WO2008105748A1

WO2008105748A1 - Method and apparatus for the joint detection of the number of signal sources and their direction of arrivals

Info

Publication number: WO2008105748A1
Application number: PCT/TR2007/000018
Authority: WO
Inventors: Temel Engin Tuncer
Original assignee: Temel Engin Tuncer
Priority date: 2007-02-26
Filing date: 2007-02-26
Publication date: 2008-09-04
Also published as: TR200906439T2

Abstract

A method and an apparatus is described for joint detection and estimation of the number of sources and their direction of arrivals (DOA) in sensor arrays. The method finds the DOA' s by employing a suitable algorithm such as MUSIC, root-MUSIC or ESPIRIT for a given order n. Then the array manifold matrix is constructed and an error is computed for the selected value of source number n. A number of values are considered for n=l, &mldr; ,nmax and the error e (n) is computed for each case. The error term is computed by considering deterministic and stochastic maximum likelihood functions. The number of sources is found as the n value which returns the minimum value of the function of error f (e(n) ) . Since the DOA' s are already computed, both the number of sources and the corresponding DOA' s are found jointly.

Description

METHOD AND APPARATUS FOR THE JOINT DETECTION OF THE NUMBER OF SIGNAL SOURCES AND THEIR DIRECTION OF ARRIVALS

TECHNICAL FIELD OF THE INVENTION

The present invention in general is related to the field of communications, wireless sensors and in general sensor arrays. The present invention is specifically related to the apparatuses and method for finding both the number of signals of the sources and their Direction of Arrivals (DOA's).

PRIOR ART Advances in electronics, telecommunications, networking and other related technologies have led to the use of sensor arrays for detection and estimation of sources. Sources can be in a variety of forms and some examples are electromagnetic sources such as cell phones, radios, radars, etc. Other examples of sources include acoustic sources like loudspeakers or human beings in a conference room, and sonic sources like submarines. These examples are not the complete list of possible sources and the possible application areas of the present invention. One of the important application and use of the presented innovation is to detect the number of sources in the environment with the help of an apparatus which consists of a number of sensors. The sensors can be selected appropriate for the type of environment and signals of interest. An incomplete list for sensors can be electromagnetic sensors such as passive or active antennas, acoustic sensors such as microphones, sonic microphones or any passive or active receiving device.

The use of multiple sensors has several advantages in terms of enhancing the communication capacity, throughput, etc. Moreover, the number of sources and their DOA's (Direction of Arrival) can be found with this apparatus. Various signal processing techniques can be used to process the signals received by each of the elements of the sensor array. The position of sensor array elements can be arbitrary or a special geometry can be chosen which then can be used advantageously in order to increase the sensitivity of the detection and estimation system.

There are a variety of methods and algorithms for the detection of the number of sources by using a sensor array. AIC (Akaike Information Criterion), MDL (Minimum Description Length), BIC (Bayesian Information Criterion), GIC (Generalized Information Criterion) are examples of information theoretic techniques for this purpose. These methods usually do not perform satisfactorily when the source and noise statistics deviate from the common assumptions. Usually signal and noise sequences are assumed to be from a Gaussian distribution. In addition, noise variance is considered to be spatially invariant and white. In this innovation, the presented methods perform significantly better even when the above assumptions do not hold. This innovation finds the number of sources in a simple and relatively efficient manner. Furthermore, DOA's for the corresponding sources are found at the same time. There is no search process and the total process of finding the number of sources as well as their DOA's requires an eigendecomposition and some matrix inverses. The accuracy of the innovation is better than the alternative techniques.

The technique/method and apparatus developed in this invention can be applied for any sensor geometries, source signals (wideband, narrowband), and source correlations (uncorrelated, correlated, coherent or multipath signals). In this respect, array interpolation or a variant technique can be used to map the sensor geometry to a uniform array which result a Vandermonde style array manifold matrix. In order to deal with the coherent signals, spatial smoothing techniques are used.

The publications related to the present invention are listed below. • R. O. Schmidt, "Multiple emitter location and signal parameter estimation", IEEE Tr. On Antennas and Propagation, Vol. 34, No.3, pp.276-280, March 1986.

• B. Friedlander, AJ. Weiss, " Direction finding using spatial smoothing with interpolated arrays", IEEE Trans, on Aerospace and Electronic Systems, Vol. 28, No.2, pp.574 - 587, April 1992.

• D.E.N. Davies, "A transformation between the phasing techniques required for linear and circular aerial arrays", Proc. Inst. Elect. Eng., Vol.112, pp.2041-2045, 1965.

• S. U. Pillai, B. H. Kwon, "Forward/backward spatial smoothing techniques for coherent signal identification", IEEE Trans, on Signal Proc, Vol.37, No.l, pp.8-15, Jan. 1989.

• H. Krim, M. Viberg, "Two decades of array signal processing research: the parametric approach", IEEE Signal Processing Magazine, vol. 13, pp.67-94, July 1996. • In "R. O. Schmidt, "Multiple emitter location and signal parameter estimation", IEEE Tr. On Antennas and Propagation, Vol. 34, No.3, pp.276-280, March 1986.", MUSIC algorithm is presented. This algorithm in its most general form requires a one-dimensional search which might be computationally expensive. Root-MUSIC is the algorithm which finds the DOA's of the source signals without a search process. Root-MUSIC is applicable to uniform linear arrays. When the array geometry is not linear two possible techniques that can be used to map the array output to a linear virtual array are presented in "B. Friedlander, AJ. Weiss, Direction finding using spatial smoothing with interpolated arrays, IEEE Trans, on Aerospace and Electronic Systems, Vol. 28, No.2, pp.574 - 587, April 1992 " and "D.E.N. Davies, A transformation between the phasing techniques required for linear and circular aerial arrays, Proc. Inst. Elect. Eng., Vol.112, pp.2041- 2045, 1965 ". These techniques are called as array interpolation and Davies' transformation respectively. When there is multipath propagation, source signals become coherent. In this case, one of the most effective techniques for linear arrays to mitigate the rank deficiency of the covariance matrix is given in "S. U. Pillai, B. H. Kwon, Forward/backward spatial smoothing techniques for coherent signal identification, IEEE Trans, on Signal Proc, Vol.37, No.l, pp.8-15, Jan. 1989". The error functions for the source estimation can be deterministic or stochastic maximum likelihood functions which are summarized in H. Krim, M. Viberg, "Two decades of array signal processing research: the parametric approach", IEEE Signal Processing Magazine, vol. 13, pp.67-94, July 1996.

AIMS OF THE INVENTION

There are a number of techniques and methods for the estimation of the number of signals in array processing. These methods make certain assumptions in order to operate in a robust manner with high accuracy. Some of the assumptions for these methods are the Gaussian distribution of the source and noise signals, white noise, spatial invariance for the noise variance, noncoherent signals, etc. When these assumptions are not valid, many of the methods fail or their performance falls to an unacceptable level. In this invention, the presented method either is not affected by the statistical characteristics of the signal and noise signals or the performance loss becomes sufficiently small and acceptable in a variety of cases. The accuracy of the estimation is high at low SNR. The method can be applied for arbitrary array geometries by employing array interpolation. When there is multipath signals, forward-backward spatial smoothing is used to mitigate the rank deficiency of the covariance matrix. The method can be applied even when the signal and noise statistics deviate from the usual assumptions. Furthermore, the method does not use a fixed and data dependent term like a threshold.

One of the most important parts of source estimation is the selection of an error criterion. In this invention, two different criteria are used namely, deterministic maximum likelihood error criterion (DTML) and stochastic maximum likelihood criterion (STML). These two criteria are used by employing root-MUSIC algorithm first. Therefore error functions are computed without a search process. The effectiveness of the invention is partly due to the accuracy and robustness of these error criteria.

The apparatus and method developed in this invention find both the number of signals (or the sources) and their DOA's. Therefore a joint estimation is done. In fact, source DOA's are a by product of the source estimation process.

BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES

In order to explain the present invention, figures have been prepared and attached to the description. The list and definition of the figures are given below. Figure - 1 illustrates a possible environment to practice the present invention.

Figure - 2 illustrates a possible operational flow diagram in order to determine the number of sources as well as their corresponding DOA's. The features of the invention in the figures have been numbered. The list and definition of the features are given below.

1- Sources

2- Incident Plane Wave 3- Sensor array

4- Receiver

5- Processing unit (source detection and DOA estimation)

6- Controller

7- System memory and storage unit 8- I/O devices, display, keyboard etc.

9- Network communication DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Embodiments of the present invention include methods and apparatuses for determining the number of signals (1) and their corresponding DOA's by employing sensor arrays (3). In the following, details of the embodiments of the present invention are described. However, other embodiments may be used with only some or all of the described aspects by those skilled in the art. Specific numbers, materials and configurations are presented only to give a better understanding of the invention. It is possible to practice other embodiments without the specific details.

For the descriptions in the present invention, the following conventions are used: • Boldface-capital letters represent matrices,

• Boldface-small letters represent vectors,

• Non-boldface letters represent scalars,

• A^H is the Hermitian transpose of the matrix A.

Figure 1 shows a possible environment in order to apply the present invention. There are M sensors in the sensor array (3). The array elements can be located arbitrarily or according to certain geometrical configuration. If the array (3) geometry is different than the uniform linear array, it is assumed that array mapping techniques such as array interpolation or Davies's transformation can be used to map the array outputs to a uniform linear array (UL-A). The signals from each sensor element (3) is applied to the receiver unit (4) where appropriate conditioning such as down conversion, demodulation, amplification, A/D conversion, etc. are done. Receiver (4) may be composed of a number of receiving devices operating in parallel and in synchronization. The outputs of the receiver (4) corresponding to each sensor (3) may be directly stored in a storage device (7) in order to do an offline processing. Otherwise the outputs are fed to the processing unit (5) where the numbers of sources (1) as well as their DOA's are determined. Overall structure may be controlled by a controlling unit (6) in order to organize the data transfer over a bus as well as realize the other necessary operations for the appropriate functioning of the system. A display and keyboard (8) may be used for interfacing the device. A network communication (9) interface is used to communicate with other devices. This unit (9) may support any one of a wide range of networking protocols. It can also be used to communicate with similar units in order to be used for location estimation when the DOA's obtained from the other devices are employed.

It is assumed that there are n₀ signals (1) which impinge on the M element uniform linear sensor array (3) in directions θi,..., θ_no. The received signal (1) at the sensor (3) outputs for a single snapshot at time t is given as, y(0 = As(O +v(0 where y(t) is a M x 1 vector, A is Mxn₀ array manifold matrix, s(t) and v(t) are the signal (1) and noise vectors respectively. Array geometry is assumed to be known with sufficient accuracy and the array manifold matrix is given as,

a tøl )= 1 exp(j2π— sin£?.)...exp(/2π(M-l)— sinέ?)

where d is the distance between the sensor elements (3), λ=c/f_c is the wavelength, c is the speed of the wave, f_c is the center frequency. The signal (1) vector s(t) is composed of n₀ signals, namely,

Above model is for narrowband signals. However this invention can be applied for the wideband signals as well with some additional processing.

As it is shown in Figure 1, the method proceeds by finding the sample covariance matrix for N snapshots as,

Maximum possible number for the sources is selected as n_max. Therefore it is assumed that the number of sources (1) is an integer between n=l and n=n_max. Since it is possible to have correlated or coherent signals, sample correlation matrix R is processed by forward-backward spatial smoothing assuming n=n_max and PxP R_n, is obtained. P is n_max+l< P≤M.

Eigenvalue and eigenvectors of RR₃ are obtained as,

R^ = VΛV*

Where

V = [V₁ V₂ ...Vp] is the matrix of eigenvectors Vj placed in the columns of V. The number of sources (1) is varied from n=l to n_max and DOA's for the sources (1) are found by using a suitable method such as root-MUSIC or ESPIRIT. For this purpose, it is assumed that n sources (1) are present and root-MUSIC algorithm is applied to RR₃ matrix which has the eigendecomposition as given above. Once the DOA angles are determined for n sources (1), θi, θ₂, ..., θ_n, array (1) manifold matrix A_n is constructed as given in the above equation. For each of the selected source (1) number, an error is computed. Error function can be either deterministic maximum likelihood (DTML) or stochastic maximum likelihood (STML). DTML error function performs very well in a variety of cases. It is especially effective for low SNR and for noncoherent signals. When the SNR is relatively high and sources (1) are coherent, STML error function can be used in order to further improve the estimation accuracy. DTML error function is given as, W(«) = Jr(Il-A₁, (A? AJ^"1 Af ]R)

STML error function can be computed by defining a number of terms, A⁺ = (A¹¹A)-¹A",

Then, STML error function is given as,

^esi_ML (») = ¹⁰S I APai_M A^H + σ_s ² _mLl I The selection of the error function can be left as a user choice or it can be done by considering some objective measures such as signal-to-noise ratio, multipath presence, etc. Therefore e(n) is taken as either e_DτM_(n) ^or esr_M-(n) function. The use of e_Dτ_M_(n) is advantageous when the SNR is low and/or there is no multipath signals. If there are multipath signals and SNR is high, esτ_M-(n) may be preferred. Once e(n) is computed for n=l,2, ..., n_max, it is normalized in order to make it independent of application dependent factors. Therefore,

A function of the normalized error is computed as follows,

where β is a constant factor that can be selected appropriately for the application at hand. A possible value of β is 0.047. The true number of sources is found as the value of n which has the minimum value of f(e(n)). In other words,

«₀ = argmin/(e)

Since the DOA angles are found before, it is possible to select the source angles as the ones corresponding to the number of sources h₀ and there is no need to do the calculations again.

The invention described above is not limited to the embodiments outlined above. Other embodiments may be practiced with modification and alteration in line and scope of the appended claims.

The steps of the method/algorithm developed in the present invention are explained below. The operations are explained in sequence in order to help better understanding of the invention. However, the order of the description does not imply that these operations are necessarily order dependent. Figure 2 shows a summary of the algorithm for joint source (1) and DOA estimation.

• The first step during the application of the method is the consideration of the array (1) geometry. If the array (1) is a uniform linear array (ULA), we proceed to the next step. If the array geometry is arbitrary, then the outputs of the array sensors are mapped to a uniform linear array by employing a mapping operation like array interpolation as described in "B. Friedlander, AJ. Weiss, Direction finding using spatial smoothing with interpolated arrays", IEEE Trans, on Aerospace and Electronic Systems, Vol. 28, No.2, pp.574 - 587, April 1992". It is possible to improve the mapping error when Wiener mapping matrix is used. Wiener array interpolation matrix is defined as,

T = A(£)R,A(£)*(A(£)R,A(0y +RJ-¹

Where an interpolation sector is defined as θ e [#_l5#₂] and this sector is uniformly divided with Aθ intervals. Source DOA is assumed to be inside the interpolation sector and array manifold is generated by considering θ_t

. |_ J rounds the number to the closest integer smaller than the number. When there is no information on the source and noise covariance matrices, a convenient mapping matrix can be obtained as,

T = σlMβ)lLφ)^H(σ]7Lφ)Aφ)^H +σ_v ²y^ι where σ² _s and σ² _v are the signal and noise variances respectively. The covariance matrix for the equivalent virtual ULA can be obtained as,

R = TRT*

~ I ^ where R = — ^y(Oy ^H if) ^{is tne} covariance matrix for the real array with array output vector,

N (=i no- • If the real array is ULA, sample covariance matrix is obtained from the sensor outputs of uniform linear array with Ν snapshots as,

A positive integer n_max is selected as the maximum number of sources. This number indicates that the number of sources can not exceed n_max . • Assuming that there may be multipath signals, forward-backward spatial smoothing is used on

R as described in S. U. Pillai, B. H. Kwon, "Forward/backward spatial smoothing techniques for coherent signal identification", IEEE Trans, on Signal Proc, Vol.37, Νo.l, pp.8-15, Jan. 1989 and

R^, is obtained. If there is no multipath, there is no need to apply the forward-backward spatial smoothing. The eigenvalues and eigenvectors of the KxK matrix R_β are found and used in the following stages repeatedly. R^ = VΛV^ where V is the matrix with eigenvectors in the columns and Λ is the diagonal matrix with eigenvalues ordered as, λi < λ₂ < ...<λ_κ.

This and the following steps are repeated for each of the selected source number n. Therefore the number of sources is assumed to be n=l,2,..., n_max and for each of the n values,, root-MUSIC or a suitable algorithm is used by employing the eigenvalues and eigenvectors of R^ matrix. The DOA's for n sources are found and the array manifold matrix for the real array, A, is constructed by using the estimated angles. If the SIMR is low or signals are noncoherent, deterministic maximum likelihood error function is found as, e_DmL(n) = trifc- A_n(A" A_nyA^»]k)

If the signals are coherent and SNR is sufficiently high, stochastic maximum likelihood error function is preferred which is found as

eSTML M = ^l0§ I ^STML ^A" + ^σlmL^l I

If the real array is not ULA, covariance and manifold matrices, namely Rand A respectively of the real array are used in the above error functions.

• Once e(n) is determined as one of the error functions e_Dτ_M_(ιO ^or %r_Mi.(n), this function is normalized as,

_Λ _ e e^~ y where | |.| | is a suitable norm. An example'being

The function of error is found as,

where β is a fixed value.

• The number of signals (or sources) are found as, «₀ = argmin/(e)

Once h₀ is found, the corresponding source DOA's are selected form the previous estimations of DOA's. The features of the apparatus developed in the present invention are explained below. Figure

1 shows the main parts/features of the apparatus. It is assumed that there are M sensors (3) to pick the signals (1) (or sources (I)) in the environment. Sensors (3) can be for any target environment such as, acoustic, electromagnetic, or sonic environments. The sensors (3) are assumed to be configured in a geometry and it is assumed to be known with sufficient accuracy. In other words, the positions of the sensors (3) are known. The sensor (3) signals are applied to the receiver (4) which is a device to downconvert the passband signals and demodulate if necessary. The sensor (3) signals may be wideband or narrowband. The receiver (4) can operate for both types of signals.

The system memory and storage (7) is used to store the copy of the sensor waveforms, estimation results, and operating system services. System memory can be Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM) or other memory devices of the like. Mass storage devices are also used to store data and estimation results. These devices (7) include but are not limited to hard disks, CDROM and DVDROM.

Other I/O devices (8) are used for input/output purpose. Keypads, keyboards, mouse, USB ports are the examples for this purpose but input/output ports are not limited by these examples. A display is used to present the estimation results on a user friendly screen.

Network communication (9) interface is used to communicate with other devices. Network communication (9) can be wired or wireless and may support any one of the wide range of networking protocols.

A controller (6) is employed in order to control the whole apparatus in terms of both hardware and software. The software includes an operating system. Hardware of the controller (6) includes the clock generation, reference oscillators, data and address bus controls. The controller (6) hardware and software is not limited by the above examples.

A processing unit (5) is employed in source detection and DOA estimation. The processing unit

(5) may be a digital signal processor (DSP) or a microprocessor. This processor may be programmed by any one of the programming languages. However, all or portions of the present invention may be implemented in hardware as well. For this purpose, Application Specific Integrated Circuit (ASIC) or

Field Programmable Gate Array (FPGA) can be used for the processing unit (5). The connections between the units of the apparatus may include multiple data and address connections.

The apparatus developed in this invention comprises a storage medium having a plurality of programming instructions designed to enable the apparatus to determine the number of sources and their DOA's according to the methods described above.

The system comprises:

• a plurality of antennas or sensors to receive a plurality of signals;

• a RF unit coupled to the antennas or sensors;

• a receiver with more than one channel to down convert the received signals; • a number of source detection and direction of arrival estimation unit coupled to the receiver to determine the number of sources and estimate their DOA's.

The device also comprises a machine readable medium having stored a plurality of programming instructions designed to enable the apparatus to determine the number of sources and their DOA's.

Claims

CLAIMS - An apparatus and a method for finding both the number of signals of the sources (1) and their Direction of Arrivals (DOA's), characterized by; a) the apparatus comprising, sensor array (3), receiver (4), processing unit for source detection and DOA estimation (5), controller (6), system memory and storage unit (7), I/O devices, display, keyboard etc. (8) and network communication (9), and b) the method comprising if the real array (1) is a uniform linear array (ULA)

• sample covariance matrix is obtained from the sensor outputs of uniform linear array with N snapshots as,

A positive integer n_max is selected as the maximum number of sources by indicating that the number of sources can not exceed n_max

• Assuming that there may be multipath signals, forward-backward spatial smoothing is used on Rand R^ is obtained, if there is no multipath, there is no need to apply the forward-backward spatial smoothing,

• the eigenvalues and eigenvectors of the KxK matrix R^ are found and used in the following stages repeatedly as

R^ = VΛV^H where V is the matrix with eigenvectors in the columns and Λ is the diagonal matrix with eigenvalues ordered as, λi < λ₂ < ...<λ_κ. • this and the following steps are repeated for each of the selected source number n,

• the number of sources is assumed to be n=l,2,..., n_max and for each of the n values, root-MUSIC or a suitable algorithm is used by employing the eigenvalues and eigenvectors of R _^ matrix.

• the DOA's for n sources are found and the array manifold matrix for the array, A, is constructed by using the estimated angles,

• If the SNR is low or signals are noncoherent, deterministic maximum likelihood error function is found as, w ⁽O = * I¹ - ^A» « ^A» ^)"' ^A* 1*)

eSTML M = ^lθS I ^ STML ^A" + ^σliML^l I

• e(n) is selected as either esτ_ML(n) or s_DTML(n). This selection is user dependent or can be done by employing a criteria such as SNR, existence of multipath sources. e(n) is computed for n=l,2, ..., n_max.

• e(n) is normalized in order to make it independent of application dependent factors. Therefore,

e =

A function of the normalized error is computed as,

where β is a constant factor that can be selected appropriately for the application at hand. A possible value of β is 0.047. • The true number of sources is found as the value of n which has the minimum value of f(e(n)). Therefore, estimated number of signals (or sources) is found as, h₀ = arg min fie)

- An apparatus and a method for finding both the number of signals of the sources (1) and their Direction of Arrivals (DOA's), characterized by; a) the apparatus comprising, sensor array (3), receiver (4), processing unit for source detection and DOA estimation (5), controller (6), system memory and storage unit (7), I/O devices, display, keyboard etc. (8) and network communication (9), and b) the method comprising if the real array (1) is NOT a uniform linear array (ULA) • the outputs of the array sensors are mapped to a uniform linear array by employing a mapping operation like array interpolation,

• mapping error is improved by Wiener array interpolation matrix which is defined as, T = Aφ)R_sAφf (MmΛΦf +R_vr

• Where an interpolation sector is defined as Θ e {θ^θ^ ^ar|d ^tnis sector is uniformly divided with Δθ intervals. Source DOA is assumed to be inside the interpolation sector and array manifold is generated by considering Q₁ = Q₁ + iAΘ, i = 0,l,...,[(<9₂ - θ_x ) / Aθj . [ J rounds the number to the closest integer smaller than the number,

• When there is no information on the source and noise covariance matrices, a convenient mapping matrix can be obtained as,

T = σ²A(θ)A(θ)^H (σ²A(θ)A(θ)^H + a²)^'1 where σ² _s and σ² _v are the signal and noise variances respectively. The covariance matrix for the equivalent virtual ULA can be obtained as,

R = TRT*

~ I ^ where R = — V y(0y ^H (0 is the covariance matrix for the real array with array

output vector, y(t) . • Assuming that there may be multipath signals, forward-backward spatial smoothing is used on Rand R^ is obtained, if there is no multipath, there is no need to apply the forward-backward spatial smoothing,

R^ = VΛV* where V is the matrix with eigenvectors in the columns and Λ is the diagonal matrix with eigenvalues ordered as, λi < X₂ < ...<λ_κ.

• this and the following steps are repeated for each of the selected source number n

• the number of sources is assumed to be n=l,2,..., n_max and for each of the n values, root-MUSIC or a suitable algorithm is used by employing the eigenvalues and eigenvectors of R^₂, matrix.

• the DOA's for n sources are found and the array manifold matrix for the array, A, is constructed by using the estimated angles, If the SNR is low or signals are noncoherent, deterministic maximum likelihood error function is found as,

_W(κ) = A¹ - A_n(Af AJ-¹ Af ]R)

• If the signals are coherent and SNR is sufficiently high, stochastic maximum likelihood error function is preferred which is found as

esi_ML («) = ^lQg I AϊW A* + σ_s ² _mLI I

• e(n) is selected as either esτ_M_(n) or SDTML(Π). This selection is user dependent or can be done by employing a criteria such as SNR, existence of multipath sources. e(n) computed for n=l,2, ..., n_max. • e(n) is normalized in order to make it independent of application dependent factors. Therefore,

_Λ _ e e⁼iki

A function of the normalized error is computed as follows,

where β is a constant factor that can be selected appropriately for the application at hand. A possible value of β is 0.047.

• The true number of sources is found as the value of n which has the minimum value of f(e(n)). Therefore estimated number of signals (or sources) is found as, n₀ = argmin/(e) n 3- An apparatus and a method for finding both the number of signals of the sources (1) and their

Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that sensors (3) can be for any acoustic, electromagnetic, or sonic environments.

4- An apparatus and a method for finding both the number of signals of the sources (1) and their

Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the sensors (3) are assumed to be configured in a geometry and it is assumed to be known with sufficient accuracy or the positions can be found by using an estimation technique. 5- An apparatus and a method for finding both the number of signals of the sources (1) and their Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the sensor (3) signals are applied to the receiver (4) which is a device to downconvert the passband signals and demodulate if necessary. 6- An apparatus and a method for finding both the number of signals of the sources (1) and their

Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the sensor (3) signals may be wideband or narrowband.

7- An apparatus and a method for finding both the number of signals of the sources (1) and their Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the receiver (4) can operate for both wideband and narrowband signals.

8- An apparatus and a method for finding both the number of signals of the sources (1) and their Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the system memory and storage (7) can be Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM) or other memory devices of the like. 9- An apparatus and a method for finding both the number of signals of the sources (1) and their

Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the system memory and storage (7) devices may be to hard disks, CDROM and DVDROM.

10- An apparatus and a method for finding both the number of signals of the sources (1) and their Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the I/O devices (8) may be keypads, keyboards, mouse or USB ports

H-An apparatus and a method for finding both the number of signals of the sources (1) and their Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the network communication (9) interface can be wired or wireless and may support any one of the wide range of networking protocols. 12- An apparatus and a method for finding both the number of signals of the sources (1) and their

Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the hardware of the controller (6) includes the clock generation, reference oscillators, data and address bus controls.

13- An apparatus and a method for finding both the number of signals of the sources (1) and their Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the processing unit (5) is employed in source detection and DOA estimation. 14- An apparatus and a method for finding both the number of signals of the sources (1) and their Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the processing unit (5) may be a digital signal processor (DSP) or a microprocessor.

15- An apparatus and a method for finding both the number of signals of the sources (1) and their Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the processing unit (5) may be programmed by any one of the programming languages.

16- An apparatus and a method for finding both the number of signals of the sources (1) and their Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that Application Specific Integrated Circuit (ASIC) or Field Programmable Gate Array (FPGA) can be used for the processing unit (5).

17- An apparatus and a method for finding both the number of signals of the sources (1) and their Direction of Arrivals (DOA's) as claimed in any of the preceding claims and characterized in that the connections between the units of the apparatus may include multiple data and address connections. 18- An apparatus comprising a storage medium having a plurality of programming instructions designed to enable the apparatus to determine the number of sources and their DOA's according to the methods in claims 1 and 2.

19- An apparatus comprising:

• a plurality of antennas or sensors to receive a plurality of signals; • a RF unit coupled to the antennas or sensors;

• a receiver with more than one channel to down convert the received signals;

• a number of source detection and direction of arrival estimation unit coupled to the receiver to determine the number of sources and estimate their DOA's.

20-An apparatus according to Claims 18 or 19 and comprises a machine readable medium having stored a plurality of programming instructions designed to enable the apparatus to determine the number of sources and their DOA's.