Signal processing method and apparatus for computing an optimal weight vector of an adaptive antenna array system

[0002] The present invention relates to a technique utilizing an array antenna; and, more particularly, to a method and apparatus for optimizing the beam pattern of an array antenna system and its applications to transmitting and receiving systems by finding a weight vector capable of maximizing the signal to interference plus noise ratio in as accurate and simple way as possible.

[0003] An antenna system that improves the performance of a wireless communication with a proper beam pattern is generally referred to as “smart antenna system (SAS)”. A theory related to the design of the SAS from a weight vector that maximizes the signal to interference plus noise ratio has been published in a prior art, [1]Ayman F. Naguib, “Adaptive Antennas for CDMA Wireless Networks”, Ph. D. Dissertation, Dept of Electrical Engineering, Stanford University, August 1996. In [1], the weight vector is obtained from an eigenvector corresponding to the largest eigenvalue of a generalized eigen-problem as follows:

[0004] R_yw=ηR_uw  (1)

[0005] where R_yis the autocovariance matrix of the received (RX) signal vector y, which is obtained from the despreader output, R_uis the autocovariance matrix of the undesired signal vector u, and λ and w are the eigenvalue and eigenvector of the eigen-problem shown in (1), respectively. In short, R_y=E[y y^H] and R_u=E[u u^H], where E[*] denotes the expectation of *.

[0006] Throughout this manuscript, vector and matrix quantities are written in lower case and upper case, respectively.

[0007] From [1], it can be observed that the optimal weight vector is the eigenvector corresponding to the largest eigenvalue of the eigen-problem shown in (1). However, since the autocovariance matrices R_yand R_ushould be computed from the expectation of the power of y and u, it is never possible in actual signal environment to form the equation (1) at every snapshot for each of which the optimal weight vector should be computed. Even if the equation is formed somehow, since the computation of an eigenvector corresponding to the largest eigenvalue of a generalized eigen-problem requires a lot of computations, there arises many serious difficulties in applying the theory of [1] to the actual wireless communication world.

[0008] Recently, as the demand of the mobile communication and other wireless telecommunications increases rapidly, there arises an extremely keen need for developing the adaptive antenna array system that adopts an optimal weight vector in as accurate and simple way as possible. However, due to the limit of conventional techniques as mentioned above, it seems impossible to cope with the rapidly growing demand with the current techniques. Therefore, it is extremely and desperately required to develop a new technology for designing a smart antenna system enhancing the communication capacity and communication quality with a realizable complexity without loss of accuracy because of the simplicity.

[0009] In order to overcome the composite problems in the conventional techniques and eventually to cope with the drastically increasing demand of the wireless communications, this invention presents a simple and accurate way of computing the weight vector that maximizes the signal to interference plus noise ratio. By applying the smart antenna system designed by the technique provided in this invention into practical wireless communications, it is indeed possible to tremendously increase the communication capacity and enhance the communication quality. The objective of this invention is to suggest an optimal beam-forming method and communication apparatus that applies this method by providing the computation of an optimal weight vector for an antenna array system operating in a time-vary signal environment such as mobile communications.

[0010] In order to accomplish this objective, this invention provides a signal processing method and apparatus that generates a weight vector which maximizes the signal to interference plus noise ratio from the received signal vectors x and y, where x (pre-correlation signal vector) and y (post-correlation signal vector) are the received signal vectors obtained at the input and output of the correlators, i.e., despreading unit, which correlate the received signals with the PN (pseudo-random noise) code of the desired signal in a given CDMA system, respectively.

[0011] The above and other objects and features of the instant invention will become apparent from the following description of preferred embodiments taken in conjunction with the accompanying drawings, in which:

[0012] FIG. 1 illustrates a block diagram illustrating the adaptive antenna array system including a signal processing apparatus in accordance with the present invention; and

[0013] FIG. 2 illustrates a flowchart describing a preferable embodiment of the signal processing method of computing an optimal weight vector of an adaptive antenna array system in accordance with the present invention.

[0014] FIG. 2 illustrates a flowchart describing a preferable embodiment of the signal processing method of computing an optimal weight vector of an adaptive antenna array system in accordance with the present invention.

[0015] As described in [1], the weight vector w that maximizes the signal to interference plus noise ratio can be found from an eigenvector corresponding to the largest eigenvalue of the eigen-problem shown in (1). It is important to note that the autocovariance matrix of the undesired signals R_ucan be written as $\begin{array}{cc}{R}_u=\frac{G}{G-1}{R}_x-\frac{1}{G-1}{R}_y& \left(2\right)\end{array}$

[0016] where G is the processing gain of a given CDMA system.

[0017] Combing (2) and (1), it can be observed that to compute the weight vector w maximizing the signal to interference plus noise ratio is equivalent to compute an eigenvector corresponding to the largest eigenvalue of the following eigen-problem:

[0018] R_yw=λR_xw  (3)

[0019] Also, equivalently, it is possible to compute the target eigenvector by finding an eigenvector corresponding to the smallest eigenvalue of the following eigen-problem:

[0020] R_xw=λR_yw  (4)

[0021] The weight vector w, i.e., the solution of the eigen-problem (3) or (4), can easily be found by utilizing the well known technique, Lagrange's formula, after modifying it with the signal processing technique presented in this invention. The theoretical background and application method of the signal processing technique based on the Lagrange's formula is well described in our previous works including [2] D. Shim and S. Choi, “A new blind adaptive algorithm based on Lagrange's formula for a real-time design of a smart antenna”, Proc. IEEE VTC98, vol. 3, Montreal, Canada, May 1998, pp. 1660-1664.

[0022] Let's first derive an adaptive procedure of computing the weight vector w from the maximum eigenvector of (3). Then, the adaptive procedure of finding the weight vector from the minimum eigenvector of (4) can easily be derived by exchanging the parameters of x (pre-correlation signal index) and y (post-correlation signal index).

[0023] Consider a functional and constraint as given in (5) in order to find the weight vector w from the maximum eigenvector of (3) by utilizing the Lagrange's formula:

[0024] Maximize w^HR_yw+λ(1−w^HR_xw) subject to w^HR_xw=1  (5)

[0025] where λ is Lagrange's multiplier which approaches the maximum eigenvalue of (3) as the iteration is proceeded. Starting from an initial guess w(0), the adaptive procedure based on Lagrange's formula updates the weight vector at each snapshot in order to converge to the weight vector satisfying (5) as follows: $\begin{array}{cc}w\left(n+1\right)=w\left(n\right)+\frac{1}{2}\mu \nabla \left(n\right)& \left(6\right)\end{array}$

[0026] where n is the snapshot index, μ denotes the adaptive gain, and is the gradient vector ∇(n) of the functional (5) with respect to the weight vector. Since the way of setting μ and ∇(n) satisfying (5) has already been disclosed in [2] and our other previous works such as Korean patent No. 17931 issued on May 25, 1996 and U.S. Pat. No. 5,808,913 issued on 1998, this invention just discloses how to determine the weight vector with the maximum eigenvector of (3) and the minimum eigenvector of (4). In order to compute the weight vector from the minimum eigenvector of (4) instead of from the maximum eigenvector of (3), it is required not only to exchange the parameters of x (pre-correlation signal index) and y (post-correlation signal index) but also to change the positive sign in (6) with negative one. Then, the functional (5) would be minimized. These two procedures, i.e., maximization and minimization procedure, are introduced as two distinct preferable embodiments in this invention.

[0027] In addition to the adaptive procedure of computing the optimal weight vector, this invention also discloses a way of determining a reference antenna element in an antenna array system in such a way that the resultant array system can exhibit the best performance in real signal environments. The way of determining the reference antenna element exposed in this invention seems to provide the best performance not only for the array system designed by the present technique of this invention but also for the general array systems designed by other techniques. The problem of determining the reference antenna element in a given array system having N elements is to determine how the phase of the received signal at each antenna element is to be synchronized. In other words, the phase of the received signal at each antenna element is synchronized to that of the reference antenna element. In order to understand the phase synchronization, let's consider the received signal obtained at the output of the despreader for the mth antenna element as follows: $\begin{array}{cc}{y}_m\left(t\right)=\sum _{n=1}^{J}s\left(t\right)\sum _{i=1}^L{e}^{\mathrm{j2\pi }\left(f_D\cos {\zeta }_{i,n}t-f_e{\tau }_{i,n}\right)}{e}^{-j\left(m-m_o\right){\mathrm{\pi sin\theta }}_{i,n}}+\mathrm{interference}+\mathrm{noise}& \left(7\right)\end{array}$

[0028] where y_m(t) is the received signal at the mth antenna element, n in $\sum _{n=1}^J$

[0029] is the finger index, J is the total number of fingers (=number of multipath clusters), s(t) is the transmitted signal from the desired user, i is the index of the scattered components in $\sum _{i=1}^L,$

[0030] and L is the total number of scattered components in a path cluster. Note that e^{j2π(fcos ζt−fτ)}denotes the fading term including the Doppler shift and propagation delay and e^{−j(m−m)πsin θ}is the inter-element phase delay. Note that, from the term e^{−j(m−m)πsin θ}, it can be observed that the signal model shown in (7) considers the angle spread and the reference antenna element is m₀th element. As mentioned earlier, to determine the reference antenna element is to determine the value for m₀.

[0031] The most serious problem in compensating the carrier phase delay for the desired signal s(t) in a given array system is that there should be only one value to compensate the carrier phase delay while the carrier phase delay for the desired signal s(t) is different at each antenna element because of the angle spread of the desired signal. The carrier phase compensation should indeed be only one value because the inter-element phase differences of the desired signal, which is determined by the incident angle of the desired signal, should be maintained to provide an appropriate beam pattern with an optimal weight vector. At the reference antenna, by substituting m₀for m in (7), the exact value for the carrier phase delay can be obtained, which in turn enables the exact phase delay compensation. However, as the antenna element located farther and farther from the reference element, i.e., |m−m₀| increases, the carrier phase delay becomes different from that at the reference antenna element. For example, when the array consists of 8 elements, if the reference antenna element has been determined with an element located at one end of the array geometry, the element located at the other end is separated from this reference element by 3.5λ, where λ denotes the wavelength at the carrier frequency, which will cause a lot of errors in carrier phase compensation. Therefore, it is strongly recommended to determine the reference antenna element with the one located at the center of the array geometry such that the distance of the farthest element from the reference element can be minimized, which in turn will minimize the error in carrier phase delay compensation.

[0032] As mentioned earlier, the problem arising in the compensation of carrier phase delay is due to the mutually contradictory facts that the exact phase delay to be compensated is different at each antenna element because of the angle spread of the desired signal while the compensation can be done only with a single value. Therefore, the compensation of the carrier phase delay for the desired signal can exactly be performed only at the reference antenna element and the compensation error increases as the antenna location is farther and farther from the reference antenna element. For example, when the number of antenna elements is 8, if an element located at one end of the array has been designated as being the reference element, the element at the other end will be separated from that reference element by about 3.5 wavelengths, which will cause a remarkable error in phase compensation. If the third or fourth antenna element has been designated as the reference one, then the element at the end of the array will be separated only by 2 wavelengths. Consequently, the error in phase compensation can be reduced considerably by selecting the reference antenna element with the one located at the center of the array geometry. Through the computer simulations, it has been found that the BER (bit error rate) due to the erroneous phase compensation can be reduced nearly one tenth by selecting the center element as the reference one.

[0033] As the first preferable embodiment, this invention discloses a method of computing the weight vector with an eigenvector corresponding to the largest eigenvalue of the eigen-problem (3) by updating the weight vector through the procedure of (7) at each snapshot such that (5) can be maximized, which is an application of the prior art, Lagrange's formula. The adaptive procedure based on the Lagrange's formula can be applied to mobile communications through the three steps as follows:

[0034] <Initial Stage> Set up an initial guess for the weight vector w. For an efficient convergence, it is recommended have the normalized and received signal vector after the despreading procedure as the initial value, i.e., y(0)/∥y(0)∥ where ∥y(0)∥={square root over ((y^H(0)y(0)))}.

[0035] <Step 1> Update the autocovariance matrices, R_x(pre-correlation autocovariance matrix) and R_y(post-correlation autocovariance matrix), with the received signal vector x(n) (a pre-correlation signal vector) and y(n) (post-correlation signal vector) of the present snapshot through the procedure shown in (8) and (9), respectively:

[0036] R_x←fR_x+x(n)x(n)^H  (8)

[0037] R_y←fR_y+y(n)y(n)^H  (9)

[0038] where the matrices are formed as R_x=x(0)x(0)^Hand R_y=y(0)y(0)^Hat the initial stage, f is a predetermined forgetting factor in the interval 0<f≦1, and the superscript H is the Hermitan operator.

[0039] <Step 2> Compute the Lagrange multiplier λ at the present snapshot from the present weight vector w, the autocovariance matrices R_xand R_ywhich have been updated by (8) and (9), respectively, and a preset adaptive gain μ as follows: $\begin{array}{cc}\lambda =\frac{\lfloor b-\sqrt{\left(b^2-\mathrm{ac}\right)}\rfloor }{a}& \left(10\right)\end{array}$

[0040] where $a=\mu w^H{R}_x^{3}w,b=\frac{\left(2w^H{R}_x^{2}w+\mu w^H{R}_x^{2}w+\mu w^H{R}_y{R}_x^{2}w\right)}{2}$

[0041] and c=μw^HR_yR_xR_yw+w^HR_yR_xw+w^HR_xR_yw.

[0042] <Step 3> Update the weight vector utilizing the present weight vector w, said Lagrange multiplier λ, said adaptive gain μ, and autocovariance matrices R_xand R_yas follows:

[0043] w←w+μ[R_yw−λR_xw]  (11)

[0044] It is possible to include an additional step for normalizing the weight vector to a unit magnitude after the update procedure shown in (11). In addition, in order to synchronize the phase of the signal at each antenna channel to the phase of the signal induced at the reference antenna element, it is recommended to normalize the weight vector after dividing every element of the resultant weight vector obtained in (11) by the weight corresponding to the reference antenna element.

[0045] The final array output z is obtained from the inner product between the present weight vector w and the post-correlation signal vector y, i.e., z=w^Hy. The weight vector is updated after the above written 3 steps have been executed at each snapshot. In order for the communication of the present invention to be continuously performed, the procedure must be returned to <Step 1> after <Step 3> with an increased snapshot index by 1. Since there are matrix operations, the computational load of the adaptive procedure shown in this preferable embodiment is O(N²) where N is the number of antenna elements.

[0046] In this preferable embodiment, an adaptive procedure of computing an eigenvector corresponding to the smallest eigenvalue of (4). The technique ultimately searches for the same weight vector that converges to an eigenvector corresponding to the largest eigenvalue of (3). To find the target eigenvector corresponding to the smallest eigenvalue of (4), the signal index x representing pre-correlation and y representing post-correlation are interchanged in <Step 3> and the sign of (11) is changed as follows:

[0047] w←w−μ[R_xw−λR_yw]  (12)

[0048] The adaptive procedure of finding an eigenvector corresponding to the smallest eigenvalue of (4), instead of that corresponding to the largest eigenvalue of (3), can be summarized as follows:

[0049] <Initial stage> Set up an initial guess w.

[0050] <Step 1> Update the autocovariance matrices, R_xdenoting a pre-correlation autocovariance matrix and R_ydenoting a post-correlation autocovariance matrix, with the received signal vector x(n) denoting a pre-correlation signal vector and y(n) denoting a post-correlation signal vector of the present snapshot through the procedure shown in (8) and (9), respectively.

[0051] <Step 2> Compute the Lagrange multiplier λ at the present snapshot from the present weight vector w, the autocovariance matrices R_xand R_ywhich have been updated by (8) and (9), respectively, and a preset adaptive gain μ as follows: $\begin{array}{cc}\lambda =\frac{\lfloor b-\sqrt{\left(b^2-\mathrm{ac}\right)}\rfloor }{a}& \left(13\right)\end{array}$

[0052] where $a=\mu w^H{R}_y^{3}w,b=\frac{\left(-2w^H{R}_y^{2}w+\mu w^H{R}_y^2{R}_{x}w+\mu w^H{R}_x{R}_y^{2}w\right)}{2}$

[0053] and c=μw^HR_xR_yR_xw−w^HR_yRxw−w^HR_xR_yw.

[0054] <Step 3> Update the weight vector utilizing the prsent weight vector w, said Lagrange multiplier λ, said adaptive gain μ, and autocovariance matrices R_xand R_yas shown in (12). n

[0055] It is possible to include an additional step for normalizing the weight vector to a unit magnitude after the update procedure shown in (12). In addition, in order to synchronize the phase of the signal at each antenna channel to the phase of the signal induced at the reference antenna element, it is recommended to normalize the weight vector after dividing every element of the resultant weight vector obtained in (12) by the weight corresponding to the reference antenna element.

[0056] The final array output z is obtained from the inner product between the present weight vector w and the post-correlation signal vector y, i.e., z=w^Hy. The weight vector is updated after the above written 3 steps have been executed at each snapshot. In order for the communication of the present invention to be continuously performed, the procedure must be returned to <Step 1> after <Step 3> with an increased snapshot index by 1. Since there are matrix operations, the computational load of the adaptive procedure shown in this preferable embodiment is O(N²) where N is the number of antenna elements.

[0057] By utilizing one of the two preferable embodiments given above, it is possible to compute a weight vector that maximizes the signal to interference plus noise ratio. The required computational load in these two procedures given in the present invention is less than any conventional methods in computing the solution of the generalized eigen-problem. It also means the required computation time has tremendously reduced compared to the conventional techniques. The simplification of the computational procedure results in not only a conspicuous reduction of system price but also a remarkable improvement in the system performance. This invention provides a novel technique of reducing the complexity of the computational procedure without affecting the accuracy in the weight vector. It is possible to reduce the computational load by excluding the accumulations all the previous received signal vectors in computing the autocovariance matrices. It means the autocovariance matrices are computed only with the instantaneous signal vectors at each snapshot. Since the key idea of utilizing the instantaneous signal vectors for reducing the computational load has been already disclosed in our previous works, i.e., Korean patent 17931 (1996. 5. 25.), U.S. Pat. No. 5,808,913, only the adaptive procedure of computing the optimal weight vector is shown in this invention.

[0058] First, the simplified adaptive procedure of computing the eigenvector corresponding to the largest eigenvalue of (3) is introduced. Then, the adaptive procedure of computing the eigenvector corresponding to the smallest eigenvalue of (4) is easily be derived, as shown previously in this invention, by interchanging the signal index x (pre-correlation) and y (post-correlation) and changing the positive sign to the negative sign in (12).

[0059] The simplified adaptive procedure of computing the weight vector with an eigenvector corresponding to the largest eigenvalue of (3), excluding all the matrix operations, can be summarized as follows:

[0060] <Initial Stage> Set up an initial guess of the weight vector w. As in the other preferable embodiments, for a fast convergence, the received signal vector obtained at the output of the despreader, i.e., y(0)/∥y(0)∥, is recommended for the initial guess where ∥y(0)∥={square root over ((y^H(0)y(0)))}.

[0061] <Step 1> Compute the Lagrange multiplier λ at the present snapshot from the present weight vector w, the received signal vectors x representing pre-correlation RX signal vector and y representing post-correlation RX signal vector, and a preset adaptive gain μ as follows: $\begin{array}{cc}\lambda =\frac{\lfloor b-\sqrt{\left(b^2-\mathrm{ac}\right)}\rfloor }{a}& \left(14\right)\end{array}$

[0062] where a=μ|δ|²α², b=|δ|²α+μαRe[γδz*] and c=μ|γ|²|z|²Re[γδz*] with x^Hx≡α, y^Hy≡β, x^Hy≡γ w^Hx≡δ, z=w^Hy and the final array output z being z=w^Hy.

[0063] <Step 2> Update the weight vector w with the present weight vector w, said Lagrange's multiplier λ, said adaptive gain μ, said signal vectors x and y, said final array output z and w^Hx≡δ as follows:

[0064] w←w+μ[yz*−λxδ*]  (15)

[0065] As in the previous preferable embodiment, the final array output z is obtained by z=w^Hy. The weight vector is updated after the above written 2 steps have been executed at each snapshot. In order for the communication of the present invention to be continuously performed, the procedure must be returned to <Step 1> after <Step 2> with an increased snapshot index by 1. As in the previous preferable embodiments, it is possible to include an additional step for normalizing the weight vector to a unit magnitude after the update procedure shown in (15). In addition, in order to synchronize the phase of the signal at each antenna channel to the phase of the signal induced at the reference antenna element, it is recommended to normalize the weight vector after dividing every element of the resultant weight vector obtained in (15) by the weight corresponding to the reference antenna element. Since there is no matrix operation in the adaptive procedure of this preferable embodiment, the computational load of the adaptive procedure shown in this preferable embodiment is O(N) where N is the number of antenna elements. It means that the optimal weight vector that maximizes the signal to interference plus noise ratio can be obtained only with the vector operations without any matrix operations.

[0066] As mentioned previously, instead of computing the eigenvector corresponding to the largest eigenvalue of (3), this embodiment introduces a simplified adaptive procedure of computing an eigenvector corresponding to the smallest eigenvalue of (4) as an optimal weight vector. As in the second preferable embodiment, the adaptive procedure can be derived from the third preferable embodiment by interchanging the signal index x representing pre-correlation and y representing post-correlation, and changing the sign when the weight vector is updated as shown in (12). The adaptive procedure can be summarized as follows.

[0067] <Initial Stage> Set up an initial guess for the weight vector w(0).

[0068] <Step 1> Compute the Lagrange multiplier λ at the present snapshot from the present weight vector w, the received signal vectorsx (pre-correlation RX signal vector) and y (post-correlation RX signal vector), and a preset adaptive gain μ as follows: $\begin{array}{cc}\lambda =\frac{\lfloor b-\sqrt{\left(b^2-\mathrm{ac}\right)}\rfloor }{a}& \left(16\right)\end{array}$

[0069] where a=μ|z|²β², b=−|z|²β+μβRe[zδ*γ*] and c=μ|γ|²|δ|²−2Re[γ*δ*z] with x^Hx≡α, y^Hy≡β, x^Hy≡γ, w^Hx≡δ and the final array output z being z=w^Hy.

[0070] <Step 2> Update the weight vector w with the present weight vector w, said Lagrange's multiplier λ, said adaptive gain μ, said signal vectors x and y, said final array output z, and w^Hx≡δ, as follows:

[0071] w←w−μ[xδ*−λyz*]  (17)

[0072] As in the previous preferable embodiments, the final array output z is obtained by z=w^Hy. The weight vector is updated after the above written 2 steps have been executed at each snapshot. In order for the communication of the present invention to be continuously performed, the procedure must be returned to Step 1> after <Step 2> with an increased snapshot index by 1. As in the previous preferable embodiments, it is possible to include an additional step for normalizing the weight vector to a unit magnitude after the update procedure shown in (17). In addition, in order to synchronize the phase of the signal at each antenna channel to the phase of the signal induced at the reference antenna element, it is recommended to normalize the weight vector after dividing every element of the resultant weight vector obtained in (17) by the weight corresponding to the reference antenna element. Since there is no matrix operation in the adaptive procedure of this preferable embodiment, the computational load of the adaptive procedure shown in this preferable embodiment is O(N) where N is the number of antenna elements. It means that the optimal weight vector that maximizes the signal to interference plus noise ratio can be obtained only with the vector operations without any matrix operations.

[0073] It is well known that the antenna array system includes a number of antenna elements, which are arranged according to a predetermined geometry. By appending a proper phase delay at each antenna channel, it is possible to control the beam pattern of a given antenna array system for either receiving signals or transmitting signals or both. The basic knowledge of the antenna array system has already been disclosed in prior arts released by the same inventor of this invention such as Korean patent (application number 893, 12171, 12172, 17931, 25377, and 73901 filed on Jan. 17, 1996, Apr. 18, 1996, Apr. 18, 1996, May 25, 1996, Jun. 28, 1996, and Dec. 26, 1997, respectively.). This invention is superior to the prior arts in terms of accuracy without loss of simplicity, which means that this invention provides an optimal weight vector is more robust than that given by the prior arts without remarkably increasing the complexity.

[0074] The preferable embodiments and the figures given in this invention have been provided in order not to restrict the application of this invention within them. They have been given merely for an easy explanation of the techniques presented in this invention. Therefore, it is certain that various applications, replacements, and/or changes of this invention should also belong to this invention itself because it is straightforward that a normal engineer with a reasonable knowledge in the related fields can easily apply, replace, and/or change the techniques of this invention within the technical boundary of this invention. In addition, since it is possible to express this invention using different terminology, the applications, replacements, and/or changes of this invention that might be presented in different terminology should also belong to this invention.

[0075] It has been shown that an array system of which the weight vector is determined by an eigenvector corresponding to the largest eigenvalue of the autocovariance matrix of the received signals can reduce the BER nearly by one tenth of a normal receiving system having a single antenna, when the autocovariance matrix is formed with the despread signals only. This has already been published by the same inventor of this invention at [2] and [3]S. Choi, et al., “Design of an adaptive antenna array for tracking the source of maximum power and its application to CDMA mobile communications”, IEEE trans on Antenna and Propagations, vol. 45, No 9, September 1997, pp. 1393-1404, and also in prior arts invented by the same inventor such as Korean patents (application number 893, 12171, 12172, 17931, 25377, and 73901 filed on Jan. 17, 1996, Apr. 18, 1996, Apr. 18, 1996, May 25, 1996, Jun. 28, 1996, and Dec. 26, 1997, respectively.). What is new in this invention is that the performance of the adaptive array system can further be improved by determining the weight vector from the solution of a generalized eigen-problem which includes the pre-correlation signals as well as the post-correlation signals, which are obtained at the output and input ports of the despreader, respectively. From the various computer simulations, though the amount of the improvement depends on a given signal environment, it seems possible to further reduce the BER nearly by a half by encountering the pre-correlation signals together with the post-correlation signals in accordance with the procedure described in this invention. However, it seems inevitable that the computational load is increased a little by appending the autocovariance matrix of the pre-correlation signals in the adaptive procedure. Besides the robustness, the technique provided in this invention has a linear complexity. More specifically speaking, the adaptive procedure given in this invention provides a solution of the generalized eigen-problem with a less amount of computation compared to any other methods that have been known in the world so far. The reduction of the computational load directly results in a superior competitiveness in price as well as a superior performance.