Abstract:
This invention is an improvement upon the basic adaptive signal processors, the Multi-Stage Wiener Filter and the cascaded canceller. The invention combines the concepts of soft weighting the adaptive weights of either type of processor disclosed herein with reiteratively processing the outputs by returning them to the input of the chosen adaptive signal processor. The combination of these functions improves the Signal to Interference plus Noise Ratio (SINR), the Probability of Detection (Pd), and/or the Bit Error Rate (BER). The invention improves statistical convergence of these types of metrics such that fewer training data samples are needed to achieve a particular satisfactory value of these metrics than would occur using traditional computational adaptive signal processors.

Description:
RELATED APPLICATIONS 
     This application is a continuation-in-Part to U.S. patent application Ser. No. 11/537,000, filed Sep. 29, 2006 now abandoned and titled “MULTISTAGE MEDIAN CASCADED CANCELLER,” which is a continuation of U.S. patent application Ser. No. 10/126,663, now U.S. Pat. No. 7,167,884, entitled “MULTISTAGE MEDIAN CASCADED CANCELLER,” the disclosures of which are fully incorporated herein. 
    
    
     FIELD OF THE INVENTION 
     The invention relates in general to an adaptive signal processing system. More specifically, the invention relates to an adaptive signal processing system using full and reduced rank signal processors that are insensitive to non-ideal data yet improve the convergence of standard algorithms while reiteratively processing signals with a minimum of training data. 
     BACKGROUND OF THE INVENTION 
     Adaptive signal processing systems have many applications, including radar reception, cellular telephone and other communications systems, and biomedical imaging. Adaptive signal processing systems utilize adaptive filtering to differentiate between the desired signal and the combination of interference and noise, i.e., thermal or receiver noise. An adaptive filter is defined by four aspects: the type of signals being processed, the structure that defines how the output signal of the filter is computed from its input signal, the parameters within this structure that can be iteratively changed to alter the filter&#39;s input-output relationship, and the adaptive algorithm that describes how the parameters are adjusted from one time instant to the next. 
     Adaptive signal processing systems are required to filter out undesirable interference and noise. Due to the lack of a priori knowledge of an external interference environment, adaptive signal processing systems require a certain amount of statistically independent “weight training” data samples to effectively estimate the input noise and interference statistics. 
     Noise and interference may often hinder the desired signal detection. Noise is usually described as ever-present receiver thermal noise, generally at a lower power level. Interference may be intentional jamming or unintentionally received radiation. In these applications, antenna arrays, for instance, may change their multidimensional reception patterns automatically in response to the signal environment in a way that optimizes the ratio of signal power to the combination of interference power plus noise power (SINR). Adaptive arrays are especially useful to protect radar and communication systems from interference when the directions of the interference are unknown or changing while attempting to receive a desired signal of known form. Adaptive arrays are capable of operating even when the antenna elements have arbitrary patterns, polarizations, and spacings. 
     In many sensor system applications, adaptive signal processing is required to remove time-varying interference signals when attempting to detect weak, desired signals, or targets. In these dynamic signal environments, the interference characteristics change rapidly, and state-of-the-art “full rank” adaptive algorithms cannot adjust the weight vector (adaptive filter) fast enough. Methods exist called “reduced rank” adaptive processors that converge their weight vectors, in terms of SINR, faster than full rank methods, however these methods often have undesirable features, such as significant computational requirements, limitations on high-volume data throughput, wider main beams, sensitive parameter adjustments with required feedback, and other “side effects”. The rank generally refers to the number of interference or other noise sources for a given array system. 
     Adaptive processors such as Sample Matrix Inversion (SMI), or the numerically equivalent Gram-Schmidt Cascaded Canceller (GSCC), utilize multi-channel, or multi-sensor, measured input data to estimate the signal environment in order to mitigate interference and noise while preserving target energy. The ability to adapt is often required because adequate a priori knowledge of the interference and noise statistics is not available. For radar applications, for example, the interference and noise environment consists of jamming, ground clutter, and receiver noise. To form weights used in a linear adaptive processor, the interference plus noise covariance matrix often is estimated, either directly or indirectly, using measured training data from the input channels. These SMI methods are known to be equivalent to procedures that minimize least squares cost functions of the input training data to produce the adaptive weight vector. Least squares methods are well known to exhibit non-robust behavior. SMI methods are known to be optimal in several respects when the input data vectors are independent and identically distributed (i.i.d.) and Gaussian. 
     The SINR convergence measure of effectiveness (MOE) is the number of stationary, independent and identically distributed (i.i.d.) data samples per input sensor (i.e., snapshots), the number of weight training data, that are required so that the average SINR of the adaptive processor is nominally within 3 dB of optimum (i.e., optimum is 0 dB). It is desired to minimize the SINR convergence MOE to accommodate non-stationary data that is due to, for example, non-homogenous clutter, multiple targets, outliers, and/or a volatile jamming environment. In addition, faster convergence may reduce computations and cost. The convergence MOE of SMI or any numerically equivalent implementation of SMI, such as the GSCC, can be attained using approximately 2N i.i.d. snapshots for weight estimation in pure stationary Gaussian interference noise environments. The integer N denotes the number of degrees of freedom (DOF), or the number of input channels, or sensors, to the adaptive processor. For example, N is the number of antenna channels (i.e., antenna elements or subarrays) for a spatially adaptive array processor, and is the number of space and time channels for Space-Time Adaptive Processing (STAP) processor. SMI&#39;s 2N convergence MOE is known to be independent of any external interference covariance matrix, i.e., independent of the effective rank of the input covariance matrix, when the i.i.d. and Gaussian assumptions are strictly satisfied. Effective rank denotes the number of eigenvalues of the input sample covariance matrix that are large compared to the remaining, ideally equal, and small, eigenvalues that are usually associated with the received noise levels. This independence feature is very useful in practice since it provides the designers of adaptive radar systems with an a priori, fixed value for the number of required training snapshots (in ideal Gaussian environments) for a given system&#39;s DOF. 
     Reduced rank processors are a class of algorithms that converge more quickly than full rank processors. A full rank processor&#39;s convergence MOE (i.e., SMI or GSCC) often is proportional to (e.g., twice) the number of input channels, N, or degrees of freedom (DOF) (e.g. DOF=10 to 1000). A reduced rank processor&#39;s convergence MOE is generally proportional to (e.g., twice) the effective rank, R, of the input interference covariance matrix, which may be much smaller than the DOF in many interference environments (e.g., effective rank=1 to 100). 
     Reduced rank refers to methods whereby, in some cases, the adaptive processor converges in SINR using fewer subspace directions than full rank, where full rank corresponds to the dimension of the input data or the adaptive DOF often denoted as the variable N. In all cases, optimal, desired convergence occurs in near 2N training samples for full rank processors and less than 2N for reduced rank processors. 
     A soft weighting processing technique is desired that can be reiteratively applied to adaptive signal processor algorithms to produce adaptive convergence rates that are as fast or faster than full rank processing algorithms. One such exemplary full rank algorithm has been described in U.S. Pat. No. 6,904,444 Picciolo, Gerlach, and Goldstein, entitled “PSUEDO-MEDIAN CASCADED CANCELLER.” Another such algorithm is the Gram-Schmidt Cascaded Canceller, and any other generic cascaded canceller algorithm, whether in full or reduced rank form, may also be implemented to make use of the invention. Examples of generic cascaded cancellers are referenced and may be found in Picciolo, M. L., Schoenig, G. N., Mili, L., Gerlach, K., “Rank-Independent Convergence For Generic Robust Adaptive Cascaded Cancellers Via Reiterative Processing”, Proceedings of IEEE International Radar Conference, Washington, D.C., May 9-12, 2005, pp. 399-404, and Picciolo, M., “Robust Adaptive Signal Processors”, PhD Dissertation, Virginia Tech, Apr. 18, 2003. Such a processing technique may also be applied to reduced rank algorithms, such as multi-stage median cascaded canceller, which has been described in U.S. Pat. No. 7,167,884 to Picciolo, Gerlach, and Goldstein, entitled “MULTI-STAGE MEDIAN CASCADED CANCELLER,” to further improve convergence. Another exemplary algorithm is a Multi-Stage Weiner Filer (MWF), which may be implemented with Gram-Schmidt weighting in its synthesis stage. 
     It is desired to have an algorithm that performs superior to full rank and reduced rank processors in practice when ideal assumptions for the input training data are violated. One such reduced rank processor that performs poorly with non-ideal training data is the FML (Fast Maximum Likelihood), which involves forming the eigenvalues/eigenvectors of the sample covariance matrix of the input data, and selecting those eigenvalues at or below the thermal noise level to be replaced by the noise power level value, and then forming an inverse matrix with the set of all eigenvectors and the set of (partially modified) eigenvalues as described by M. Steiner, and K. Gerlach, “Fast Converging Adaptive Processor For A Structured Covariance Matrix”, IEEE Trans. Aerospace and Elect. Syst., Vol. 36, No. 4, October 2000, pp. 1115-1126. Another such processor is the PCI (Principal Components&#39; Inverse), which involves forming the eigenvalues/eigenvectors of the sample covariance matrix of the input data, and selecting those eigenvectors associated with the largest eigenvalues, and forming an inverse matrix with that subset of eigenvectors and associated eigenvalues as described by J. R. Guerci and J. S. Bergin in “Principal Components, Covariance Matrix Tapers, and the Subspace Leakage Problem”, IEEE Trans. Aerospace and Electronic Systems, Vol. 38 No. 1, January 2002, pp. 152-162. 
     It is further desired to have an algorithm that is simple, computationally fast, and significantly improves the convergence rate of full and reduced rank processors such as cascaded cancellers and MWFs in terms of important metrics such as SINR, Probability of Detection (Pd), and Bit Error Rate (BER). It is desired to achieve flexibility for adaptive processing applications that require fast convergence (due to low sample support and/or computational restrictions), low adaptive sidelobes, and high adaptive filter resolution (i.e., high number in input channels or degrees of freedom). 
     SUMMARY OF THE INVENTION 
     The present invention provides an adaptive signal processing method and system that uses a soft-weight that may be reiteratively applied to full and reduced rank algorithms, such as cascaded cancellers or an MWF to improve the results of an adaptive signal processor in terms of SINR, Probability of Detection, and/or Bit Error Rate. Specifically, the invention improves the statistical convergence rate of these types of metrics such that fewer training data samples, less than 2N, are needed to achieve a particular satisfactory value of these metrics than would occur by using conventional adaptive processors instead. This is an important purpose because sufficient numbers of high quality (i.e., “stationary”) training samples are not always available from the measured data. 
     With this invention, algorithm designers are free to use new canceller algorithms tailored to the data environment at hand, in order, for example, to optimize filter performance to non-Gaussian/non-stationary input statistics, add features to compensate for multiple targets and/or outliers contaminating training data, to improve numerical efficiency, etc. . . . , all-the-while reducing the number of training samples needed for reduced rank SINR convergence. 
     In preferred embodiments, this invention applies a soft weight value to a standard weight of a cascaded canceller. For a Gram-Schmidt cascaded canceller, the Gram-Schmidt weight is multiplied by the soft-weight value to produce the desired results. For any other cascaded canceller, the adaptive weight, whether Gram-Schmidt or another weight, value is multiplied by the soft-weight value. For a Multi-Stage Weiner Filter with Gram-Schmidt weights applied to the synthesis stage, the adaptive, Gram-Schmidt weight is multiplied by the soft-weight value. In certain embodiments, such as the multi-stage median cascaded canceller, pseudo-median cascaded canceller, Gram-Schmidt cascaded canceller, or any other generic cascaded canceller, the soft weight value may be reiteratively applied to further improve the convergence and produce reduced-rank characteristics. 
     A preferred embodiment of the invention provides a method for determining a soft-weight value to be applied to an adaptive signal processing algorithm comprising the steps of: i) selecting a value; ii) generating a data set of training values; iii) providing an adaptive signal processor simulator; iv) inputting the training values into the simulator, v) inputting the selected value into the simulator; vi) measuring a signal power output value of the simulator; vii) varying the selected value; and viii) repeating steps i)-vii) so long as the measured signal power output value decreases. 
     A further preferred embodiment of the invention provides a method wherein varying the selected value further comprises choosing the selected value from the range 0 to 2. 
     A further preferred embodiment of the invention provides a method wherein the selected value comprises the soft weight value. 
     A further preferred embodiment of the invention provides a method wherein generating a data set of training values further comprises producing a first data matrix of size defined by a number of degrees of freedom [N] of a sensor input array and twice a minimum expected effective rank, [R min ], corresponding to a simulated interference plus noise environment. 
     A further preferred embodiment of the invention provides a method wherein generating a data set of training values further comprises producing a second data matrix of size defined by a number of degrees of freedom [N] of a sensor input array and twice a maximum expected effective rank, [R max ], corresponding to a simulated interference plus noise environment. 
     A further preferred embodiment of the invention provides a method wherein the soft weight value is selected such that a signal to interference power plus noise ratio [SINR] converges to an average of −3 dB from optimal in less than 2N training samples, where N is the number of degrees of freedom. 
     A further preferred embodiment of the invention provides a method wherein the simulator simulates a pseudo-median cascaded canceller adaptive signal processor. 
     A further preferred embodiment of the invention provides a method wherein at least one adaptive weight of the pseudo-median cascaded canceller is multiplied by the selected value. 
     A further preferred embodiment of the invention provides a method wherein the simulator simulates a Gram-Schmidt cascaded canceller algorithm. 
     A further preferred embodiment of the invention provides a method wherein at least one Gram-Schmidt weight of the Gram-Schmidt cascaded canceller is multiplied by the selected value. 
     A further preferred embodiment of the invention provides a method wherein the simulator simulates a generic cascaded canceller algorithm. 
     A further preferred embodiment of the invention provides a method wherein at least one adaptive weight of the generic cascaded canceller is multiplied by the selected value. 
     A further preferred embodiment of the invention provides a method wherein the simulator simulates a multi-stage median cascaded canceller. 
     A further preferred embodiment of the invention provides a method wherein at least one adaptive weight of the multi-stage median cascaded canceller is multiplied by the selected value. 
     A further preferred embodiment of the invention provides a method wherein the simulator simulates a Multi-Stage Weiner Filter algorithm. 
     A further preferred embodiment of the invention provides a method wherein the Multi-Stage Weiner Filter comprises a plurality of stages such that the number of stages is selected to be equal to an effective rank of an interference plus noise environment. 
     A further preferred embodiment of the invention provides a method wherein the Multi-Stage Weiner Filter comprises a plurality of stages such that the number of stages is selected to be greater than a minimum effective rank of an interference plus noise environment. 
     A further preferred embodiment of the invention provides a method wherein the Multi-Stage Weiner Filter comprises a plurality of stages such that the number of stages required for optimal convergence is less than the number of degrees of freedom. 
     A further preferred embodiment of the invention provides a method wherein at least one Weiner weight is multiplied by the selected value. 
     A further preferred embodiment of the invention provides a method wherein at least one Gram-Schmidt weight is applied in the synthesis stage. 
     A further preferred embodiment of the invention provides a method wherein the soft weight value is increased until the measured signal power output value reaches an unacceptable power output. 
     Another preferred embodiment of the invention provides a method for reiteratively applying a soft-weight value to an adaptive signal processor comprising: i) taking a plurality of measurements in an interference plus noise data environment; ii) inputting each of the plurality of measurements into an input of an adaptive signal processor algorithm; iii) applying a soft weight value to a plurality of building blocks of the adaptive signal processor algorithm; iv) determining a main channel column output of the adaptive signal processor algorithm for each of the plurality of measurements input into the adaptive signal processor algorithm; v) squaring the main channel column output of the adaptive signal processor algorithm for each of the plurality of measurements; vi) storing each squared value for each of the plurality of measurements; vii) determining a representative average value of the stored squared values once each of the plurality of measurements has been input into the adaptive signal processor algorithm; viii) performing each of steps i) through vii) until the representative average value increases from the prior iteration; counting a number of iterations required to perform steps i) to vii) until the representative average value increases from the prior iteration; ix) and storing one less than the number of iterations required to perform the steps i) to vii) prior to the representative average value increasing from the prior iteration. 
     A further preferred embodiment of the invention provides a method wherein the plurality of measurements comprise measurements from each of a plurality of sensor inputs. 
     A further preferred embodiment of the invention provides a method, which further comprising retrieving the stored number of iterations. 
     A further preferred embodiment of the invention provides a method wherein applying the soft weight value includes determining the soft weight value. 
     A further preferred embodiment of the invention provides a method wherein determining a soft weight value further comprises the steps of: i) selecting a value; ii) generating a data set of training values; iii) providing an adaptive signal processor simulator; iv) inputting the training values into the simulator, v) inputting the selected value into the simulator; vi) measuring a signal power output value of the simulator; vii) varying the selected value; and viii) repeating steps i)-vii) so long as the measured signal power output value decreases. 
     A further preferred embodiment of the invention provides a method wherein varying the selected value further comprises choosing the selected value from the range 0 to 2. 
     A further preferred embodiment of the invention provides a method wherein the selected value is the soft weight value. 
     A further preferred embodiment of the invention provides a method wherein generating a data set of training values further comprises producing a first data matrix of size defined by a number of degrees of freedom [N] of a sensor input array and twice a minimum expected effective rank, [R min ], corresponding to a simulated interference plus noise environment. 
     A further preferred embodiment of the invention provides a method wherein generating a data set of training values further comprises producing a second data matrix of size defined by a number of degrees of freedom [N] of a sensor input array and twice a maximum expected effective rank, [R max ], corresponding to a simulated interference plus noise environment. 
     A further preferred embodiment of the invention provides a method wherein the soft weight value is selected such that a signal to power plus noise ratio [SINR] converges to an average of −3 dB from optimal in less than 2N training samples, where N is the number of degrees of freedom. 
     A further preferred embodiment of the invention provides a method wherein the simulator simulates a cascaded canceller. 
     A further preferred embodiment of the invention provides a method wherein the cascaded canceller comprises a pseudo-median cascaded canceller. 
     A further preferred embodiment of the invention provides a method wherein at least one adaptive weight of the pseudo-median cascaded canceller is multiplied by the selected value. 
     A further preferred embodiment of the invention provides a method wherein the cascaded canceller comprises a Gram-Schmidt cascaded canceller algorithm. 
     A further preferred embodiment of the invention provides a method wherein at least one Gram-Schmidt weight of the Gram-Schmidt cascaded canceller is multiplied by the selected value. 
     A further preferred embodiment of the invention provides a method wherein the cascaded canceller comprises a generic cascaded canceller algorithm. 
     A further preferred embodiment of the invention provides a method wherein at least one adaptive weight of the generic cascaded canceller is multiplied by the selected value. 
     A further preferred embodiment of the invention provides a method wherein the cascaded canceller comprises a multi-stage median cascaded canceller algorithm. 
     A further preferred embodiment of the invention provides a method wherein at least one adaptive weight of the multi-stage median cascaded canceller is multiplied by the selected value. 
     A further preferred embodiment of the invention provides a method wherein the simulator simulates a Multi-Stage Weiner Filter algorithm. 
     A further preferred embodiment of the invention provides a method wherein the Multi-Stage Weiner Filter comprises a plurality of stages such that the number of stages is selected to be equal to an effective rank of an interference environment. 
     A further preferred embodiment of the invention provides a method wherein the Multi-Stage Weiner Filter comprises a plurality of stages such that the number of stages is selected to be greater than a minimum effective rank of an interference environment. 
     A further preferred embodiment of the invention provides a method wherein the Multi-Stage Weiner Filter comprises a plurality of stages such that the number of stages required for optimal convergence is less than the number of degrees of freedom. 
     A further preferred embodiment of the invention provides a method wherein at least one Weiner weight is multiplied by the selected value. 
     A further preferred embodiment of the invention provides a method wherein at least one Gram-Schmidt weight is applied in the synthesis stage. 
     A further preferred embodiment of the invention provides a method wherein at least one Gram-Schmidt weight is multiplied by the selected value. 
     A further preferred embodiment of the invention provides a method wherein the soft weight value is increased until the measured signal power output value reaches an unacceptable power output. 
     Another preferred embodiment of the invention provides a system for reiteratively applying a soft-weight value, comprising: a plurality of sensor inputs for measuring signals within an interference plus noise environment with a variable effective rank; a filter comprising an adaptive signal processor; a controller to perform the following steps: input the measured signals into the filter; apply a soft weight value to the filter; compute an output of the adaptive signal processor; a memory means; and an output means. 
     A further preferred embodiment of the invention provides a system wherein a plurality of degrees of freedom provided by the sensor inputs provides the measured target signals. 
     A further preferred embodiment of the invention provides a system wherein the memory means has stored upon it a number of iterations. 
     A further preferred embodiment of the invention provides a system wherein the controller retrieves from the memory means a stored number of iterations, such that the measured signals are input into the filter a number of times as specified by the number of iterations. 
     A further preferred embodiment of the invention provides a system wherein the adaptive signal processor is a Gram-Schmidt Cascaded Canceller. 
     A further preferred embodiment of the invention provides a system wherein the controller applies the soft weight value by multiplying at least one Gram-Schmidt weight of the Gram-Schmidt cascade canceller by the soft weight value. 
     A further preferred embodiment of the invention provides a system wherein the adaptive signal processor is a multi-stage median cascaded canceller. 
     A further preferred embodiment of the invention provides a system wherein the controller applies the soft weight value by multiplying at least one adaptive weight of the multi-stage median cascaded canceller by the soft weight value. 
     A further preferred embodiment of the invention provides a system wherein the adaptive signal processor is a generic cascaded canceller. 
     A further preferred embodiment of the invention provides a system wherein the controller applies the soft weight value by multiplying at least one adaptive weight of the generic cascaded canceller by the soft weight value. 
     A further preferred embodiment of the invention provides a system wherein the adaptive signal processor is a pseudo-median cascaded canceller. 
     A further preferred embodiment of the invention provides a system wherein the controller applies the soft weight value by multiplying at least one adaptive weight of the pseudo-median cascaded canceller by the soft weight value. 
     A further preferred embodiment of the invention provides a system wherein the adaptive signal processor is a Multi-Stage Weiner filter. 
     A further preferred embodiment of the invention provides a system wherein the Multi-Stage Weiner filter comprises a pre-determined number of stages. 
     A further preferred embodiment of the invention provides a system wherein the Multi-Stage Weiner Filter comprises a plurality of stages such that the number of stages is selected to be equal to an effective rank of an interference plus noise environment. 
     A further preferred embodiment of the invention provides a system wherein the Multi-Stage Weiner Filter comprises a plurality of stages such that the number of stages is selected to be greater than a minimum effective rank of an interference plus noise environment. 
     A further preferred embodiment of the invention provides a system wherein the Multi-Stage Weiner Filter comprises a plurality of stages such that the number of stages required for optimal convergence is less than the number of degrees of freedom. 
     A further preferred embodiment of the invention provides a system wherein the controller applies the soft weight value by multiplying at least one Weiner weight of the Multi-stage Weiner Filter by the soft weight value. 
     A further preferred embodiment of the invention provides a system wherein at least one Gram-Schmidt weight is applied to the synthesis stage. 
     A further preferred embodiment of the invention provides a system wherein the controller applies the soft weight value by multiplying at least one Gram-Schmidt weight of the Multi-Stage Weiner Filter by the soft weight value. 
     Another preferred embodiment of the invention provides a method for adaptive signal processing, comprising: measuring a signal in an interference plus noise environment; inputting the measured signal into a filter algorithm; filtering the measured signal to eliminate interference; applying a soft weight to the algorithm; and determining the filter&#39;s output. 
     A further preferred embodiment of the invention provides a method wherein the measured signal comprises a target signal, an additive noise, and an interference. 
     A further preferred embodiment of the invention provides a method wherein the filtering comprises a cascaded canceller algorithm. 
     A further preferred embodiment of the invention provides a method wherein the cascaded canceller algorithm is a Gram-Schmidt cascaded canceller algorithm. 
     A further preferred embodiment of the invention provides a method wherein applying the soft weight value further comprises multiplying a Gram-Schmidt weight by the soft weight value. 
     A further preferred embodiment of the invention provides a method wherein the cascaded canceller algorithm is a pseudo-median cascaded canceller algorithm. 
     A further preferred embodiment of the invention provides a method wherein the cascaded canceller algorithm is a multi-stage median cascaded canceller. 
     A further preferred embodiment of the invention provides a method wherein the cascaded canceller algorithm is a generic cascaded canceller algorithm. 
     A further preferred embodiment of the invention provides a method wherein applying the soft weight value further comprises multiplying an adaptive weight by the soft weight value. 
     A further preferred embodiment of the invention provides a method wherein the filtering comprises a Multi-Stage Weiner Filter algorithm. 
     A further preferred embodiment of the invention provides a method wherein applying the soft weight value further comprises multiplying a Weiner weight by the soft weight value. 
     A further preferred embodiment of the invention provides a method wherein the filtering further comprises applying at least one Gram-Schmidt weight in the synthesis stage. 
     A further preferred embodiment of the invention provides a method wherein applying the soft weight value further comprises multiplying the Gram-Schmidt weight by the soft weight value. 
     A further preferred embodiment of the invention provides a method wherein the applying a soft weight value further comprises selecting a soft weight value between 0 and 2. 
     A further preferred embodiment of the invention provides a method wherein applying the soft weight value further comprises selecting a soft weight value such that a signal to power plus noise ratio [SINR] converges to an average of −3 dB from optimal in less than 2N training samples, where N is the number of degrees of freedom. 
     A further preferred embodiment of the invention provides a method wherein selecting a soft weight value further comprises selecting a value such that adaptive sidelobe heights are low. 
     Another preferred embodiment of the invention provides an adaptive signal processor comprising: a filter; a soft weight generator; and an output. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the filter further comprises an input from the soft weight generator. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the soft weight generator generates a soft weight value between 0 and 2. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the filter further comprises a cascaded canceller that applies the soft weight value. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the cascaded canceller further comprises a Gram-Schmidt cascaded canceller. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein applying the soft weight value further comprises multiplying a Gram-Schmidt weight by the soft weight value. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the cascaded canceller further comprises a pseudo-median cascaded canceller. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the cascaded canceller further comprises a median multi-stage cascaded canceller. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the cascaded canceller further comprises a generic cascaded canceller. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein applying a soft weight value further comprises multiplying the adaptive weight by the soft weight value. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the filter comprises a Multi-stage Weiner filter that applies the soft weight value. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the Multi-Stage Weiner Filter comprises a plurality of stages such that the number of stages is selected to be equal to an effective rank of an interference plus noise environment. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the Multi-Stage Weiner Filter comprises a plurality of stages such that the number of stages is selected to be greater than a minimum effective rank of an interference plus noise environment. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the Multi-Stage Weiner Filter comprises a plurality of stages such that the number of stages required for optimal convergence is less than the number of degrees of freedom. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein at least one Gram-Schmidt weight is applied in the synthesis stage. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein applying the soft weight value further comprises multiplying the Gram-Schmidt weight by the soft weight value. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein applying the soft weight value further comprises multiplying the Weiner weight by the soft weight value. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the soft weight value is selected such that a signal to power plus noise ratio [SINR] converges to an average of −3 dB from optimal in less than 2N training samples, where N is the number of degrees of freedom. 
     A further preferred embodiment of the invention provides an adaptive signal processor wherein the soft weight generator generates a soft weight value such that adaptive sidelobe heights are low. 
     Other advantages and features of the invention will become apparent from the following detailed description of the preferred embodiments and the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  shows a generic reiterative cascaded canceller (RCC) where output channels are directed back to the input channels to improve SINR convergence performance in accordance of the present invention. 
         FIG. 1B  shows any single building block canceller within the RCC structure shown in  FIG. 1A . 
         FIG. 2A  shows a prior art Gram-Schmidt Cascaded Canceller (GSCC), or SMI, convergence curve for various target outlier power levels with no soft weighting or reiteration. 
         FIG. 2B  shows a GSCC or SMI convergence curve for various target outlier power levels with the soft weighting and reiteration algorithms applied. 
         FIG. 3A  shows prior art sidelobe levels of a GSCC or SMI adaptive signal processor, with no soft weighting or reiteration algorithms applied, compared with the optimum, desired levels. 
         FIG. 3B  shows sidelobe levels of a GSCC or SMI adaptive signal processor, with soft weighting and reiteration algorithms applied, compared with the optimum, desired levels. 
         FIG. 4  shows a Multi-Stage Weiner Filter (MWF) with the inventive soft weights and reiteration algorithms applied. 
         FIG. 5A  is a prior art graph of the standard MWF processor convergence without the soft weighting or reiteration algorithms applied. 
         FIG. 5B  is a graph of the MWF processor convergence with soft-weighting and three iterations. 
         FIG. 6A  shows a prior art graph of the sidelobe levels of an MWF adaptive signal processor, with no soft weighting and reiteration algorithms applied, compared with the optimum, desired levels. 
         FIG. 6B  shows a graph of the sidelobe levels of an MWF adaptive signal processor, with soft weighting and reiteration algorithms applied, compared with the optimum, desired levels. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The invention is a new processing technique for adaptive signal processors. An adaptive signal processor in accordance with this invention may be equivalently implemented as a cascaded canceller via the Gram-Schmidt cascaded canceller algorithm, a median cascaded canceller, a pseudo-median cascaded canceller, or any other generic cascaded canceller methodology. An adaptive signal processor may also be implemented as an MWF, hence the invention has broad application. The invention preferably creates the output characteristics of reduced rank adaptive processors from full rank processor, or further improves reduced rank characteristics, by applying soft-weight values. Reiteratively applying the soft-weight values to the preferred embodiments may also improve convergence and provide additional reduced rank characteristics. Reduced rank refers to methods whereby the adaptive processor converges in SINR, and requires fewer training data, often proportional to the number of interference sources, than full rank, where full rank corresponds to the case of using the full rank dimension of the input data. The full dimension corresponds to the number of sensor inputs in an array, often denoted as the variable N. Input sensors provide the measurement data that is input to and processed by the adaptive signal processor. Examples of input sensors are, without limitation, antennae, charge-couple devices, user data-input devices (such as a computer keyboard), electro-optical sensors, and/or hyper-spectral sensors, which form virtual data. 
     Turning now to  FIG. 1A , which depicts the signal flow for reiteratively applying a soft weight value to a generic cascaded canceller  100 , the input signal  102  is applied to each building block  104  of the cascaded canceller as shown in  FIG. 1B . It should be understood by one of ordinary skill in the art that the number of inputs is exemplary, only, and generally any number of inputs are possible. Each building block  104  may perform the complex conjugation of one of the input signals  102  with the multiplication of the conjugated adaptive weight value, w g , and the soft weight value or conjugated soft weight value when the soft-weight value is complex, w sw , to produce the output  106 , y, y=z−(w sw  w g )*x, of each building block  104 . Each building block  104  may also apply the soft weight without conjugation. The cascaded canceller  100  may be comprised of a single or possibly multiple adaptive cancellers, collectively considered a single linear adaptive processor. Applying the soft weight value, w sw , along with processing the input signals reiteratively by returning  110  the output channels, y,  108  back  110  to the inputs  102  results in an improved SINR, Probability of Detection, and BER. Input  112  is processed specially and input back to itself. 
     No particular algorithm is required to be used in each canceller building block. The invention may use any algorithm that either perfectly decorrelates (e.g., Gram Schmidt) or partially decorrelates (e.g., Median Cascaded Canceller or any other generic cascaded canceller) the input data channels. Once the baseline adaptive algorithm or algorithms is or are chosen, adaptive weights of the algorithm are then each soft-weighted themselves by a generally complex or real number prior to being applied. 
     Reiterative processing refers to either 1) the case where one cascaded canceller structure is used and its outputs are redirected back  110  into the inputs one or more times, I, (I&gt;=1) in order to improve the form of the output data for any set of valuable purposes, or 2) the case where multiple cancellers are used in cascade to effectively mimic re-directing the outputs back through the input to achieve the same purposes. Reiteration is occurring when I is greater than one. Soft-weighting refers to modifying the adaptive weights prior to application of those weights by multiplying the adaptive weights by generally complex scalar values in order to change their values. A soft weight value is selected between 0 and 2 and applied to the filter structure. Illustratively, a number of training values corresponding to twice the maximum expected effective rank are developed by a data simulator (e.g., randomly selected data based on patterns in an interference plus noise environment). A measured, or primary, data set is combined with the training data values in a data matrix and input into the processor in order to train the adaptive weights while contemporaneously also applying the soft weight value. This value is then varied through a number of iterations until the desired output metrics for the selected filter are obtained. The instantaneous power output of the selected filter is measured and squared for each primary data input. A representative average of the squared instantaneous power outputs is taken. A representative average may be a mean, a median, a trim mean, a straight average, or any other average of the squared values that would be understood by one of ordinary skill in the art. The selected soft weight value is then increased as the primary data is input into the filter, with each primary data set requiring an individual iteration, until an undesirable power output occurs. An undesirable power output is determined by measuring and comparing the output power of the primary data and subsequent iterations. When the power output measurement difference between a subsequent and its directly preceding iteration is 1 dB, this is the soft weight value that should be used. Once the adaptive weights are modified, the invention produces superior performance in terms of the prescribed desired metrics. Although it is not necessary to use reiteration in every case, this feature further reduces the number of required training samples of the overall processor. 
     Turning to  FIGS. 2A and 2B , the statistical convergence of the processor is improved.  FIGS. 2A and 2B  are graphical demonstrations of an antenna array of twenty (20) antennae and five (5) barrage jammers (e.g., interference sources). The graphs are plots of the average performance when random data samples are input into the processor.  FIG. 2A  is the prior art convergence graph  200  of the number of training samples compared with the normalized SINR for a GSCC without the application of a soft-weight value. To achieve SINR convergence  202  to within 3 dB of the optimal (i.e., 0 db, and, therefore, a convergence of −3 dB), the traditional Gram Schmidt cascaded canceller requires thirty-five (35) training samples  204  for this example. In comparison,  FIG. 2B  is a graphical demonstration  250  of the same system and input data with the soft weighting factor and reiteration applied. The convergence  252  to the −3 dB range after applying the soft weight and reiterative processing to the traditional Gram-Schmidt cascaded canceller is drastically reduced. The application of the invention requires only eleven (11) training samples  254  for the system with the same input data. When the number of antennae in the array (the Degrees of Freedom, or number of overall signal inputs) increases even more, the number of training samples required is drastically reduced from the number that would be required without using soft weights and reiteration. 
       FIGS. 3A and 3B  are graphical representations of the adaptive sidelobe pattern improvements of the soft weighting and reiterative algorithms as applied to the traditional Gram Schmidt cascaded canceller. The graphs are plots of the average performance when random data samples are input into the processor. The graph represents array gain patterns as a function of the azimuth angle relative to the antenna array axis. As shown in  FIG. 3A , the sidelobes  302  for the GSCC without application of the reiterative and soft weighting algorithms are substantially higher than and divergent from the optimum  304 .  FIG. 3B  is the resulting graph of the sidelobes  352  after the soft weighting and reiterative algorithms have been applied. As can be seen, the sidelobe pattern nearly matches the optimum  354  levels. This reduction of the sidelobe levels reduces the amount of uncancelled interference passed on by the filters and greatly reduces the number of false alarms. 
       FIG. 4  is a representation of a Multi-stage Weiner Filter (MWF)  400 . The MWF  400  is an adaptive signal processor that may operate to provide reduced rank processing. The analysis stage  402  decomposes the input data vector matrix into its Krylov subspaces. The synthesis stage  404  subtracts, using a Weiner filter equivalent  406 , the correlated interference from the d o  channel using a subset of the generated Krylov bases. Using a number of Krylov bases less than the number of Degrees of Freedom, or number of antennae in the array, allows the MWF to operate as a reduced rank processor. When soft-weighting is applied to the Gram-Schmidt, or synthesis, stage  404 , the modified MWF may converge faster, especially if the number of Krylov bases originally chosen was too large. The soft-weight value, w sw , is multiplied with the adaptive weight value, or Weiner weight, w i , to achieve a weighted value, w′ i =w i w sw , that is applied at each stage of the synthesis half  404  of the filtering process, X n-1 (k)=ε n (k), thus the output is ε n (k), but the output of interest in most applications is ε o (k) after the final iteration is completed. To apply the reiterative algorithm, the output of the filter  408  is then returned to the input  410 . The number of necessary iterations may be calculated during the operation of the processor after the soft weight factor is determined using all off-line simulations with simulated training data. Using actual data, the processing through the MWF  400  is accomplished until the power level of the output ceases to decrease and begins to increase. The soft weight value, w sw , may be any complex number that provides a convergence benefit to the overall adaptive canceller. The soft weight applied to each MWF Wiener weight, w i , may be chosen to be real, imaginary, or complex and may be generally unique to each MWF Wiener weight. 
     This embodiment uses a standard MWF as a baseline architecture. However it is not required to use the standard MWF Wiener algorithm for its adaptive weight algorithm in each building block in the synthesis stage. In fact, the invention may use any algorithm (including the MWF or Gram-Schmidt algorithm) that either perfectly decorrelates (e.g., Gram Schmidt) or partially decorrelates (e.g., Median Cascaded Canceller or any other generic cascaded canceller algorithm) the input data channels. Once the baseline adaptive algorithm or algorithms is or are chosen, adaptive weights are then each soft weighed themselves by a generally complex or real number prior to being applied. For this embodiment, soft-weighting refers to modifying the MWF Wiener weights prior to application of those weights by multiplying the said adaptive weights by generally complex scalar values in order to change their values. Once the adaptive weights are modified, the invention produces superior performance in terms of the metrics desired. It is not necessary to use reiterative processing in every case; however, this feature further reduces the training data of the processor. 
     As is described with reference to  FIGS. 5A and 5B , the statistical convergence of the processor is improved.  FIGS. 5A and 5B  are graphical demonstrations of an antenna array of twenty (20) antennae and five (5) barrage jammers. The graphs are plots of the average performance when random data samples are input into the processor. The convergence graph  500 , the number of training samples compared with the normalized SINR, for a prior art MWF without the application of a soft weight value or reiteration is shown in  FIG. 5A . To achieve a convergence  502  of −3 dB, the MWF requires thirty-four (34) training samples  504 . In comparison,  FIG. 5B  is a graphical demonstration  550  of the same system with the soft weighting and reiteration applied and using the same input data. The convergence  552  to the −3 dB range after applying the soft weight factor and reiterative processing to the MWF is drastically reduced for the same system and input data. The application of the invention requires only twelve (12) training samples  554  for the system. When the number of antennae in the array increases, the number of training samples required is reduced from the number that would be required without using soft weights and reiteration. 
       FIGS. 6A and 6B  are graphical representations of the adaptive sidelobe pattern improvements of the soft weighting and reiterative algorithms as applied to the traditional MWF. The graphs are plots of the average performance when random data samples are input into the processor. The graph represents array gain patterns as a function of the azimuth angle relative to the antenna array axis. As shown in  FIG. 6A , the prior art graph  600  of the sidelobes  602  for the MWF without application of the reiterative and soft weighting algorithms are substantially higher than and divergent from the optimum  604 .  FIG. 6B  is the resulting graph  650  of the sidelobes  652  after the soft weighting and reiterative algorithms have been applied. As can be seen, the sidelobe pattern nearly matches the optimum  654  levels. This reduction of the sidelobe levels reduces the amount of uncancelled interference passed on by the filters and greatly reduces the number of false alarms. 
     As will be understood by one of ordinary skill in the art, the preferred embodiments may be applied as a method, as a system, or as an apparatus. When incorporated into a system, a controller may be necessary to operate the invention. An illustrative controller may be a computer capable of receiving and storing electronic data, performing algorithmic or other computational functions, and/or storing the results of a particular algorithm. One of ordinary skill in the art will appreciate the computational requirements of a controller necessary to implement the system. The controller may contain, or be electronically connected to, an electronic memory storage device capable of storing electronic data in magnetic or any other electronic format, such as flash memory, that it is accessible by the controller or any other processor. The system may also have output means such as a printer, screen, or any other output device that may output the results of the invention in a readable manner. 
     The invention may also be implemented as a stand-alone apparatus composed of integrated circuits or other processors, as well as memory for electronic storage. Such an apparatus may also include, as a separate unit or integrated into the processor, a soft weight value generator which selects a soft weight value to be applied to an adaptive signal processor in accordance with the present invention. 
     The invention has been described with reference to certain preferred embodiments thereof. It will be understood to those skilled in the art, however, that modification and variations are possible within the scope of the appended claims.