Abstract:
A Multi Input Multi Output (MIMO) Wireless Communication System method and apparatus are proposed whereby in a 2-way wireless communication system with scattering, random and imperfectly estimated propagation channels the ubiquitous and inherent MIMO cross-talk interference problem is solved so that robust and predictable Extended Communication Range and Extended Data Rate are achieved.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]    This application claims the benefit of the following US PTO Provisional Applications:  
         [0002]    a. Nissani (Nissensohn), D. N., ‘Wireless Communication Multi Antenna Array Method and Apparatus providing Extended Range and Extended Rate across Random or Imperfectly Estimated Channels’, U.S. PTO 60/409,048, filed Sep. 9, 2002  
         [0003]    b. Nissani (Nissensohn), D. N., ‘Channel Acquisition, Equalization and Processing Method and Apparatus for Multi Antenna Array Wireless Communication Systems’, U.S. PTO 60/419306, filed Oct. 18, 2002  
         [0004]    c. Nissani (Nissensohn), D. N., ‘Multi Input Multi Output Wireless Communication Method and Apparatus providing Extended Range and Extended Rate across Imperfectly Estimated Channels’, U.S. PTO 60/429018, filed Nov. 26, 2002  
     
    
     
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT  
         [0005]    Not Applicable  
         CITED REFERENCES  
         [0006]    The following references are cited within this invention description:  
           [0007]    [1] Foschini, J. G., ‘Wireless communications system having a layered space-time architecture employing multi-element antennas’, U.S. Pat. No. 6,097,771  
           [0008]    [2] Foschini, J. G., ‘Wireless communications system having a space-time architecture employing multi-element antennas at both the transmitter and receiver’, U.S. Pat. No. 6,317,466  
           [0009]    [3] Telatar, E. I., ‘Capacity of Multi-antenna Gaussian Channels’, Technical Memorandum, Bell Laboratories, October 1995  
           [0010]    [4] Nissani (Nissensohn), D. N, ‘Multi Antenna Array Method and Apparatus providing unified Antenna Array Gain, Diversity Gain and Extended Data Rate in OFDM Communication Systems’, U.S. PTO 60/401370, Jul. 20, 2002  
           [0011]    [5] Proakis, J. G., ‘Digital Communications’, McGraw-Hill, 1995  
           [0012]    [6] Van Trees, H., ‘Detection, Estimation and Modulation Theory’, Wiley, 1968  
           [0013]    [7] Stewart, G. W., ‘Perturbation Theory for the Singular Value Decomposition’ UMIACS-TR-90-124, September 1990  
           [0014]    [8] Duda, R. O., Hart, P. E., ‘Pattern Classification and Scene Analysis’, Wiley &amp; Sons,  
           [0015]    [9] Gallager, R. G., ‘Information Theory And Reliable Communication’, MIT, 1968  
           [0016]    [10] Paulraj, A. J., et al. ‘Method and wireless systems using multiple antennas and adaptive control for maximizing a communication parameter’, U.S. Pat. No. 6,351,499  
           [0017]    [11] Nissani (Nissensohn), D. N., ‘The MIMO cross-talk interference problem—a novel solution’, internal Technical Report, March 2003  
         BACKGROUND OF THE INVENTION  
         [0018]    This invention relates in general to Multi Input Multi Output (MIMO) 2-way Wireless Communication Systems. More specifically, this invention is related to MIMO 2-way Wireless Communication Systems where Multiple Antenna Arrays (MAA) are used in some of the system communication devices, where the propagation Channel Matrix is random, where Channel Information is available at both the Transmitter and Receiving sides, and where said propagation Channel Matrix information is imperfectly estimated.  
           [0019]    During recent years Multi Input Multi Output (MIMO) schemes were proposed for Wireless Communication Systems whereby some of the system communication devices include Multiple Antenna Arrays (MAA) and associated transmission and reception circuitry. MIMO systems, when operated in richly scattering channels (such as typical urban and indoor channels in conjunction with properly designed antenna arrays) may exhibit antenna array gain, space diversity gain (and thus Extended Range), and, in certain cases, the ability to effectively multiply the overall data rate transferred thru the channel by means of splitting the data stream into several sub-streams, each transferred through one of a set of separate propagation channel ‘modes’ (and thus achieving Extended Rate). Note that while the term Extended Capacity could be used instead of both Extended Range/Rate (since range can be usually traded off by rate and vice-versa) we prefer the latter distinction along this text to distinguish between the ‘conventional’ array/diversity gains on one hand, and the ability to transmit several data sub-streams in parallel, which may be achieved only when the 2 communicating sides include an MAA, on the other.  
           [0020]    In some of these schemes, relevant to this invention, the propagation complex Channel transfer Matrix H of R×L elements is estimated at one or both of the receiving sides during a Training Stage, where L and R denote the number of antennas and corresponding circuitry in the Left and Right side devices respectively (and usually L and/or R&gt;1). A standard Singular Value Decomposition operation (usually denoted SVD in elementary matrix algebra texts) is subsequently conducted on this estimated channel matrix so that H=UDV′ where U and V are RxR and LxL unitary matrices whose columns are the eigen-vectors of HH′ and H′H respectively, D is an RxL diagonal matrix, and ( )′ denotes the matrix conjugate transpose operator.  
           [0021]    The diagonal elements Di of the matrix D, known as the Singular Values of H, are the (non-negative, real) square roots of the eigen-values of H′H, and, as such, are proportional to the gain of each of the channel H fore-mentioned parallel transmission ‘modes’. In some of these same MAA schemes another diagonal real Power Allocation Matrix A is applied at the transmitting side to the data symbols vector s, prior to any other processing so that equal power is allocated to each of the user data sub-streams, or (other times) alternatively so that the data sub-stream components associated to channel ‘modes’ with more favorable gain (i.e. greater magnitude Singular Values) are allocated more power following the ‘water pouring’ algorithm described in e.g. [9], and vice-versa, and so that the overall transmitted power is constrained.  
           [0022]    At the end of this Training Stage, information related to this channel matrix H (or to relevant parts of its SVD decomposition) resides at both Left and Right sides, the Transmitting side (say Left) applies the unitary complex matrix V as a transmission weight upon the transmitted vector sequence, and the Receiving side (say Right) applies the unitary complex matrix U′ as its reception weight upon the received vector.  
           [0023]    Summarizing in matrix notation the signal processing executed in some of these fore-mentioned schemes as described above, denoting by s the (usually complex) source data sub-stream vector (of dimension M≦min {L, R}), by x the complex base-band representation of the transmitted signal vector (of dimension L, assuming without loss of generality that Left is the Transmitting side), by y the complex base-band representation of the received signal vector (of dimension R, assuming Right is the Receiving side), by r the recovered data sub-stream complex vector, and neglecting the receiving circuitry (and possibly interference) noise, we have:  
           
         x=VAs  
       
             y=Hx= ( UDV′ ) x=UDV′VAs    
             r=U′y= ( U′U ) D ( V′V ) As=DAs   Eq. 1  
           [0024]    where we have exploited the fact that both U and V are unitary (U′U=I where I is the Identity matrix, etc.). Hence, since both D and A are diagonal, each element of r is a (scaled) version of a corresponding element of s, as required for perfect and simple data recovery.  
           [0025]    Other MAA schemes, similar in purpose and nature, were also described (e.g. [4]) whereby the actual processing is conducted at the Frequency Domain, rather than the Time Domain, thus allowing optimization of the said Weighting Matrices to each useful bandwidth slot, for example each OFDM sub-carrier, as would be required in the presence of Frequency Selective Fading propagation channels.  
           [0026]    Still other MIMO schemes, less relevant to the present invention but also similar in purpose were described (e.g. [1], [2]) whereby no Channel Matrix information is required at the transmitting side, whereby the propagation complex Channel transfer Matrix H of RxL elements is assumed to be known only at the Receiving side, and whereby the received data recovery is performed by means of applying specific solution methods to the Equation y=Hx where y, H and x are as defined above.  
           [0027]    It is generally implicitly assumed in these schemes that the propagation channel matrix H is perfectly estimated during a so called Channel Training (or Acquisition) Stage so that perfect information about the channel is available at the end of said Training Stage at the receiving and, (if required) the transmitting sides. It is also generally assumed that the channel matrix H elements are complex random variables and, as such, that the Singular Values of H are random variables as well. The processing nature of the for-mentioned Channel Matrix Acquisition Stage is generally ignored, in contrast with non-MIMO wireless communication systems where (Scalar) Channel initial estimation methods have been extensively studied and applied (e.g. [5]).  
           [0028]    The assumption concerning perfect channel estimation is generally not valid. Typical propagation channels and receiving circuitry are noisy and the channel Training Stage is usually time limited. Since the channel matrix estimation error depends on both the channel measurements Signal to Noise Ratio (SNR) and on the number of measurements, the estimated result, denoted Hn is usually different from the actual channel matrix H, that is Hn=H+dH where dH is the estimation error. The Singular Value Decomposition of Hn is UnDnVn′ where, again, the subscript n denotes the noisy version of the actual corresponding counterparts UDV′ which were described above. Replacing in Equation 1 these noisy versions we get:  
             r=Un′y =( Un′U ) D ( V′Vn )As  Eq. 2  
           [0029]    where we do not get the perfect signal recovery as described in Equation 1 since Un′ U and V′Vn do not equal the Identity matrix anymore, so that the recovered data sub-stream elements of the vector s include cross-talk noise from the other sub-stream elements.  
           [0030]    As predicted by Matrix Perturbation Theory (e.g. [7]), the achieved cross-talk SNR depends on the norm of the perturbation dH, which in our case depends on the channel measurements SNR and the number of measurements, as well as on certain relationships between the singular values of H, which are random in our case since the matrix H is assumed to be random.  
           [0031]    In the context of the present invention it is also assumed that the Channel Matrix is relatively time invariant, that is only negligible changes in the matrix H occur during the duration of a transmission burst. This last assumption is reasonable when the relative motion between the communication devices is slow, such as in WLAN and Fixed Wireless Access Networks, or when the transmission bursts are of short duration (relative to the Doppler period), as is usually the case in Cellular Networks.  
         OBJECTIVES AND ADVANTAGES OF THE INVENTION  
         [0032]    A main objective of the present invention is to propose a comprehensive Method and corresponding Apparatus by which Extended Range and Extended Rate robust and predictable communication performance can be achieved in Wireless MIMO Communication Systems with imperfect Channel Matrix estimation.  
           [0033]    A second main objective of our present invention consists of the introduction and definition of a Channel Matrix Metrics to evaluate the level of for-mentioned cross-talk interference induced by different Channel Matrices.  
           [0034]    A third main objective of our present invention consists of the introduction and application, in relation to the for-mentioned Channel Matrix Metrics, of Pre-Equalizer operators used to transform a Channel Matrix instance, with given Channel Matrix Metrics into another, prescribed, Channel Matrix with more favorable Channel Matrix Metrics, and of different possible strategies to prescribe such Pre-Equalizer operators.  
           [0035]    A fourth main objective of the present invention consists of the introduction of the concept of ‘Good’ and ‘Bad’ channels, of corresponding Discriminating Functions, of Method and Apparatus required to classify said random instances of Channel Matrices as ‘Good’ or ‘Bad’, and of a Pre-Equalizer operator required to transform a said ‘Bad’ channel into a said ‘Good’ channel so that the loss incurred in said transformation is minimal.  
           [0036]    A fifth main objective of our present invention consists of the introduction of the concept of net total (cross-talk and thermal) SNR gain and of Method and Apparatus required to solve for a modified channel with optimal said net total SNR gain and of a Pre-Equalizer operator required to transform an original channel into said optimal channel.  
           [0037]    A sixth main objective of our present invention consists of the definition and characterization of a Post-Equalizer operator used to cancel residual sub-stream interference, and the Method and Apparatus required to calculate said Post-Equalizer and to apply it to the received signal.  
           [0038]    A seventh main objective of our present invention consists of the characterization and definition of MIMO Training Matrices devised so that a given side device may initially estimate, or acquire, the radio waves propagation Channel Matrix and relevant information derived thereof between itself and the other side device for purpose of further being able to efficiently transmit to, or receive from, said other side device and the corresponding Method and Apparatus to achieve this.  
           [0039]    A major advantage of the proposed invention is the significant user data Signal-to-Noise-Ratio (SNR) enhancement achieved, relative to systems not applying the methods described herein, with the immediate result of relative increase in communication system capacity and the derived range and user data rate.  
           [0040]    Another advantage of the proposed invention is that it achieves the stated objectives with no major impact on communication device implementation complexity.  
           [0041]    Still another advantage of the proposed invention is that it achieves the stated objectives with no increase in total transmitted power.  
           [0042]    Still another advantage of the proposed invention is that other known techniques such as Adaptive Modulation and Interference Cancellation may be applied on top of the techniques introduced in this invention to further enhance communication performance  
           [0043]    Still another advantage of the present invention is that it is directly applicable both to MIMO Communication Systems whereby MAA Processing at the transmitting and receiving sides is applied at the time domain, as well as to MIMO Communication Systems whereby MAA Processing is applied at the frequency domain such as in OFDM MIMO Communication Systems (e.g. [4]).  
           [0044]    Still other advantage of the proposed invention is that when an MAA device in which the current invention is implemented communicates with a (non MAA featured) Single Antenna device, then the MAA featured device transmitted signal does not differ in no modulation significant way from a signal transmitted by such a said Single Antenna device thus allowing compatible communication between MAA and Single Antenna devices.  
         SUMMARY OF THE INVENTION  
         [0045]    The proposed invention comprises a 2-way Wireless Communication Network, said Network including at least 2 communication devices, at least one of said communication devices comprising a Multi Antenna Array (MAA) element with its associated transmitting, receiving and processing circuits.  
           [0046]    While in the course of this invention description, by way of example and for the sake of clarity and brevity, a MIMO processing scheme based on the execution of said processing at the time domain, will be generally assumed, it is emphasized that this invention is directly applicable to other schemes as well, such as wherein the MIMO processing is executed at the frequency domain (such as in [4]).  
           [0047]    In accordance with the principles of this invention a pre-set MIMO Training Matrix S 0  (MTM in short), known to all communicating devices is generated and transmitted by (say) the Left side device and received and processed by (say) the Right side device, in such a manner so that at the end of said processing by the Right side device a (naturally noisy but in some sense optimal) estimate Hn of the Channel Matrix H and associated modified channel Hm, Transmission Weighting Matrix V, Reception Weighting Matrix U, Power Allocation Matrix A, and Pre-Equalizer Matrix P are calculated, relevant parts of said Channel Matrix derived information subsequently transferred to the Left side device (by means of an implicit ‘reverse’ channel), or alternatively, said training process repeated from Right side to Left side so that, in any case, at the end of such process, the required Channel Matrix information derivations are available and allocated to each relevant side.  
           [0048]    In further accordance with the principles of the present invention another pre-set MTM S 1 , similarly known to all communicating devices is generated and transmitted by (say) the Left side device and received and processed by (say) the Right side device in such a manner so that at the end of said processing by the Right side device a Post-Equalizer Matrix Q is calculated and available at the Right side device.  
           [0049]    As stated above our present invention consists of the characterization, definition, calculation and usage of these so called MIMO Training Matrices S 0  and S 1 , Transmission Weighting Matrix V, Reception Weighting Matrix U, Pre-Equalizer Matrix P, Post-Equalizer Matrix Q, and Power Allocation Matrix A devised so that efficient user data transmission may take place between a Transmitting side device and a Receiving side device within a MIMO Wireless Communication System.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0050]    [0050]FIG. 1 describes a typical deployment scenario of a 2-way MIMO Wireless Communication Network.  
         [0051]    [0051]FIG. 2 provides some characterizations of user data sub-streams cross-talk performance of random Channel Matrices.  
         [0052]    [0052]FIG. 3 presents a base-band block diagram of the Transmitter Segment of one MIMO Wireless Communication device and the Receiver Segment of another MIMO Wireless Communication device.  
         [0053]    [0053]FIG. 4 shows simulated Bit Error Rate (BER) vs. Eb/No performance results of a particular embodiment of the present invention 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0054]    A typical instance of a 2-way Wireless MIMO Network is shown in FIG. 1. According to the present invention such a Network should include at least 2 communication devices, such as  11 ,  12 ,  13 , or  14 , at least one of which should include a MIMO device such as those figuratively represented by  12  or  13 . Typically (but not necessarily) a Wire-line access Network  10  (such as a Local Area Network, or a Wide Area Network, or ‘the Internet’, or a Cellular Network Backbone) will be connected to part of the wireless communication devices, such devices usually called Access Points (APs), or Base-Stations, examples of which,  11  and  12 , are shown in FIG. 1.  
         [0055]    Other wireless communication devices, such as  13  or  14 , will stand alone, intercommunicating among themselves, or with the Wire-line Access Network  10 , through APs  11  and  12 . As further shown in FIG. 1 APs and Mobile Stations alike may comprise a Multi Antenna Array (MAA)  16  and its associated transmission, reception and processing circuitry, such as devices  12  (an AP) and  13  (a Mobile) in FIG. 1, while others, like  11  (an AP) and  14  (a Mobile) may consist of ‘simple’ non-MAA featured devices.  
         [0056]    Between each and every pair of the MIMO Network communication devices a propagation Channel, such as  15 , characterizing the propagation effects during signal transmission from  12  to  13  as shown in FIG. 1, may be defined. It should be noted that the propagation Channel characterizing signal transmission from  13  to  12 , not shown in FIG. 1, may be identical to the characteristics of Channel  15  in the original direction (i.e. from  12  to  13 ), as is the case when signal transmission in both directions is executed over the same carrier frequency at slightly different times (as in a Time Division Duplex, TDD scheme), while in other cases, such as when signal transmission is carried on over different carrier frequencies in both directions (as in Frequency Division Duplex, FDD scheme), the Channel characteristics may differ.  
         [0057]    The wireless Channel  15  between any two specified devices such as  12  and  13  of FIG. 1, in indoor and urban Network deployments, may typically be described by a complex random RxL matrix H, where R denotes the number of antennas in the Right side, MAA device  13 , L denotes the number of antennas in the Left side, MAA device  12 , and each element Hij in row i and column j of H defines the (complex base-band) response between reception antenna i of  13  and transmission antenna j of  12 .  
         [0058]    According to the present invention, H will be a complex scalar if both communication devices are of ‘simple’ non MAA featured type (such as  11  and  14  in FIG.  1 ); will be a one-dimensional vector if only one of the devices is MAA featured (such as the pair  11 - 13  in FIG. 1); and will be a 2-dimensional matrix when both communication devices are MAA featured (such as  12  and  13  in FIG. 1).  
         [0059]    In an indoor or urban wireless Network deployment, due to the scattering nature of the propagation channel, the elements of the matrices H will typically (but not necessarily) be weakly mutually correlated random variables, provided that the Multi Antenna Array elements are properly spaced and designed. In a typical deployment of the proposed invention the Channel Matrix  15  will be quasi static and will only vary negligibly since the time the H estimates, or the information derived thereof, are made available at both Right and Left sides just prior to transmission start, and till the end of the transmission burst period.  
         [0060]    Due to the Channel  15  signal attenuation and interference properties, to inherent physical limitations of the Receiving side components, to practical limitations in channel training stage duration, and to practical or regulatory limitations in transmission power the estimate of Channel  15  will be usually noisy, and will be thus denoted by Hn to distinguish it from the fore mentioned actual Channel Matrix H.  
         [0061]    It will also generally be assumed along this invention description that immediately prior to said Channel Acquisition the processes of Carrier Frequency and Symbol Timing information estimation and extraction have been completed so that both Carrier Frequency and Symbol Timing are known, down to reasonable accuracy, to the Receiving side communication device.  
         [0062]    [0062]FIG. 2 provides, under the context of motivation, some random Channel Matrices characterization, essential to the exposition of the present invention. As result of the channel noisy estimate, degradation of the self-orthogonality property of U and V (the fore mentioned unitary matrices, outcomes of the SVD of H) takes place, and cross-talk noise power is induced at each of the user data vector elements s i  by the other sub-streams vector elements s j , i≠j.  
         [0063]    This cross-talk power limits the attainable Signal To Noise Ratio (SNR) at each of the user sub-streams. As it turns out to be, the vast majority of the (randomly picked) Channel Matrices H suffers from unacceptable cross-talk noise. To demonstrate this we associate with any realization of the random Channel Matrix H a Matrix Metrics Si, i=1,2, . . . M, M≦{L,R}, as follows:  
           Si=Si ( H; {overscore (γ)}), so that Pr{xtlk_SNR_i&gt;Si}=T, i=1,2, . . . M  
         [0064]    where {overscore (γ)} is the mean channel SNR, and T is some appropriate demanding threshold (T=0.9 could be a typical value).  
         [0065]    While the relation between the value of Si and an instance of the random Channel H is functionally deterministic, the Matrix Metrics Si, being a function of the Random Matrices H, are themselves random variables. The Cumulative Probability Density Function (cdf) of Si is shown in 21, 22 of FIG. 2, for i=1 and 2, L=R=3, {overscore (γ)}=20 db, and T=0.9. As evident from  21  and  22  of FIG. 2 not ‘all matrices are born equal’; for example only a small portion (about 20%) of the whole population of H matrices maintain a cross-talk SNR — 1&gt;20 db, which is the minimum we would demand (in this example) in order not to cause our MIMO system to be cross-talk noise limited (rather than thermal noise limited).  
         [0066]    It should be then clear by now, that plain and direct application of weight matrices Vn and Un in the Transmitting and Receiving sides respectively, will be practically useless under reasonable conditions of imperfect channel estimation.  
         [0067]    As analyzed by Matrix Perturbation Theory (e.g. [7]) the magnitude of the orthogonality error is related to the norm of the perturbation matrix dH, as well as to certain relationships between the singular values Di of the matrix H, which are obviously a direct result of the specific instance of the random matrix H. Hence Si=Si (H; {overscore (γ)})=Si(D(H); {overscore (γ)}) as is illustratively shown for example in  23  and  24  of FIG. 2 for S 1  and S 2  respectively, where, for simplicity only 2 dimensions, D 1  and D 2  are shown, and where the points to the right of the Discriminant Function (see e.g. [8]) F 1  (D 1 , D 2 ; T 1 )=0 in 23 (and the Discriminant Function F 2  (D 1 , D 2 ; T 2 )=0 in 24) define all the points in the Singular Values Feature Space spanned by D 1 &gt;0 and D 2 &gt;0 for which S 1 &gt;T 1  in  23  of FIG. 2 (and S 2 &gt;T 2  in  24  of FIG. 2), where T 1  and T 2  are properly defined real scalar thresholds.  
         [0068]    Hence the set of all points (D 1 , D 2 ) in this Feature Space for which F 1  (D 1 , D 2 ; T 1 )≧0 satisfy S 1 ≧T 1  and is denominated ‘G1’ in 23 (‘G’ for ‘Good’ in the sense that their corresponding Channel Matrices H have relatively high data sub-stream s i  cross-talk SNR) and vice-versa, the set of all points (D 1 , D 2 ) in this Feature Space for which F 1  (D 1 , D 2 ; T 2 )&lt;0 maintain S 1 &lt;T 1  and is denominated ‘B1’ in  23  (‘B’ for ‘Bad’ in the sense that their corresponding Channel Matrices H have relatively low data sub-stream s i  cross-talk SNR). Similarly, the set of all points (D 1 , D 2 ) in this Feature Space for which F 2  (D 1 , D 2 ; T 2 )≧0 satisfy S 2 ≧T 2  and is denominated ‘G2’ in 24 and vice-versa, the set of all points (D 1 , D 2 ) in this Feature Space for which F 2  (D 1 , D 2 ; T 2 )&lt;0 maintain S 2 &lt;T 2  and is denominated ‘B2’ in 24 in said sense.  
         [0069]    Generally stated, for i=1, 2, . . . ,M  
           F   i ( D   1   ,D   2   ,D   M   ;T   i )≧0           Si≧T   i             DεGi   Predicate 1a  
           F   i (D 1   ,D   2   ,D   M   ;T   i )&lt;0           Si&lt;T   i             DεBi   Predicate 1b  
         [0070]    It can be shown, for example for the L=R=3 case, that the Discriminant Function F 1  for S 1  can be approximated by a Hyper-plane as is illustrated in  23  of FIG. 2 i.e. F 1  (D 1 , D 2 , D 3 ; T 1 )=a D 1 +bD 2 +cD 3 +d(T 1 )=0, where a, b, c and d are constants. It can also be shown that the higher order Discriminant Functions, i.e. Fi (D 1 , D 2 , D 3 ; T i )=0, i=2,3 can be approximated by higher order polynomial Hyper-surfaces such as illustrated in  24  of FIG. 2 for F 2 .  
         [0071]    The specific functional and parametric description of said Hyper-surfaces for Fi, i=1, 2 . . . can be found by analytic or numeric methods by anyone skilled in the art and are non-essential to the present invention. Other equivalent representations of S i =S i  (D) are possible. For example, definition of a sequence of thresholds T 1  (and/or T 2 ), in-lieu of the for-mentioned single threshold(s) allows for the description of S 1  (D) (and/or S 2  (D)) by means of a sequence of ‘isometrics’ Hyper-surfaces. From this said sequence of iso-Metrics Hyper-surfaces an explicit approximated polynomial in D expression of S 1  (D) (and/or S 2  (D)) can be derived by application of e.g. standard curve fitting techniques by anyone skilled in the art.  
         [0072]    Referring again to said Discriminant Functions representation, demanding of a Channel Matrix H (with its corresponding Singular Values Di, i=1,2, . . . ,M) the fulfillment of high cross-talk SNR for sub-streams s i , i=1,2, . . . M (or a sub-set of said data sub-streams) is equivalent to demand that the Singular Values vector D of H belongs to the intersection of the corresponding sets G1, G2, etc, denoted ‘G’ in  25  of FIG. 2. Hence, the Singular Values of all the ‘Good’ matrices lie in the closed set G=G 1 ∩G 2  in  25 . Since in a Wireless MIMO Communication System a randomly picked H has large probability of having bad cross-talk SNR for at least some of the user data sub-streams (as evident from  21  and  22  of FIG. 2) the ability to transform this Channel Matrix H into a modified Hm with better sub-streams cross-talk properties is desired and is an essential (but not sole) feature of this present invention.  
         [0073]    This provides a primary motivation to modify the Channel Matrix as measured by the Transmitting and Receiving sides so that more favorable matrices are observed. According to the proposed invention, and as a result of the above exposed motivation sources, a Pre-Equalizer Matrix P, a modified Channel Matrix Hm, and several additional artifacts are introduced as described in the following paragraphs.  
         [0074]    It should also be noted that different Matrix Metrics definitions than that given above as example are possible, such as the expected value of the cross-talk SNR, the median value of said cross-talk SNR, or others, the essential point in this invention being the creation of a function that relates some measure of the cross-talk SNR to the singular values of the Channel Matrix.  
         [0075]    [0075]FIG. 3 presents a simplified Block Diagram of the Transmitter segment ( 30  to  33 ,  16   a ) of a Left side device and of the Receiver segment ( 16   b ,  35  to  38 ) of a Right side device. For the sake of simplicity the Left side device includes a Transmitter segment only and the Right side device includes a Receiver segment only, while it should be clear that in a 2-way wireless Communication System each side would typically include both a Transmitter and a Receiver segment.  
         [0076]    While in the course of this invention description, by way of example, a MIMO scheme based on the execution of channel and symbol processing at the time domain will be generally assumed, it should be evident that this invention is directly applicable to other schemes as well such as wherein the MAA processing is executed at the frequency domain (such as in OFDM based systems, e.g. [4]).  
         [0077]    Also, while in the course of this invention description, by way of example and for the sake of simplicity, a MIMO scheme will be generally assumed whereby all the Channel Processing including the estimation of the Channel Matrix Hn, the Singular Value Decomposition of Hn, the calculation of the Transmission Weighting Matrix V, the Pre-Equalizer Matrix P, the Power Allocation Matrix A, the Receiving Weighting Matrix U and the Post-Equalizer Matrix Q are carried out at the (say Right) Receiving side and the required operators, namely A, V and P are concurrently and implicitly transferred to the Transmitting (say Left) side by means of an implicit feed-back communication channel, such a scheme being typically (but not exclusively) characteristic of Frequency Division Duplex systems (FDD, whereby the forward and reverse links are maintained in different frequency channels), it should be readily understood that this invention is directly applicable to other schemes as well, such as wherein part of said matrices are calculated at one (say Right) side and other part on the other (say Left) side as may be typical of Time Division Duplex systems (TDD, whereby the forward and reverse links are carried over the same frequency channel and where advantage may be taken of the Channel Reciprocity Theorem).  
         [0078]    [0078]FIG. 3 depicts, in matrix operator notation, the main invention relevant base-band elements of said communication devices while Radio Frequency circuitry, usually included in such Wireless Communication devices and several base-band operators and processes such as Radio Frequency Amplifiers, Mixers, Analog-To-Digital Converters, Time/Frequency Acquisition, Automatic Gain Control, etc. are omitted from FIG. 3 for the sake of brevity, being immaterial to the essence of the present invention.  
         [0079]    In a possible embodiment of our proposed invention a pre-set and pre-stored vector finite sequence [s 0 (m)], m=1, 2, . . . , aL, 30, is generated at the Left side device for purpose of the Channel Matrix estimation by the Right side device, where m denotes the (discrete) time index, L is the number of Left side Antenna Array  16   a  elements, and a≧1 is a constant the significance of which will be clarified later on.  
         [0080]    This sequence can be better viewed as a matrix S 0  of dimension MxaL, where each matrix column is a vector s 0 (m) of dimension M≦min{R,L}. In possible embodiments of this invention the vector sequence [s 0 (m)]  30  is further processed, vector by vector, by a Power Allocation diagonal matrix A L0 ′  31 , of dimension MxM, by a typically unitary Weighting Matrix V L0 ′  32 , of dimension MxL, and by a Pre-Equalizer Matrix P L0 ,  33 , resulting in a pre-set, MIMO Training Matrix (MTM) X 0  of dimension LxaL at the MAA  16   a , the subscript ‘0’ in A L0 , V L0  and P L0  denoting that these matrices carry at this (pre channel estimate) stage just the initial default values so as to transform S 0  into a desired X 0 , and the subscript L denoting that these operators belong to the Left side.  
         [0081]    The Transmitting device total transmitted power E[x(m)′x(m)], where E [.] denotes the expected value operator, is constrained to (say) unity by proper setting of the diagonal elements of A L0 , by keeping V L0  unitary and by proper selection of P L0 ; for example A L0 =V L0 =P L0 =I (the identity matrix), so that X 0 =S 0  will typically be suitable, so long as the constraint on total transmitted output power (E[x(m)′x(m)]=1) is maintained.  
         [0082]    The generated matrix X 0  is then radiated, column after column, by means of the L elements of the Multi Antenna Array  16   a , into a typically scattering channel  15 , received by the Right side R elements of MAA  16   b , corrupted by noise (usually assumed white, with Gaussian probability distribution), resulting in a finite discrete time vector sequence y(m), m=1,2, . . . ,aL, again better viewed as a matrix Y of dimension RxaL. This matrix Y is typically processed, column by column, by a pre-set unitary Weighting Matrix U R0    35  so that a recovered sequence r(m) results as described by Eq. 1 and 2 above, and further processed by a pre-set Post-Equalizer diagonal matrix Q R0    36 .  
         [0083]    Again, the fact that the operators  35 ,  36  carry initial default values at this stage, and that they are mainly shown for the sake of consistency with other, subsequent communication stages and clarity of description, is emphasized by the ‘0’ subscripts; for example U R0 =Q R0 =I so that Z=Y will, here too, be typically suitable.  
         [0084]    As described above, the channel  15  may be usefully perceived as a complex matrix H of dimension RxL, said matrix representing the (usually flat, frequency non-selective) fading response of the channel, the governing equation in this case being  
           Z=Q   RO   U   R0   HP   L0   V   L0   &#39;A   L0   S   0   +N   Eq. 3  
         [0085]    or, equivalently but in a simpler form,  
         Y=HX 0   +N   Eq.4  
         [0086]    where N denotes the (usually white, complex Gaussian) receiving noise matrix of dimension RxaL, and our purpose being to estimate the Channel Matrix H given the pre-set, pre-stored transmitted matrix S 0    20 ,  28  (or, equivalently X 0 ) and the received measured matrix Z (or, equivalently, Y), and to subsequently calculate the operators A L , V L , P L , U R , and Q R  required by both devices for subsequent efficient user data transmission, as will be elaborated later.  
         [0087]    For convenience it is beneficial to separate Eq. 4 into R separate canonical row vector equations  
         [ y ( i, 1) y ( i, 2). . .  y ( i,aL )]=[ H ( i, 1) H ( i, 2). . .  H ( i,L )] X   0   +[N ( i, 1) N (i,2). . . ( i,aL )]  Eq. 5  
         [0088]    where i=1,2, . . . ,R, and the row vector [y (i,m)], m=1,2, . . . ,aL contains, for each Right side MAA element  16   b  the received sequence of aL symbols after being transmitted and distorted by the channel row vector [H(i,j)], j=1,2, . . . ,L and corrupted by the noise row vector [N(i,m)], m=1,2, . . . ,aL.  
         [0089]    This Channel initial Estimation (sometimes called Channel Acquisition) is carried out in the Channel Processor  37  by means of application of any suitable estimation technique (such as MLE, MMSE, LSE, etc, each optimal in some specified sense, see e.g. [6]), the selected technique itself being immaterial to the proposed invention. Taking the Least Squares Estimation (LSE) method as example, and assuming that the elements of the noise matrix N are independent and identically distributed (i.i.d.) Gaussian random variables, the Channel Matrix row vector estimates Hn(i) are  
           Hn ( i )= y ( i ) Cn   −1   X   0   ′[X   0   Cn   −1   X   0 ′] −1 , i=1,2, . . . R  Eq. 6  
         [0090]    where the ‘n’ subscript in Hn denotes the usually noisy nature of the H estimator and where Cn is the noise row vector N(i,m) Covariance Matrix (Cn=σ 2  I when N(i,m) elements are independent and identically distributed as is typically assumed).  
         [0091]    The LSE estimation error, as reflected by its Covariance Matrix is in this case  
           E [( H ( i )− Hn ( i ))( H ( i )− Hn ( i ))′]=[ X   0   Cn   −1   X   0 ′] −1   Eq. 7  
         [0092]    with i=1,2, . . . R.  
         [0093]    It may be verified that the estimation error (Eq. 7) is minimal when the eigenvalues λi of (X 0  X 0  ′) satisfy λi=λj=a, and that the error is inversely proportional to aL i.e. to the number of transmitted symbols in the MIMO Training Matrix X 0  (or, equivalently in S 0 ) and to the noise variance σ 2 .  
         [0094]    It may also be verified that a sufficient condition for the existence of an estimate Hn is that the matrix [X 0 X 0 ′] is not ill-conditioned, nor of course singular. An additional (usually regulatory) requirement on the columns of X 0  would typically be the constraint on the overall (say unity) transmitted power, that is the requirement that trace (X 0 ′X 0 )=aL.  
         [0095]    Finally, according to this said possible embodiment of our proposed invention, Equation 6, which represents the first of the main processing results of the proposed Channel Processor  37 , may be written and executed in a more concise matrix form as  
         Hn=YCn −1   X   0   ′[X   0   Cn   −1   X   0 ′] −1   Eq. 8  
         [0096]    where it is evident that the product Cn −1 X 0 ′[X 0 Cn −1 X 0 ′] −1  (or equivalently S 0 ′[S 0 S 0 ′] −1 ) can be pre-calculated and pre-stored inside  38  of FIG. 3 so that upon reception of the measurement matrix Y (or, equivalently, Z), a simple matrix multiplication is executed by means of circuitry (or software) immaterial to the invention itself and which may be implemented by a variety of techniques well known to those ordinarily skilled in the art. It should also be noted that if a&lt;1 then [X 0  Cn −1  X 0 ′] is not of full rank and its inverse does not exist, hence the requirement for a≧1.  
         [0097]    In further accordance with one possible embodiment of the present invention, following the estimation of Hn as described above, the Right side device may proceed to calculate PL by means of (Singular Value) Decomposition of Hn=UnDnVn′ and evaluation of the Discriminant Functions Fi, i=1,2, . . . M as specified and described by Predicate  1  in the context of FIG. 2 above.  
         [0098]    If Fi≧0 for all user data sub-streams of interest, as will be rarely the case (given the probabilities exposed during FIG. 2 description), then our Channel Matrix Hn is ‘Good’ and we may set P L =I so that our modified Channel Matrix Hm,  39  of FIG. 3, will remain Hm=HP L =H. If Fi&lt;0 for at least some of the sub-streams s i  of interest, as will be usually the case, we should transform our ‘Bad’ H into a ‘Good’ Hm by the application of a Pre-Equalizer operator P L  which should be calculated so that the modified Channel Matrix Hm,  39 , enjoy Singular Values Dm which reside in the ‘G’ closed set (as defined for the data sub-streams and corresponding Discriminant Functions of interest).  
         [0099]    It can be shown that the best Pre-Equalizer (in the sense of SNR maximization) should yield Singular Values Dm (of the modified Channel Matrix Hm,  39 ) which solve the constrained functional minimization problem  
                 min     D                 m                       β        (       D   m     ;     D   n       )         =         min     D                 m            trace   (       P   L          P   L   ′       )       =       min     D                 m              ∑   i            (     Dmi   /   Dni     )     2                     Eq   .              9        a                               
 
         [0100]    subject to the constraint  
                 D                 m     ∈   G     =       ⋂   i          G   i                 Eq   .              9        b                               
 
         [0101]    where Dmi are the Singular Values vector components of the modified Channel Hm, Dni are the Singular Values vector components of the Channel Matrix Hn, G is the closed set of Dm which correspond to ‘Good’ Channel Matrices as described above in the context of FIG. 2, and the index i runs across the set of desired sub-streams (i≦M).  
         [0102]    Equation 9 represents a constrained minimization problem which can be solved and implemented by a variety of methods well known to those skilled in the art, the specific method of solution and implementation being immaterial to the essence of this present invention. Inspection of Eq. 9a reveals that the minimization of the functional β is equivalent to the minimization of the norm of the vector Dm, when this norm is calibrated by the components of our original Channel Matrix estimate Singular Values vector Dn, that is the solution Dm is, in a certain sense, the ‘minimum size’ Dm vector.  
         [0103]    It can also be shown that, since the Pre-Equalizer operator P is located at the Transmitter side, the functional β represents actually the power attenuation factor by which the data user vector s has to be attenuated in order to compensate for the ‘gain’ provided by the Pre-Equalizer P and maintain the constraint of unity overall transmitted power; in this case β represents the user data signal SNR loss due to our utilization of the modified Channel Hm,  39 .  
         [0104]    If this SNR loss becomes too high (β&gt;&gt;1) then one or more sub-streams (usually with the highest index i) may be given up which weakens the constraint of Eq. 9b and reduces the resulting minimal value of β and the corresponding for-mentioned SNR loss. Giving up all the sub-streams s i  except the first (i.e. s 1 ) returns the MIMO system operation to plain coherent diversity mode, where it enjoys from both diversity and Multiple Antenna Array gains.  
         [0105]    According to the present invention, after having computed the optimal Dm by the process outlined above, the Pre-Equalizer P L  and the corresponding Transmitting and Receiving Weighting Matrices may be immediately calculated by  
           P   L   =VnDn   −1   Dm   Eq. 10a  
         [0106]    where Vn and Dn are the results of the Singular Value Decomposition of our original Channel Matrix estimate Hn (Hn=UnDnVn′) and where a pseudo-inverse of Dn may be used in those cases where Dn −1  is not defined; it can be immediately verified that the Singular Values of the modified channel (HnP L =UnDnVn′VnDn−Dm=UnDmI) indeed are the ‘Good’ Dm as required, and that  
         U R =Un  Eq. 10b  
         and  
         V L =I  Eq. 10c  
         [0107]    Finally, the Power Allocation Matrix A L ,  31 , may be calculated so that the total transmitted power constraint (to, say, unity) is satisfied. In the simple case, brought herein for illustration only and without affecting the generality of the present invention, whereby equal power is allocated to each sub-stream vector component it can be readily seen that  
           A   L =(1/{square root}{square root over (β)}) I   Eq. 10d  
         [0108]    It is readily recognized that the operations described by Eq. 10 consist of matrix multiplications, transpositions and inversions, such operations being easily implemented by those skilled in the art by either dedicated circuitry or software.  
         [0109]    As mentioned above, other strategies and their corresponding invention embodiments can be applied for the specification and calculation of the modified Channel Matrix Hm and its associated Singular Value Matrix Dm and Pre-Equalizer P. According to another such possible embodiment of the present invention the modified channel singular values matrix Dm can be found by maximization of a functional consisting of some weighted sum of the net total SNR gains of the different sub-streams, said net SNR gains being the result of the channel modification, for example  
               min     D   m              ∑   i            a   i     ·     log        (         ρ   i          (       D   m     ;     γ   _       )       /     (         ρ   i          (       D   n     ;     γ   _       )       ·     β        (       D   m     ,     D   n       )         )       )                   Eq   .              11                               
 
         [0110]    subject to  
         D m1 ≧D m2 ≧ . . . ≧D mM ≧0  Eq. 11a  
         [0111]    where the total sub-stream SNR ρ i  is defined as the SNR with both cross-talk and receiver (thermal) noise included, where, again, {overscore (γ)} is the mean channel SNR, where α i ≧0 are some suitably defined scalar weighting factors, and where the Pre-Equalizer loss β(Dm,Dn) is defined as above. Said total sub-stream SNR ρ i  may be calculated by anyone skilled in the art, since its components, namely the received sub-stream signal power, the cross-talk noise power, and the thermal noise power are readily computable.  
         [0112]    Following said optimization the Pre-Equalizer P L , the Weighting Matrices U R  and V L  and the Power Allocation Matrix A L  can be calculated by application of Equations 10a,b,c,d as above.  
         [0113]    Still other embodiments of the present invention are possible in the context of the calculation of the singular values Dm of the modified channel, according to suitable and different to be optimized functional formulations, the general essential points being the definition of a Matrix Metrics which associates some measure of the sub-streams cross-talk SNR to the singular values of a channel matrix, and the solution of said functional optimization problem, followed by the calculation of the Pre-Equalizer, Transmitting and Receiving Weighting Matrices and Power Allocation Matrix.  
         [0114]    We have shown so far how, in conformance with this present invention, after having the Left side device transmitted a MIMO Training Matrix S 0 , most necessary channel information required for proper and efficient user data transmission is acquired and calculated.  
         [0115]    As mentioned above, the required parts of this information (namely A L , V L  and P L ) may be subsequently transferred to the Left side device by means of a reverse channel, or, as would typically (but not necessarily) be the case in TDD based systems, another similar MTM S 0  could be transmitted, this time from the Right side device to the Left side device for the purpose of said information calculation.  
         [0116]    In further accordance with the proposed invention, after having calculated the for-mentioned operators, and after having replaced their for-mentioned initial values with the results of this calculation, at both the Transmitting (say Left) and Receiving (say Right) sides, a pre-set and pre-stored vector finite sequence [s 1 (m)], m=1,2, . . . ,bM,  30 , where b≧1 is a (typically integer) constant, the significance of which will be clarified later on and M is, as before, the number of separate user data sub-streams (M≦min{R, L}), is generated at the Transmitter (say) Left side device for purpose of the calculation of the Post-Equalizer Q R ,  36 , by the Receiving (say) Right side device.  
         [0117]    In a possible embodiment of this invention, easier to explain and understand, this sequence can be better viewed as a sequence of b concatenated diagonal matrices S 1 , each of dimension MxM. The S 1  MTM concatenated matrix is then processed, column after column, by the operators  31 ,  32 ,  33  so that a transmitted waveform x(m) is generated and radiated by the MAA elements 16a according to:  
           x ( m )= P   L   V   L   A   L   s   1 ( m )  Eq. 12  
         [0118]    where m=1,2, . . . ,bM, and where x(m) is constrained again, as required, to (say) unity output total power by proper value assignment to the Power Allocation Matrix A L    31 .  
         [0119]    These transmitted column vectors are affected by the propagation channel H  15 , and received by the MAA elements  16   b  of the Receiving (Right side) device, so that  
                     y        (   m   )       =              H                   x        (   m   )         =         (     H                   P   L       )          V   L                     A     L                         s   1          (   m   )         =                   =            H                 m                   V   L                     A   L                       s   1          (   m   )                       Eq   .              13                               
 
         [0120]    where m=1,2, . . . ,M and where (thermal) receiving side noise is omitted for simplicity.  
         [0121]    The received waveform vector r(m) will now be  
                     r        (   m   )       =              U   R                     ‘       y        (   m   )       =       U   R                     ‘       H                 m                   V   L                     A     L                         s   1          (   m   )         =                                      =            (       U   R          ‘     U                 m     )                   D                 m                   (     V                 m                   ‘     V   L     )                     A   L                       s   1          (   m   )                             Eq   .              14                               
 
         [0122]    with n=1,2, . . . ,M.  
         [0123]    Since the unitary matrices U R ′ and Um (and V L  and Vm′ for the same purpose) are derived from slightly different versions of matrices (namely Hn and H correspondingly) their product does not exactly equal the identity matrix I. In particular the off-diagonal elements of said product matrices do not equal zero (as would be the case with perfect channel estimation) and thus, as was extensively elaborated above, cross-talk noise between the several user data sub-streams s i  result, the impact of which may be significantly ameliorated when applying the novel concept of the Pre-Equalizer matrix P as proposed above in the context of this invention.  
         [0124]    Due to the estimation noise affecting U R  and V L  the diagonal elements of said products however, are themselves each a complex scalar (usually close to but not equal to 1), so that the sub-streams s i  are, separately each, magnitude and phase distorted. According to the proposed invention, by utilizing the (possibly b times concatenated) for-mentioned diagonal matrix S 1,  the Channel Processor  37  calculates a Post-Equalizer diagonal Matrix Q R ,  36 , which after substituting the default initial value Q R0  in the Post-Equalizer  36 , is able to correct said magnitude and phase distortion at each sub-stream, significantly enhancing the received SNR at the received vector z(m).  
         [0125]    For the simple case where b=1, a single diagonal matrix S 1  of dimension MxM is used, and denoting its diagonal elements by S 1 (i, m), i=m=1,2, . . . ,M, the Post-Equalizer diagonal Matrix corresponding elements Q R  (i, m) take the form  
           Q   R ( i,m )= S   1 ( i,m )/ r ( i,m )  Eq. 15  
         [0126]    for i=m=1,2, . . . ,M, the calculation of which may be implemented by a variety of techniques well known to those ordinarily skilled in the art.  
         [0127]    In analogy with the S 0  MTM training case described above, using a longer S 1  MTM (b&gt;1) results in lower Q R  estimation error at the expense of increased channel usage overhead. It is also worthwhile to note that, for effective actual implementation, the operators Q R  and U R  (as well as P L  and V L ) may be combined, after having been calculated by the Channel Processor  37 , into a single (hardware or software based) operation, for complexity reduction.  
         [0128]    Having completed the calculation of the Post-Equalizer Matrix Q R ,  36 , its value replaces the for-mentioned initial value Q R0 , the Training/Acquisition Stage is terminated, and the Left and Right sides MIMO Wireless Communication devices may proceed, according to the present invention, to multi sub-stream user data transmission.  
         [0129]    [0129]FIG. 4 presents BER vs. Eb/No comparative plots,  41 ,  42 , and  43  of the simulated performance of a MIMO system, with L=R=3, a=b=1, and QPSK modulation for s1, s2 and s3 sub-streams respectively. The lower left (best, denoted by ‘+’) curves on each plot  41 ,  42  and  43  are based on an ‘ideal’ MIMO model (no channel estimate error, no cross-talk interference, no artifacts), the center (better, denoted by ‘o’) curves are based on the principles exposed in this invention (imperfect channel estimate, cross-talk interference, with artifacts), and the upper right (worst, denoted by ‘x’) curves represent simulation results for a ‘naïve’ MIMO system (imperfect channel estimate, cross-talk interference, no artifacts) such as in [3].  
         [0130]    Inspecting, as a matter of example, the center curve of  41  of FIG. 4, it can be noticed that a performance gain of approximately 20 db (at 10E-6 BER) with regards to the performance of a ‘naïve’ MIMO system such as [3] is achieved, while a performance gap of about 5 db (at same 10E-6 BER) remains between this and an ‘ideal’ MIMO system.  
         [0131]    It should be finally noted that the cross-talk SNR and Singular Values analysis on which this invention is based, is fundamentally different than other well known techniques, such as for-mentioned Adaptive Modulation ([10]) and Sequential Interference Cancellation ([1], [2]); this fundamental difference allows in principle the superposition of such techniques, on top of the techniques of the present invention, to possibly further enhance performance.  
         [0132]    The principles on which this invention is based are further described in great detail and appropriate language in [11].