Abstract:
The reduction of echo noise in satellite communications includes receiving an aggregate signal from multiple remote stations, where the aggregate signal includes a transmit signal, whose bandwidth is in the range of 0.1 MHz to 66 MHz, is previously sent from a hub to the multiple receiving stations, computing a scaled, delayed and distorted replica of the transmit signal and using the replica to compensate for satellite transponder nonlinearities and reduce echo noise interference from a received aggregate signal received by the hub from the multiple remote stations.

Description:
RELATED APPLICATION 
     This application claims priority to provisional application Ser. No. 60/791,206, filed Apr. 12, 2006, which is hereby incorporated by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to systems used in satellite communication. More particularly, the present invention provides for the reduction of noise in satellite signals in carrier-in-carrier satellite communications. 
     2. Background of the Related Art 
     Each direction of a conventional duplex radio link typically uses different carrier frequencies. If the same frequency was used for both directions, the transmit signal, which can be 4-5 orders of magnitude larger, can swamp the received signal. In satellite relay systems, such as illustrated in  FIG. 1 , transmit and receive antenna dishes point narrow beams at the geo-stationary satellite. (In “carrier-in-carrier” satellite radio relays, with overlapped up- and down-link frequency bands, as illustrated in  FIG. 2 , the returned transmit signal to the intended receive signal ratio is nominally the near- to far-end antenna gain ratio multiplied by the ratio of required near- to far-end C/N (carrier-to-noise) ratios.) 
     VSAT networks typically consist of one or more earth stations with large diameter antennas (called “hubs” or H) that link (to each other, as well as to terrestrial networks) earth stations with N smaller antennas (called “remote stations” or R 1 -R N ). The hub typically modulates a single carrier at a high rate to transmit data, via a signal H, to the remote stations using time division multiple access, while it receives the aggregate signal A containing the relatively low rate data R k  signals from remote stations at different carrier frequencies. Thus, required C/N ratios are typically higher for signals emanating from the hub as compared to those from the remote stations (being nominally in the ratio of their respective data rates). 
     As shown in  FIG. 1 , the hub and the remote stations receive the aggregate signal A. The H d  signal, within aggregate signal A, is a copy of the Hub&#39;s original wideband H uplink signal that has suffered from delays in time, shifts in frequency, changes in amplitude or other distortions (due to satellite transponder&#39;s non-linear amplitude and phase responses). At the remote stations the H d  signal is the “desired signal”. At the hub, the H d  signal is an unwanted “echo” signal. The hub must subtract out a replica of the H d  signal from the received aggregate signal (A) to produce the desired composite remote stations&#39; signals plus noise and inter-modulation products. 
     Since the returned transmit R k  signals, within aggregate signal A, are typically much weaker at the (more numerous) remote stations than the desired H d  receive signal, due to both the lower transmit signal power as well as lower antenna gain, no echo reduction of any unwanted R k  transmit signals is normally required at the remote stations. 
     While echo cancellation methodologies, as discussed above, have been employed in telephony, such systems cannot be applied wholesale to the satellite communications environment. Echo suppression in telephony, such as line cancellation and acoustic echo cancellation is normally limited to 30-35 dB. Such methods are not, however, amenable to satellite echo cancellers because transponder distortion, with both normalized gain and phase approximately quadratic (at sufficient back-off) with respect to amplitude, cannot be approximated as a small-order, e.g., quadratic filter. In addition, due to the large bandwidths and high data rates of modern satellite signals, echo suppression techniques used in telephony are not practical for satellite signals. Thus, there is a need for noise reduction technology in satellite communications that can properly scale, delay and/or distort at least a portion of the transmitted signal to at least partially compensate for echo noise effects. 
     SUMMARY OF THE INVENTION 
     Accordingly, it is the primary object of the invention to reduce echo noise in satellite communications. The process includes transmitting a transmit signal, H, from a hub to multiple remote stations; receiving an aggregate signal, A, comprising the remote stations&#39; signals, R 1  . . . R N , plus a delayed and distorted replica of the transmit signal, H d ; computing a scaled, delayed and distorted replica of the transmit signal and using the replica to compensate for satellite transponder nonlinearities and perform echo noise reduction on the aggregate signal received by the hub from the satellite. The process is linear such that it supports the operational scenarios illustrated in  FIG. 3 . 
     In some embodiments, the computing step includes decimating the received aggregate signal through a series of filters that are dependent on the bandwidth of the received aggregate signal. In addition, the method can also include determining whether the transmit signal is present in the aggregate signal and performing the computing step when it is determined that the transmit signal is present. 
     The computing step may include correcting for distortion in the aggregate signal by determining normalized gain and phase error in the aggregate signal to compute the replica of the H d  signal. The computing step may also include performing Doppler tracking by determining a conjugate of the aggregate signal to determine a Doppler shift and applying the Doppler shift to compute the replica. Also, the computing step may include determining a delay in the aggregate signal by computing a least mean square fractional sample of the aggregate signal and tracking changes therein to determine the delay. 
     In additional embodiments, a system for echo noise interference reduction in satellite communications is also disclosed having receiving means for receiving an aggregate signal from multiple remote stations, where the aggregate signal includes a transmit signal previously sent from a hub to the multiple receiving stations, computing means for computing a scaled, delayed and distorted replica of the transmit signal and echo noise reduction means for using the replica to reduce echo noise from a received aggregate signal received by the hub from the multiple remote stations. 
     In additional embodiments, an article of manufacture, having a computer-readable medium having stored thereon instructions for compensating for satellite transponder nonlinearities and reducing echo noise in satellite communications, the instructions which, when performed by a processor, cause the processor to execute the steps receiving an aggregate signal from multiple remote stations, where the aggregate signal includes an echo of the transmit signal previously sent from a hub to the multiple receiving stations, computing a scaled, delayed and distorted replica of the echo signal and using the replica to compensate for satellite transponder nonlinearities and reduce echo noise from a received aggregate signal received by the hub. 
     These and other objects of the invention, as well as many of the intended advantages thereof, will become more readily apparent when reference is made to the following description, taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  shows the a satellite communications system in accordance with embodiments of the invention. 
         FIG. 2  illustrates a carrier-in-carrier signals used in the satellite communications system in accordance with embodiments of the invention. 
         FIG. 3  shows the operational scenarios for a noise reduction system in accordance with preferred embodiments of the invention. 
         FIG. 4  shows a state transition diagram for a noise reduction system in accordance with preferred embodiments of the invention. 
         FIG. 5  shows the overall signal processing chain for the noise reduction system in accordance with preferred embodiments of the invention. 
         FIG. 6  provides an expansion of the decimating filters illustrated in  FIG. 5 . 
         FIG. 7  provides an expansion of the interpolating filters illustrated in  FIG. 5 . 
         FIG. 8  shows a residual amplitude and phase distortion estimation and correction module in accordance with preferred embodiments of the invention. 
         FIG. 9  shows a Doppler tracking module according to preferred embodiments of the invention. 
         FIG. 10  shows a least mean square (LMS) update module in accordance with preferred embodiments of the invention. 
         FIG. 11  shows a coarse timing and Doppler acquisition module in accordance with preferred embodiments of the invention. 
         FIG. 12  shows a finer time acquisition module in accordance with preferred embodiments of the invention. 
         FIG. 13  shows a final acquisition module according to preferred embodiments of the invention. 
         FIG. 14  illustrates an exemplary hardware block diagram in accordance with preferred embodiments of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In describing a preferred embodiment of the invention illustrated in the drawings, specific terminology will be resorted to for the sake of clarity. However, the invention is not intended to be limited to the specific terms so selected, and it is to be understood that each specific term includes all technical equivalents that operate in similar manner to accomplish a similar purpose. 
     The present invention acts to reduce noise through echo noise reduction. If the signal H d , as illustrated in  FIG. 2 , is considered as being an interfering echo signal within signal A, then the extraction of the desired R N  signals is achieved by echo reduction. That is, the Noise Reduction System (NRS) removes signal H d  (by way of subtraction), at the hub, from the received aggregate signal A. The NRS continually tracks, and compensates for, the dynamic differences between the H and H d  signals&#39; parameters to minimize the bit error rate (BER) degradation of each of the demodulated R k  signals. In certain embodiments, the transmit signal has a bandwidth of 25 MHz or 66 MHz and can also utilize transmit signals with bandwidths below those values. 
     The present invention utilizes a process that is linear such that it supports the operational scenarios illustrated in  FIG. 3 . In the first operational scenario, the signal received by the hub station is from multiple narrowband remote stations and NRS is used at the hub location, but is not needed at the remote stations where the hub carrier power at the remote stations is large relative to the interfering remote carriers. In the second scenario, a single wideband remote station is involved and NRS is employed at the hub but not needed at the remote stations where the difference between the desired hub carrier power at the remote stations and the interfering remote carrier is greater than or equal to 10 dB. The third scenario is identical to the second with the exception that the difference between the desired hub carrier power at the remote stations and the interfering remote carrier is not greater than or equal to 10 dB, and thus NRS is used at the remote station. In scenario four, the difference is very small, because the hub and remote carriers are at almost equal power, and NRS is used at both the remote station and the hub. Scenario five illustrates the above discussed scenarios can be applied to multiple hub carriers since the NRS functions linearly. 
     The overall signal processing chain for the present invention is illustrated in  FIG. 4 . Illustrated are four states, namely self-test, acquisition, adapt and bypass. On power on, a self-test is run and the system passes to the next stage unless there is a failure. The next stage, the bypass stage, determines whether the carrier channel H is present or there is a problem in later stages. The next stage, acquisition, obtains the H signal so that it can be modified. Thereafter, the adapt stage suppresses the H d  echo signal from the received signal A and tracks and compensates for changes therein. A more detailed signal process structure for the present invention is discussed below. 
     A functional block diagram of the present invention is shown in  FIG. 5 , according to certain embodiments of the invention. The function of the system will delay in time, shift in frequency, and amplify/attenuate the H signal to generate an Estimated H d  signal that is as similar as possible to the H d  signal. This echo noise reduction methodology is preferably used in satellite relay systems following the recent availability of computational resources to process 3×10 7  Hz bandwidth satellite signals and memory resources to store transmitted data for the 300 ms satellite channel delay at 35×10 6  complex samples/sec. 
     The general concepts of the noise reduction system of the present invention are discussed herein. For a network configuration such as that illustrated in  FIG. 1 , where the Hub&#39;s antenna diameter is larger then the Remote&#39;s antenna diameter, the R k  signals transmitted by the Remote Stations are lower power than the Hub&#39;s H transmitted signal, in that case the carrier-to-interference relation received at the remote station could be enough to recover the Hub carrier. Thereafter, the effect at the hub carrier of the remote signal is determined. The power composes (A) at satellite modem input is given by:
 
 A=H   d   +R   1   +•••+R   N   =H   d   +R   Comp   (1)
 
where, R Comp =total remote carriers&#39; powers compose transmitted inside Hub Carrier, H=Hub carrier power transmitted, and R n =Remote carrier power transmitted for a remote station n.
 
     Thereafter, N is the maximum number of remote carriers (R) hidden in the Hub carrier that is given by: 
                   N   =         W     S   H           W     S   R       *     f   g         =         W     S   H         W     S   R         *     1     f   g                   (   2   )               
where, Ws H =Hub Carrier Bandwidth (Symbol Rate), Ws R =Remote Carrier Bandwidth (Symbol Rate), W R =Ws R *f g  is the Satellite Allocated Bandwidth for a Remote carrier (R n ) and f g =Guard Factor (bandwidth spacing between adjacent remote carriers)=1, 4 times the most frequency value used.
 
     In addition: 
                       H   d       R   Comp       =       H   d       (       R   1     +       R   2     ⁢           ⁢   …   ⁢           ⁢     R   n         )               (   3   )               
Thereafter, considering the case where R I =R 2 =••=R N , this result in:
 
                       H   d       R   Comp       =         H   d       (       R   1     +       R   2     ⁢           ⁢   …   ⁢           ⁢     R   n         )       =         H   d       N   ×   R       =       (       H   d     R     )     *     (     1   N     )                   (   4   )                   H     R   Comp       =         (     H   R     )     *     (     1   N     )       =         (     H   R     )     *     (       1     W     S   H             W     S   R       *     f   g         )       =       (       H     W     S   H           R     W     S   R           )     *     f   g             ⁢     
     ⁢     where   ⁢     :       ⁢     
     ⁢       (     R     W     S   R         )     =         R   o     ⁢             ⁢             ⁢   Remote   ⁢           ⁢   Signal   ⁢             ⁢             ⁢   Power   ⁢           ⁢     Density   ⁢     
     (     R     W     S   R         )       =       H   o     ⁢           ⁢   Hub   ⁢           ⁢   Signal   ⁢           ⁢   Power   ⁢           ⁢   Density                 (   5   )               
and f g =Guard factor among an R carrier. Then equation (5) can be rewritten as:
 
     
       
         
           
             
               
                 
                   
                     
                       H 
                       d 
                     
                     
                       R 
                       Comp 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           H 
                           o 
                         
                         
                           R 
                           o 
                         
                       
                       ) 
                     
                     * 
                     
                       f 
                       g 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Because the Hub&#39;s wideband signal H, in the form of H d , is higher power within the aggregate signal A than the Remote Stations&#39; R k  signals, it can be demodulated by the Remote Stations. (Ratio 
             (       H   o       R   o       )         
represents the power density difference between remote and Hub Carrier as seen using a spectrum analyzer.) Then equation (6) can be written in a relative way as:
 
     
       
         
           
             
               
                 
                   
                     
                       H 
                       d 
                     
                     
                       R 
                       Comp 
                     
                   
                   = 
                   
                     E 
                     * 
                     
                       f 
                       g 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     or 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     H 
                     
                       R 
                       Comp 
                     
                   
                   = 
                   
                     
                       E 
                       dB 
                     
                     + 
                     
                       F 
                       dB 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     In accordance with the satellite link calculation, it can be said that the power density ratio (or E dB ) will depend of: antennas size, Modulation Type and Code forward error correction (FEC) used in the satellite link. 
     There fore in this way the new 
               (     C   N     )     Total         
in the remote station will be given by:
 
     
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
                           C 
                           N 
                         
                         ) 
                       
                       Total 
                       Remote 
                     
                     = 
                     
                       
                         
                           ( 
                           
                             C 
                             N 
                           
                           ) 
                         
                         UP 
                       
                       ⊗ 
                       
                         
                           ( 
                           
                             C 
                             N 
                           
                           ) 
                         
                         Down 
                       
                       ⊗ 
                       
                         ( 
                         
                           C 
                           
                             I 
                             M 
                           
                         
                         ) 
                       
                       ⊗ 
                       
                         
                           ( 
                           
                             C 
                             N 
                           
                           ) 
                         
                         Rcomp 
                       
                     
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     where 
                     : 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ( 
                       
                         C 
                         N 
                       
                       ) 
                     
                     Rcomp 
                   
                   = 
                   
                     
                       H 
                       d 
                     
                     
                       R 
                       Comp 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   Z 
                   = 
                   
                     
                       X 
                       ⊗ 
                       Y 
                     
                     = 
                     
                       10 
                       ⁢ 
                       
                         Log 
                         ⁡ 
                         
                           [ 
                           
                             
                               1 
                               
                                 10 
                                 
                                   X 
                                   10 
                                 
                               
                             
                             + 
                             
                               1 
                               
                                 10 
                                 
                                   Y 
                                   10 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
               (     C   N     )     Rcomp         
represents the new noise interference or degradation value added at satellite link.
 
     Turning now to an analysis of the hub station interference, it can be assumed that the power density of the signal H is given by: 
                     H   o     =     H     Ws   H               (   12   )               
The total interference power (I H ) of (H) signal over a remote carrier (R) is given by:
 
     
       
         
           
             
               
                 
                   
                     I 
                     H 
                   
                   = 
                   
                     
                       
                         H 
                         o 
                       
                       * 
                       
                         Ws 
                         R 
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             H 
                             
                               Ws 
                               H 
                             
                           
                           ) 
                         
                         * 
                         
                           Ws 
                           R 
                         
                       
                       = 
                       
                         H 
                         * 
                         
                           ( 
                           
                             
                               Ws 
                               R 
                             
                             
                               Ws 
                               H 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     The power relation between remote and Hub signals interference received at the Hub station can be written as: 
     
       
         
           
             
               
                 
                   
                     R 
                     
                       I 
                       H 
                     
                   
                   = 
                   
                     
                       R 
                       
                         H 
                         * 
                         
                           ( 
                           
                             
                               Ws 
                               R 
                             
                             
                               Ws 
                               H 
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         ( 
                         
                           R 
                           H 
                         
                         ) 
                       
                       * 
                       
                         ( 
                         
                           
                             Ws 
                             H 
                           
                           
                             Ws 
                             R 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       R 
                       
                         I 
                         H 
                       
                     
                     = 
                     
                       
                         ( 
                         
                           R 
                           
                             Ws 
                             R 
                           
                         
                         ) 
                       
                       
                         ( 
                         
                           H 
                           
                             Ws 
                             H 
                           
                         
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       Thus 
                       : 
                       
                          
                       
                       ⁢ 
                       
                         ( 
                         
                           R 
                           
                             Ws 
                             R 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         R 
                         o 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         Remote Signal Power Density 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         R 
                         
                           Ws 
                           R 
                         
                       
                       ) 
                     
                     = 
                     
                       
                         H 
                         o 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         Hub Signal Power Density 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Replacing R o  and H o  in equation (13), we have: 
                     R     I   H       =       (       (     R     Ws   R       )       (     H     Ws   H       )       )     =         R   o       H   o       =     1     (       H   o       R   o       )                   (   16   )               
where:
 
             (       H   o       R   o       )         
Represents E dB ; then (2.5) can be written in a relative way as:
 
     
       
         
           
             
               
                 
                   
                     
                       
                         R 
                         
                           I 
                           H 
                         
                       
                       = 
                       
                         
                           1 
                           
                             ( 
                             
                               
                                 H 
                                 o 
                               
                               
                                 R 
                                 o 
                               
                             
                             ) 
                           
                         
                         = 
                         
                           1 
                           E 
                         
                       
                     
                     , 
                     or 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       R 
                       
                         I 
                         H 
                       
                     
                     = 
                     
                       - 
                       
                         E 
                         dB 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     In the hub side after the canceller system, the H d  hub signal interference will be attenuated by Z dB (Attenuation factor). Then, the relation given by equation (16) will be modified as: 
                       R     Ic   H       =       1     (       H   o       z     R   o         )       =         1     (       H   o       R   o       )       *   z     =       z   E     ⁢           ⁢   or           ⁢                   (   19   )                 R     Ic   H       =       Z   dB     -     E   dB               (   20   )               
Therefore in this way the new C/N in the hub station will be given by:
 
                       (     C   N     )     Total   Hub     =         (     C   N     )     UP     ⊗       (     C   N     )     Down     ⊗     (     C     I   M       )     ⊗       (     C     I   H       )     Hcaccire               (   21   )               
Where
 
               (     C     I   H       )     Hcaccire         
represents the new noise interference or degradation value added at satellite link for Hub Carrier.
 
     Aspects of the reduction of satellite echo signals include delay (to ±½ sample) and Doppler acquisition, time (including fractional sample) delay and Doppler tracking. The suppression by incorporating low-complexity distortion compensation into the echo reduction process is further described in  FIG. 5 . 
     Both signals H and A are digitized at the IF frequency of 70 MHz, SAW filtered, quadrature down-converted, and decimated (by a factor consistent with signal bandwidth) to obtain complex base-band samples. The decimating filters are expanded in  FIG. 6 , where the number of stages applied depends on the bandwidth. At the output of the echo reduction process, signals are interpolated, as illustrated in  FIG. 7 , where that interpolation is also a function of the bandwidth and uses an equivalent number of stages. 
     The baseband signal H enters a buffer that accounts for integer sample delay (that is initially acquired and subsequently tracked), then distorted prior to being frequency shifted and fractional-sample delayed (by an adaptive FIR filter) to generate a replica of H d , before being subtracted from A to yield the baseband signals, R k . This signal may then be up-converted back to IF for presentation to remote-station demodulators/decoders, where other processing can further mitigate distortion effects on each R k . 
       FIG. 8  describes the process by which the LMS delay equalizer output, H d , time-aligned to A, is used to iteratively update estimates of AM-Normgain and AM-PM curves. Log normalized |H| is inferred from log normalized |H d | through fixed-point iteration in the AM-Normgain array, f, i.e., if g{•}={log(|H d |/E|H d |)−f(•)}, then fixed-point iteration is g{g{ . . . }}=g n (•) until g n {log(|H d |/E|H d |)}+f{g n [log(|H d |/E|H d |]}−log [|H d /E|H d ] is less than a resolution threshold (e.g., ⅙ dB) or g n {log(|H d |/E|H d |} exceeds an upper limit (e.g., 4 dB). 
     The AM-Normgain correction array, indexed by log normalized |H|, is updated by filtering (e.g., using a dc unity gain, first-order filter) log(|A|/E|A|)−log(|H d |/E|H d |). This array is periodically integrated into the AM-Normgain array, after bias subtraction and adaptive filter gain compensation. AM-Phase correction array update is based on arg(A)-arg(H). The envelope estimate of R is also biased by excess mean square error (MSE) from the fractional sample delay adaptation; thus, R&#39;s envelope divided by (1+μL σ H′   2 ) 0.5  is N&#39;s. 
     Finally, to minimize noise effects on the final map, the AM-normgain and AM-PM arrays are forced to least probability weighted squares polynomial (e.g., for the nonlinear satellite channel, parabolic fits, y=1−az 2 , 0&lt;a&lt;a max  and φ=bz 2 , 0&lt;b&lt;b mas ) of normalized envelopes. 
       FIG. 9  illustrates a delayed phase-locked loop for Doppler tracking. One of the half-band filter (HBF) stages of the fixed decimation is implemented on the two channels prior to the complex multiplication block; the variable chain and 5 stages of the fixed decimation chain are after the multiplication block to reduce computational burden. The bandwidth-dependent “remainder” (with 8-0 stages) of the 0-8 half-band decimation chain, the HBF block, depicted in  FIG. 9  is used as the “variable decimation chain”. The “fixed decimation chain” consists of 5 stages of the half-band filter followed by a decimation of 2 (for an overall decimation of 32). 
     Fractional sample time delay (of H′) inclusion in adaptive filters is performed, where the integer sample delay is initially obtained by an initial time delay estimation (such as, by a FFT-based ambiguity function/cross-correlation computation) and subsequently the integer sample closest to the adaptive filter&#39;s weight vector&#39;s centroid is tracked. Suppose that H′ k ∈Z L  is stationary zero-mean vector random process with autocorrelation matrix Ω=E[H′ k H′ k   T ]∀k, the reference signal, A k ∈Z, being a stationary zero-mean scalar random process and w k ∈R L  is the weight vector at the kth time step. 
     For this adaptive filter, the error is ε k =A k Σw k H′ k ,w k ∈R L . Assume that H′k and Ak are stationary with cross-correlation vector p=E[A k ·H′ k ]∀k. Using a MSE cost function ξ=E|ε k | 2 =E|A k |− 2 −2p T w+w T Ωw, it is easily shown that for full rank &#39;Ω, the weight vector that minimizes ξ is w opt =&#39;Ω −1 p. The MSE when using w opt  is denoted as ξ opt . The Widrow-Hopf LMS algorithm, as illustrated in  FIG. 10 , estimates w opt  when &#39;Ω .  and p are unknown using an instantaneous error |ε k | 2  via w k+1 =w k +2μRe{ε k H′* k }, with * connoting complex conjugate. 
     For large enough k, i.e., in steady state, for an arbitrary initial w 0 , E[w k ]=w opt  when 0&lt;μ≦[3Tr(&#39;Ω)] −1 , with w k  exhibiting Brownian motion around w opt , the excess MSE is approximated by ξ excess =μξ opt Tr(&#39;Ω). It is preferable to separate the attenuation factor, α, of H d  in A (by multiplying A by σ H /(2σ A )&lt;α −1 &lt;σ H /σ A ) from the time delay adaptation. 
     The matrix &#39;Ω .  of H′ k  (for the outbound communication signal) is tri-diagonal when the signal is over-sampled by a factor less than 2. All principal diagonal terms being positive and greater than off-diagonal terms ensure &#39;Ω&#39;s full rank, and thus, with μ≦[3Lσ H′   2 ] −1 , ξ excess =μξ opt Lσ H′   2 . 
       FIG. 11  illustrates a coarse timing and Doppler acquisition module. Initiated on “power-on” and when, in “adaptive mode”, the threshold test in “Distortion correction” fails for a period more than twice the LMS algorithm&#39;s convergence duration. This function assumes an aperiodic, noise-like (white) symbol sequence with spectral shaping and SAW filter limiting bandwidth to 25 MHz (i.e., spectral occupancy is 25/35) or other bandwidth limit. Time delay is acquired by FFT-based computation of cross-correlations between signal H and A. A 3-pass (each with a different time scale and positive residual lag) approach to time delay and Doppler estimation is adopted because the computational complexity to compute cross-correlations over a 300 ms span, at 35 million complex samples/s, overwhelms the computational power and on-chip memory of any current processing engine, sorting through the multitude of correlation peaks in a single-pass scheme is complex and achieving fine Doppler acquisition (over a ±20 Hz range) would require an unreasonably large FFT size. 
       FIGS. 11 and 12  provide two-step zooming-in for fine time resolution, applied to the range, with no Doppler.  FIG. 12  provides for finer time acquisition and  FIG. 13  provides for final acquisition. Each stage uses 512 samples corresponding to a search window, and a time resolution, to repeat the time determination over 10 blocks. 
       FIG. 14  provides an exemplary hardware configuration according to specific embodiments of the present invention. Therein, specific connections are detailed, such as connection to a control computer through RS-232 interface, as well power converting and conditioning of the input power source. The input signal is filtered, buffered and converted into digital signals for input into the field-programmable gate array (FPGA) processor. The FPGA is connected to DRAM and EEPROM memories and a master clock signal, and after processing, as discussed above, the filtered echo-reduced signal is output. 
     An LMS echo reduction system with distortion compensation has been described wherein the amplitude and phase distortion characteristics are automatically acquired and tracked from the received signal (when echo dominates the received signal), the expressions for excess error with and without distortion compensation are obtained and distortion compensation is enabled when H/R exceeds a threshold. 
     The foregoing description and drawings should be considered as illustrative only of the principles of the invention. The invention may be configured in a variety of shapes and sizes and is not intended to be limited by the preferred embodiment. Numerous applications of the invention will readily occur to those skilled in the art. Therefore, it is not desired to limit the invention to the specific examples disclosed or the exact construction and operation shown and described. Rather, all suitable modifications and equivalents may be resorted to, falling within the scope of the invention.