMBER, (θ1,θ2)=(40°,50°).

SNR

Value Mean Variance Error(rms) Success

Percent

6 32.1002

49.0669

1.1024×103

0.0060×103

33.5871

2.581926.67%

8 40.5336

49.5003

0.0006×103

0.0005×103

0.9311

0.8365

43.33%

10 40.2003

49.2003

0.0004×103

0.0004×103

0.6832

0.605556.67%

12 40.0336

49.7003

0.0002×103

0.0004×103

0.4830

0.7070

76.67%

14 40.0336

49.9336

0.0001×103

0.0001×103

0.3162

0.365190.00%

SNR

ValueMean Variance Error(rms) Success

Percent

-30 39.6669

49.7669

1.8850

2.4609

1.3904

1.559930%

-25 40.1336

50.2002

0.3953

0.4413

0.6325

0.683250%

-20 40.0002

49.9336

0.2069

0.1333

0.4472

0.365190%

-15 40.0002

50.0002

0.0009

0.0009

0.0003

0.0003100%

-10 40.0002

50.0002

0.0004

0.0004

0.0003

0.0003100%

Elements

NumberMeans Variances Error(rms) Success

Percent

3-28.0397

50.7403

4.2502×103

0.0498×103

93.7796

7.02712.00%

4-14.4998

47.8202

4.2137×103

0.0131×103

84.2595

7.197512.00%

532.4602

49.1602

0.9777×103

0.0044×103

31.8593

6.236028.00%

640.2603

49.8003

0.0005×103

0.0006×103

1.4000

1.4690 52.00%

740.1603

49.9003

0.0002×103

0.0003×103

1.0003

1.244974.00%

SnapshotsNumber

Means Variances Error(rms) SuccessPercent

103.9003

48.1403

3.5000×103

0.0078×103

68.7983

3.3375

24.00%

2035.1802

49.2402

0.6670×103

0.0006×103

26.0165

1.0945

50.00%

3037.7402

49.3402

0.3404×103

0.0008×103

18.4027

1.1044

46.00%

4040.3003

49.8403

0.0004×103

0.0003×103

0.7072

0.5999

64.00%

5040.0203

49.8003

0.0003×103

0.0002×103

0.5099

0.5291

82.00%

SnapshotsNumber

Means Variances Error(rms) SuccessPercent

1040.0003

50.0003

0.2136×10-7

0.2136×10-7

0.2988

0.2988100%

2040.0002

50.0002

0.1760×10-7

0.1760×10-7

0.2599

0.2599100%

3040.0003

50.0003

0.1873×10-7

0.1873×10-7

0.2929

0.2929100%

4040.0003

50.0003

0.2446×10-7

0.2446×10-7

0.3093

0.3093 100%

5040.0002

50.0002

0.2624×10-7

0.2624×10-7

0.3081

0.3081100%


978-1-4577-1442-9/11/$26.00 ©2011 IEEE 152

7/30/2019 06095424


V. Conclusion

In this paper the improvement of MUSIC algorithm by

means of MIMO array is investigated. It has been shown that

by using of MIMO configuration the achievement to high

performance of the MUSIC algorithm is possible without

requirement to utilization of more elements, snapshots orhigh SNR. Simulation results demonstrate in SNR= -20 even

super-resolution algorithms like MUSIC fails to estimate

DOA. There is a similar condition about the elements andsnapshot number; by M=3, or K=20 the sharp peaks

corresponding to incoming angles in the MUSIC spectrumcompletely disappear. But MIMO array results in this same

condition are considerable; MUSIC algorithm in MIMO

configuration can easily detect and localize the input angles

with high accuracy. The algorithm is repeated in 100

independent Monte-Carlo tests and the means, variances,

errors and resolution probability is computed. Obtained

results confirm the significant enhancement of performance

by using of MIMO arrays.

REFRENCES

[1] R. Boyer and G. Bouleux, “Oblique projections for Direction-of-Arrivalestimation with prior knowledge,” IEEE transactions on signal processing,

VOL. 56, NO. 4, April 2008.

[2] Y. Wu, H. Liu and H. C. So. “Fast and Accurate Direction-of-ArrivalEstimation for a single source,” Progress In Electromagnetics Research C,Vol. 6, 13–20, 2009.

[3] M. Grice, Direction Of Arrival estimation using super-resolutionalgorithms, MSc.Thesis, California State Polytechnic University, Pomona,2007.

[4] Z. Aliyazicioglu, H.K. Hwang. M. Grice, A. Yakovley, “Sensitivityanalysis for direction of arrival estimation using a Root-MUSIC algorithm,”Engineering Letters, 16:3, EL_16_3_13, 2009.

[5] F. Belloni, A. Richter and V. Koivunen, Performance of ROOT-MUSICalgorithm using REAL-WORLD arrays, Signal Processing Laboratory,SMARAD CoE, Helsinki University of Technology (HUT) Otakaari 5A,02150, Espoo, Finland, 2006.

[6] A.D Waite, SONAR for practicing engineers, John Wiley &Sons Ltd,Baflhs Lane, Chichester, West Sussex PO19 l, England, Third Edition, 2002.

[7] D. H. Johnson, Dan E. Dudgeon, Array signal processing concepts andtechniques," P T R Prentice Hall Inc, A Division of Simon & SchusterEnglewood Cliffs, New Jersey 07632, 1993. [8] R. A. Schimidt, Signal subspace approach to multiple emitter locationand spectral estimation, Ph.D. dissertation, Stanford University,StandfordCalif, 1981.

[9] S. Haykin, J. Litva, and T. J. Shepherd, Radar Array Processing, NewYork: Springer-Verlag, 1993.

[10] J. Huang et al., “Performance analysis of DOA estimation for MIMOSONAR based on,” IEEE/SP 15th Workshop on Statistical SignalProcessing, pp. 269-272, Aug 2009.

[11] M. Jiang, J. Huang, W. Han and F. Chu, “Research on Target DOAEstimation Method Using MIMO Sonar," Conference on IndustrialElectronics and Applications 4th IEEE, pp. 1982-1984 May 2009.

[12] I. Bekkerman and J. Tabrikian, “Target Detection and LocalizationUsing MIMO Radars and Sonars,” IEEE Trans. On Signal Processing, vol.54, no. 10, Oct., pp. 3873-388, 2006.

[13] J. M. Samhan, R. M. Shubair, and M. A. Al-Qutayri, “Design andimplementation of an adaptive smart antenna system, innovation ininformation technology,” IEEE, pp.1-4, Nov 2006.

[14] MI-Ardi Ebrahim, Raed M. Shubair, and E. Al. M. Mohammed,“Performance evaluation of Direction Finding algorithms for adaptiveantennas,” Conference on Electronics, Circuits and Systems proceedings of the 10th IEEE International, VOL 2, pp. 735-738, Dec 2003.


978-1-4577-1442-9/11/$26.00 ©2011 IEEE 153

06095424

Documents