Direction-of-arrival estimation method based onsix-port technology

S.O. Tatu, K. Wu and T.A. Denidni

Abstract: A new direction-of-arrival estimation method based on six-port technology is presented.In order to obtain the beam direction, the proposed circuit uses a two-channel multi-band receiverand analogue signal processing of the six-port circuit output signals. A practical approach forestimating the beam direction has also been proposed. This approach, based on the detection of theminimum magnitude of the in-quadrature output signal, avoids the necessity of computing theangle-of-arrival value. A dual-band prototype circuit was designed and fabricated. Simulationresults in the S and C frequency bands are presented and discussed. In order to validate thismethod, measurements were carried out in the C-band. These results show a maximal angle-of-arrival estimation error of about 3%. Therefore, low-cost direction-of-arrival measurements can beperformed using this new method.

1 Introduction

During recent years, scientific and technical interest in six-port technology has been increasing, owing to its ability toperform accurate low-cost microwave measurements [1] andits broad range of applications. Various studies have beendone for different applications such as direct conversionreceivers, radar sensors and beam-direction-finding circuits.

In the field of direct conversion receivers, the six-portcircuit was initially used to perform direct demodulation ofQPSK signals [2, 3]. Then the direct demodulation of Ka-band MPSK/QAM high data-rate signals was successfullyachieved [4]. Recently higher-frequency six-port circuitshave also been designed for W-band collision-avoidanceradar sensor applications [5].

A direction-finding antenna system using a six-portjunction operating as a homodyne vector analyser has beenpresented in [6]. For this purpose, a conventional six-portring architecture with three ‘qi points’ was used. This systemuses numerical computation of the circuit output signalsand a laborious calibration procedure: this approach stemsfrom early six-port applications as a low-cost networkanalyser [1]. In spite of this calibration procedure, thereported error was around 2%.

More recently, a novel method has been proposed tocalibrate the six-port-based wave correlator by using aphase shifter connected to one of the input ports [7]. In thiswork, a conventional (three ‘qi points’) six-port circuit witha different architecture was used and an improvedmeasurement error of 0.5% was reported.

The main purpose of this paper is to demonstrate thata comparable angle-of-arrival estimation error can beobtained using a low-cost circuit based on a different six-port architecture ( four ‘qi points’) and a new simpler signalprocessing approach.

A new multi-band circuit for both direct conversion andbeam-direction-finding applications was recently designedby the present authors. This new six-port circuit iscomposed of four 901-rounded hybrid couplers and isfabricated using monolithic hybrid microwave integratedcircuit (MHMIC) technology [8]. In the present paper, thisnew six-port architecture and analogue signal processing(ASP) of the output voltages are used to design a low-cost/high-performance circuit operating in two different (S and C)frequency bands. Initial S-band results were presented in aprevious conference paper [9].

Simulation and measurement results are presented anddiscussed in the following Sections. The six-port simulationmodel obtained using the S-parameter finite elementmethod was validated by measurements performed on thefabricated circuit [8]. In order to demonstrate this newdirection-of-arrival estimation method, a prototype of thebeam-direction-finding circuit was fabricated and testedwith excellent results.

2 The six-port circuit phase discriminator

A typical six-port is a passive circuit having two input portsand four output ports. Each RF output signal is a differentlinear combination of the two RF input signals, dependingon the circuit architecture.

Recently, a four ‘qi points’ multi-port circuit has beendesigned for multi-band operations [8]. TheMHMICmulti-port circuit presented in Fig. 1 is fabricated on an85� 85mm substrate with relative permittivity of 6.15and thickness of 1.27mm. The ports are designated in theusual fashion: ports 1 to 4 are the RF output ports andports 5 and 6 are the RF input ports. Two 50O loads areconnected to ports 7 and 8. Because this multi-port circuithas six ports available for input and output signals, this isfor all practical purposes a six-port circuit. The outputE-mail: tatu@emt.inrs.ca

S.O. Tatu and T.A. Denidni are with Institut National de Recherche

Scientifique – !Energie Mat!eriaux et T!el!ecommunications, laboratoire RF, 800de la Gaucheti"ere Ouest, R. 6900, Montr!eal, Qu!ebec, Canada, H5A 1K6

K. Wu is with !Ecole Polytechnique de Montr!eal, Centre de Recherche Poly-Grames, Pavillon Lassonde, 2500, Chemin Polytechnique, Montr!eal, Qu!ebec,Canada, H3T 1J4

r The Institution of Engineering and Technology 2006

IEE Proceedings online no. 20050239

doi:10.1049/ip-map:20050239

Paper first received 18th October 2005 and in revised form 29th January 2006

IEE Proc.-Microw. Antennas Propag., Vol. 153, No. 3, June 2006 263

baseband signals are obtained using wideband powerdetectors.

Figures 2 and 3 show the simulated and measured returnloss at RF input ports 5 and 6. As is well-known, the returnloss values are a primary indicator of the operatingfrequency. These values show excellent results in terms ofreturn losses over both frequency bands.

Owing to the circuit architecture (see the signal pathbetween inputs and outputs of the circuit), the magnitude ofa typical transmission S-parameter has a theoretical value of�6dB because each input signal passes through two 3dBhybrid couplers, as shown in Fig. 1. All transmission lossesin the circuit were analysed, and typical values of simulatedand measured transmission loss are shown in Fig. 4. Thehorizontal line indicates the theoretical value of thisattenuation. It can be observed that the circuit exhibits thistransmission loss value on both frequency bands of interest.

According to six-port theory [4, 8], the output normalisedwaves and their magnitudes can be expressed as

bi ¼ a5 � S5i þ a6 � S6i

¼ a � expðjj5Þ þ a � a � expðjj6Þ ð1Þ

jbij ¼a2� 1� a � expðjDjÞ exp �jði� 1Þp

2

h i��� ���; i ¼ 1; 2; 3; 4 ð2Þ

where a is the magnitude of the input normalised wave atport 5, a is the ratio of the amplitudes of the inputnormalised waves (amplitude at port 6 over amplitude atport 5) and Dj is the phase difference between the inputnormalised waves. According to (2), the minimum value ofthe magnitude of each output normalised wave magnitudeis given by

jbijmin ¼a2� j1� aj; i ¼ 1; 2; 3; 4 ð3Þ

In the beam-direction-finding application, a is equal to 1because both RF input signals have the same power.Therefore, the minimum value of the magnitude of eachoutput normalised wave is zero, in accordance with thedefinition of the ‘qi point’ presented below.

The fundamental characteristic of any multi-port net-work, that determines the performance of this network inmeasurement applications, is determined by the position ofthe ‘qi points’. Remember that, according to six-port theory,a ‘qi point’ is a complex number, the solution of theequation jbij ¼ 0. The number of ‘qi points’ of a givenmulti-port circuit is equal to the total number of solutionsof the equations jbij ¼ 0, for all output ports, which is afunction of the circuit architecture. Equation (2) shows thatthis circuit has all four ‘qi points’ located on the unit circleand spaced by 901 multiples at 0, p/2, p, and 3p/2 for i¼ 1to 4, respectively.

A new approach was proposed in [4] for PSK/QAMdemodulation in six-port direct conversion receivers, usinganalogue signal processing of the four six-port detectedoutput voltages (Vi). Two signals, in-phase (I ) and in-quadrature (Q), are obtained as follows

I ¼ V3 � V1 ¼ K � a2 � cosðDjÞ ð4Þ

Q ¼ V4 � V2 ¼ K � a2 � sinðDjÞ ð5ÞIn these equations, K is a constant that depends on thepower detector characteristics and on the baseband circuitgain. Using previous I/Q signals, a baseband vector can bedefined in the complex plane by the following equation

G ¼ I þ jQ ¼ K � a2 � expðjDjÞ ð6ÞThis equation shows that the phase of the G vector is equalto the phase difference between RF input signals (Dj).

1

3

4

2

5

6

7

8

Fig. 1 Block diagram of the six-port circuit

Frequency, GHz

Mag

nitu

de S

55, d

B

Simulations

Measurements

2 3 4 5 6 71

-30

-20

-10

-40

0

Fig. 2 Simulated and measured return loss at RF input port 5

Frequency, GHz

Mag

nitu

de S

66, d

B

Simulations

Measurements

2 3 4 5 6 71

-30

-20

-10

-40

0

Fig. 3 Simulated and measured return loss at RF input port 6

-20

-10

-30

0

Mag

nitu

de S

51, d

B

Frequency, GHz2 3 4 5 6 71

Simulations

Measurements

Fig. 4 Typical values for simulated and measured transmission loss

264 IEE Proc.-Microw. Antennas Propag., Vol. 153, No. 3, June 2006

Therefore, this RF phase difference can be directlymeasured using both I and Q signals.

Usually, for a direct conversion receiver (DCR), the LOpower level exceeds the RF input level. However, for thebeam-direction-finding circuit application, the magnitude ofboth RF input signals is the same, and, as alreadydemonstrated, the minimum value of the magnitude ofeach output normalised wave is effectively zero. The outputpower range over the phase difference between RF inputs istherefore extended in comparison to a DCR. As a directresult, the phase measurement errors can be expected todecrease.

3 Operating principle of the beam-direction-finding circuit

A two-dimensional approach to direction of arrivalestimation is proposed in this paper. Figure 5 shows aschematic view of the geometrical model. The receivingantennas are separated by a distance d. Owing to the angle-of-arrival y, a path difference (Dx) between the twopropagation paths will appear. Consequently, the RF inputsignals will be phase shifted with respect to each other by anangle Dj.

As is well-known, the phase difference between the RFinput signals is directly related to the path difference, andcan be expressed as

Dx ¼ l � Dj2p

ð7Þ

Therefore the angle-of-arrival y, can be obtained as follows

sin y ¼ Dxd¼ l

d� Dj2p

ð8Þ

From (7), it can be concluded that the two waves will arrivein phase if the path difference is zero or an integer numberof wavelengths. Furthermore, to avoid any ambiguity, thedistance between the two antennas is chosen to be equal tohalf the wavelength at the operating frequency. Using thisassumption and (6), (8) becomes

sin y ¼ Djp¼ 1

p� phaseðGÞ ð9Þ

A block diagram for the beam-direction-finding circuit,according to this geometrical model, is presented in Fig. 6.Two antennas, which feed the low-noise amplifiers, areconnected to the six-port RF inputs. Then the six-portoutput signals are detected, amplified and processedaccording to (4) and (5), and consequently the basebandcomplex signal (G) is obtained. In order to perform initialdirection of arrival estimations, the G vector can be directlyvisualised on an oscilloscope screen (in XY format) asillustrated in the same figure. According to (9), the position

of the point on the screen is related to the angle-of-arrival y.In addition, (6) shows that if the imaginary part of G isequal to zero, the RF input signals are in phase.

We also observed that at every operating frequency, aninternal phase difference between two transmission pathsalready exists, owing to the physical lay-out of the six-portcircuit. Therefore, according to six-port circuit theory, aninitial phase adjustment must be performed. After thisadjustment, if the antenna system is rotated in thehorizontal plane, the imaginary part of G becomes equalto zero when y¼ 01. As a further step, the angle-of-arrival ycan be calculated using (9).

4 Simulation results

System simulations were performed using the 2004commercial version of the Advanced Design System(ADS) simulator from Agilent Technologies.

Harmonic balance simulations were initially performedfor the proposed multi-band six-port circuit. Figures 7 and 8

dd

x ∆x θ

array element

wave front

Fig. 5 Schematic view of the geometrical model

5

6

six-port+

-

+

-

3

1

2

4x y

I

Q

LNA

LNA

5

6

six-port+

-

+

-

+

-

+

-

3

1

2

4x y

I

Q

LNA

LNA

LNA

LNA

Φ

Fig. 6 Block diagram of the beam-direction-finding circuit

∆�, deg

Mag

. Out

put s

igna

ls, V

S-band

90 180 2700 360

0.2

0.4

0.6

0.0

0.8

θ

Fig. 7 Magnitudes of the output six-port signals against the phasedifference between RF inputs (S-band)

∆�, deg

Mag

. Out

put s

igna

ls, V

90 180 2700 360

0.2

0.4

0.6

0.0

0.8

C-band

Fig. 8 Magnitudes of the output six-port signals against the phasedifference between RF inputs (C-band)

IEE Proc.-Microw. Antennas Propag., Vol. 153, No. 3, June 2006 265

show the magnitudes of the output six-port signals againstthe phase difference between RF inputs, with an RF powerinput level of 0dBm and at two different operatingfrequencies (2.45GHz and 5.8GHz respectively). In bothdiagrams, symbols have been added to the data plot. Thesolid line represents the magnitude of the signal at outputport 1 and the lines with circles, triangles and stars representthe values for output ports 2, 3 and 4, respectively. As canbe seen, the simulated and theoretical results obtained inSection 2 are in good accord with these figures; theminimum voltage magnitudes are situated at 901 phasemultiplies, with minimal errors.

The beam-direction-finding circuit simulation model usestwo omni-directional two-band antennas, two low-noiseamplifiers (LNA) with 20dB gain and the computer modelof the six-port circuit, including the associated powerdetectors and the baseband circuit.

The simulations were performed at both operatingfrequencies 2.45GHz (S-band) and 5.8GHz (C-band).The transmitter power was set to 0dBm and the pathlengths were equal to 1.5m. In order to enable comparisonsof simulated and measured values, the path lengths werechosen to fit the test bench dimensions. We noted that theobserved amplitudes of the I/Q signals increased comparedto the earlier results presented in [9], because the gain of thebaseband circuit was increased by 20dB.

The propagation paths were simulated using the Friismodel [10]. As is well-known, the Friis equation is thetheoretical foundation of radio system link analysis. Itexpresses the received power in terms of transmitted power,antenna gains, range and frequency, and thus forms thebasis for all wireless system design. According to the Friisequation the received power (expressed as W) variesinversely as the square of the operating frequency and asthe square of the distance between the transmitter and thereceiver.

Figure 9 shows the shape of the G vector obtained bysweeping the RF input phase difference. As expected, twoconcentric circles are obtained. Assuming that the gain ofthe antennas is constant, the difference in the radii is relatedto the free-space supplementary attenuation loss at C-bandfrequencies. According to the Friis equation, for a constantdistance between transmitter and receiver, this attenuationis directly proportional to the operating frequency:

DAðdBÞ ¼ A2ðdBÞ � A1ðdBÞ ¼ 20 logf2

f1ð10Þ

Therefore, a supplementary attenuation of about 8dB mustbe considered for the C-band in comparison to the S-bandvalues.

For the proposed six-port architecture, the variation ofthe circle radius (the G vector magnitude), measured in dB,is equal to the RF input power variation (DPin), asdemonstrated in a previous paper [4]

D Gj jðdBÞ ¼ DPinðdBÞ ð11Þ

This supplementary C-band attenuation leads to a reduc-tion in the circle radius to about 40% of the S-band value.This result is confirmed by the simulation results shown inFig. 9.

Figures 10 and 11 show the I/Q output signals against thephase difference between RF inputs, for both frequencybands. Two sinusoidal waves shifted by 901 were obtained,as expressed in (4) and (5). If the phase difference is equal tozero, the Q signal value is zero and the I signal is at amaximum, as shown in (6).

The G circle radius is also related to the distance betweentransmitter and receiver, according to the Friis equation. Ifthis distance changes the magnitude of the output signalswill also change. However, extreme values of these signalswill be obtained at the same phase difference between RFinputs.

In practice, to avoid any ambiguity concerning thedirection of arrival, the distance between receiving antennas

-1.0 -0.5 0.0 0.5 1.0-1.5 1.5

S-band

C-band

I, V

Q, V

Fig. 9 Circular G-vector shape for the two frequency-band case

∆�, deg

I

I/Q s

igna

ls, V

Q

-90 0 90-180 180

-1.0

-0.5

0.0

0.5

1.0

-1.5

1.5

Fig. 10 Beam direction circuit output signals against the phasedifference between RF inputs at the S-band operating frequency

Q

I/Q s

igna

ls, V

I

-90 900-180 180

-0.25

0.00

0.25

-0.50

0.50

∆�, deg

Fig. 11 Beam direction circuit output signals against the phasedifference between RF inputs at the C-band operating frequency

266 IEE Proc.-Microw. Antennas Propag., Vol. 153, No. 3, June 2006

is chosen as half of the wavelength (6.1 cm for S-band and2.6 cm for C-band, respectively), as mentioned in Section 3.

We observe that the only difference between thesimulation results corresponding to these two frequenciesis the values of the I/Q signal amplitudes. The outputquadrature signals have the same shape over a 3601Djsweep. Owing to this perfect resemblance, some results willbe presented for only one of the two frequency bands. TheS-band was chosen for practical reasons related to the patchantenna dimensions (in order to avoid ambiguities, asexplained earlier).

Figure 12 shows the same I/Q output signals against theangle-of-arrival of an S-band signal. The I signal attains itsmaximum value if the RF input signals are in phase and theQ signal passes through zero, under the same conditions.Therefore, any of these signals can be used for purposes ofbeam-direction-finding.

The angle-of-arrival (y) can be obtained according to (9),using the phase difference between the two RF inputsignals. This phase difference is supplied by the basebandquadrature signal measurements. Simulation results for thecalculated angle-of-arrival against the RF phase sweep werepresented in [9]. These results confirm that the ambiguity inthe angle-of-arrival has been avoided due to the correctchoice of the distance between the receiving antennas. Atthe same time, they show that, if the angle-of-arrivals is lessthan 301, the relationship between Dj and y is quasi-linear.

Considering the maximum value of the angle-of-arrival(901), the error of the calculated angle-of-arrival (yc) againstthe true angle (y) can be obtained using the followingequation

yerror ¼y�c � y�

90�� 100 ð12Þ

We note that this error is related to the six-port circuitdesign and fabrication. According to (4) and (5), for anideal six-port circuit, the phase of the G vector is equal tothe phase difference between RF input signals (Dj). In thisideal case, there it is no error in the angle-of-arrivalestimation.

Comparisons of the simulated angle-of-arrival estimationerrors, obtained using the proposed six-port circuitcomputer model, with the actual angle-of-arrival valuesare presented in Fig. 13 for the S-band and Fig. 14 for theC-band. As expected, the angle-of-arrival estimation errorsare related to the six-port circuit DC offset values. The

maximum value of this offset is about 20mV for the S-bandand C-band operating frequencies, representing 2% of themaximum value of the output signals. Therefore, thepresent simulations confirm that the angle-of-arrival errorremains in the same range within a few percent, validatingthe proposed beam-direction-finding circuit design and themethod of estimation.

5 Measurement results

A test bench was designed and implemented using theMHMIC six-port circuit and related components. Aphotograph of this bench is shown in Fig. 15. An RFsignal generator and a patch transmitter antenna make upthe transmitter. To obtain various angles of arrival, thetransmitting antenna can slide on a rail, as shown in theFigure. The six-port beam-direction-finding prototype usestwo other identical antennas, connected as shown in theblock diagram in Fig. 6. In order to visualise the G vectordirectly on the screen, an oscilloscope in XY format is used.If the transmitter antenna position changes, the pointdefined by the G vector follows a circular path on thescreen, as described in Section 4. The phase of this vectorcan be estimated directly or can be calculated with higherprecision using signal processing methods.

Figure 16 shows a photograph of the six-port directionfinding prototype. Two dual-band patch antennas with4dBi gain feed two 20dB-gain LNAs connected to the six-port circuit RF inputs. In order to avoid ambiguities owingto the patch antenna dimensions (see the figure), theoperating frequency is chosen to be 2.45GHz. The antennaspacing is therefore 6.1 cm, which represents half thewavelength at 2.45GHz.

Four wide-band RF power detectors (Wiltron, model75KC50) connected to the six-port circuit outputs are usedto generate the input signals for the baseband circuit. This

Input �, deg

I/Q s

igna

ls, V

I Q

-45 45-90 900

-1.0

-0.5

0.0

0.5

1.0

-1.5

1.5

Fig. 12 Simulation results for the beam-direction-finding circuitoutput signals against the angle-of-arrival at the S-band frequency

-45 45-90 900

0

1

-1

2

Input �, deg

� er

ror,

%

Fig. 13 Simulated S-band angle-of-arrival estimation error againstthe physical angle-of-arrival

-45 45-90 900

0

1

-1

2

Input �, deg�

erro

r, %

Fig. 14 Simulated C-band angle-of-arrival estimation erroragainst the physical angle-of-arrival

IEE Proc.-Microw. Antennas Propag., Vol. 153, No. 3, June 2006 267

baseband circuit, constructed using high-speed operationalamplifiers, generates the I/Q signals according to six-portcircuit theory [4, 5]. This measurement set-up is similar tothe system simulation set-up presented in the previousSection: the distance between the transmitter antenna andthe proposed prototype is set to 1.5m, the signal generatorpower is set to 0dBm and the gain of the baseband circuit isincreased by 20dB, compared to the initial set-up presentedin [9]. During measurements, the angle-of-arrival is sweptover a 601 range using the transmitter sliding antenna.

Figure 17 shows the measured I/Q signals against theangle-of-arrival. As predicted by theory and confirmed bysimulations, the I signal is an even function having amaximum value at 01, and the Q signal is an odd functionthat is zero for the same angle value. The amplitudes of themeasured signals are similar to the simulation resultspresented in Fig. 12, at the same operating frequency.

A practical method for obtaining the direction of arrivalconsists of rotating the beam-direction-finding circuit (or ofthe receiver antennas only) and measuring the magnitude of

the in-quadrature signal (Q). During the beam-direction-finding circuit rotation the in-quadrature signal value passesthrough its minimum value, corresponding to an angle-of-arrival of 01 (see Fig. 18). As a consequence of this directangle measurement in the coordinate system, the angle-of-arrival calculation becomes useless if this hardware methodis used.

During these measurements, the angle-of-arrival wasswept over a 601 range, from �301 to 301. According to (9),the phase difference between the RF inputs will lie within a1801 range, from�901 to+901. Therefore, the G vector willfollow a half-circle trajectory in the complex plane.

Figure 19 shows a plot in XY format, similar to theoscilloscope screen image, of the measured values of the Qsignal against the I signal. On this diagram, the measure-ment points are marked by stars. Point A corresponds to anangle-of-arrival of – 301. If the value of the angle-of-arrivalbecomes zero this point shifts to O. Finally, point Bcorresponds to an angle-of-arrival of +301.

As can be seen, this shape is close to circular, as predictedby the earlier theoretical discussion. The errors are relatedto circuit fabrication and measurement precision. The fivestars encircled by the dotted line correspond to angle-of-arrival values of �51, �31, 01, 31 and 51, respectively. Theother measurement points correspond to 51 step changes inthe angle-of-arrival.

As can be seen in the same figure, this curve intercepts thehorizontal axis very close to the central point O, which

Tx ant

RF gen.

Fig. 15 Photograph of the direction finding prototype test bench

Power detector

Base bandcircuit

Patch antenna

Phase shifter

LNA

Six-port

Fig. 16 Photograph of the six-port beam-direction-finding proto-type circuit

Q

I

-20 -10 0 10 20-30 30

-1.0

-0.5

0.0

0.5

1.0

-1.5

1.5

I/Q s

igna

ls, V

Input �, deg

Fig. 17 Measurement results for the beam-direction-finding circuitoutput signals against the angle-of-arrival

Q m

agni

tude

, V

0.4

0.8

0.0

1.2

-20 -10 0 10 20-30 30Input �, deg

Fig. 18 Magnitude of the in-quadrature measured signal (Q)against the angle-of-arrival

-1.0 -0.5 0.0 0.5 1.0-1.5 1.5

-1.0

-0.5

0.0

0.5

1.0

-1.5

1.5

I signal, V

Q s

igna

l, V

A

B

O

Fig. 19 Shape of the measured G vector in the complex plane

268 IEE Proc.-Microw. Antennas Propag., Vol. 153, No. 3, June 2006

indicates an estimated measurement error of about 11corresponding to an angle-of-arrival equal to 01.

The relative error of the angle-of-arrival is calculatedusing the measured values of the output quadrature signalsand (12). The results presented in Fig. 20 show a maximumerror of about 3%, associated with the angle-of-arrivalvalues that were considered. These results are similar tothose obtained by simulation and confirm once again thevalidity of the proposed method for the direction of arrivalestimation.

6 Conclusions

A new method to estimate the direction of arrival of amicrowave signal, based on six-port technology, has beenproposed in this paper. A dual-band prototype of theproposed circuit has been designed, fabricated and tested.

In order to obtain the beam direction, the phasedifference between the RF input signals is measured usingthe output in-phase and in-quadrature baseband signals ofthe prototype. These signal values are directly related to theangle-of-arrival as has been demonstrated. In addition, toestimate the direction of arrival, a practical approach,involving detection of the minimum magnitude of the in-quadrature signal has also been proposed. This practicalapproach avoids the necessity of calculating the angle-of-arrival value.

The results obtained with the proposed circuit indicateexcellent agreement between theory, simulation and mea-surements. These results show that the magnitude of theangle-of-arrival estimation error is less than 3% in bothoperating frequency bands and prove that low-costdirection of arrival measurements can be performed usingthe proposed approach.

A phased-array driver circuit to improve the reception ofthe microwave signals can be designed using the resultspresented here. A constructive interference analysis betweenreceived signals, using a two-antenna array, will beperformed for each angle-of-arrival, using a control circuitbased on a six-port phase discriminator and a controlledphase shifter. The RF input power of a microwave receiverwill therefore be maximised for an arbitrary angle-of-arrival. The signal-to-noise ratio at the microwave receiverRF input will be considerably increased and the bit-error-rate value of the communication system will therefore bedramatically improved.

7 Acknowledgments

The financial support of the National Science EngineeringResearch Council (NSERC) of Canada is gratefullyacknowledged. The authors would like to thank Professor

R.G. Bosisio of the Poly-Grames Research Centre ( !EcolePolytechnique deMontr!eal) for the valuable contribution tothis paper and technical personnel of the same researchcentre for the six-port circuit fabrication.

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-2

0

2

-4

4

-20 -10 0 10 20-30 30Input �, deg

� er

ror,

%

Fig. 20 Relative error values for calculated against observedangles of arrival, using measurement results for I/Q values

IEE Proc.-Microw. Antennas Propag., Vol. 153, No. 3, June 2006 269