Abstract:
Apparatus and methods relating to channel equalization include a method including: generating a first output signal in a frequency domain based on a communications signal of a channel; determining a first channel response based on the first output signal and one or more pilot signals of the communications signal; generating a first equalized signal based on the first output signal and the first determined channel response; generating a first decision signal based on the first equalized signal; generating an output signal in a time domain based on the first decision signal; determining a second channel response based on the time domain output signal; generating a second output signal in the frequency domain based on the second channel response; generating a second equalized signal based on the first and second output signals and the time domain output signal; and generating a second decision signal based on the second equalized signal.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of and claims the benefit of the priority of U.S. patent application Ser. No. 12/642,443, filed Dec. 18, 2009, entitled “Channel Equalization in Receivers”, to issue as U.S. Pat. No. 7,826,576, on Nov. 2, 2010, which is a continuation of and claims the benefit of the priority of U.S. patent application Ser. No. 11/291,584, filed Nov. 30, 2005, entitled “Channel Equalization in Receivers”, now U.S. Pat. No. 7,646,833, issued on Jan. 12, 2010, which claims the benefit of the priority of U.S. Provisional Application Ser. No. 60/684,093, filed May 23, 2005, and entitled “An OFDM Receiver for Timing-Varying Channels”; each of these prior applications is hereby incorporated by reference. 
    
    
     BACKGROUND 
     This document relates to channel equalization in receivers. 
     When a signal is transmitted over a channel, the received signal may be different from the transmitted signal. For example, a signal transmitted wirelessly may be attenuated by the time it reaches a receiver. These changes to the transmitted signal are called channel effects. If, for example, a transmitter or a receiver are moving during transmission or reception, respectively, the channel effects may include Doppler effects. 
     Receivers may employ systems and techniques to model these channel effects and remove or reduce them through channel equalization. 
     SUMMARY 
     According to an aspect of the described systems and techniques, a method includes obtaining a communications signal of a channel and removing, in the frequency domain, channel effects from the communications signal, where the removing includes generating, in the time domain, one or more time-varying channel response estimates. 
     In some implementations, the removing channel effects also includes estimating a time-invariant channel response based at least in part on the communications signal; generating a first estimated signal based at least in part on the time-invariant channel response; and generating a second estimated signal based at least in part on a first time-varying channel response. Also, the generating one or more time-varying channel response estimates can include generating the first time-varying channel response based at least in part on the first estimated signal. 
     In some implementations of the method, the obtaining the communications signal includes receiving the communications signal. 
     In some implementations, the removing channel effects also includes generating a second time-varying channel response based at least in part on the second estimated input signal and generating a third estimated input signal based at least in part on the second time-varying channel response. 
     In some implementations, the removing channel effects also includes iteratively generating additional time-varying channel responses and additional estimated input signals until a final estimated input signal is determined to be acceptable based at least in part on one of the generated additional estimated input signals. 
     In some implementations, the estimating a time-invariant channel response includes receiving one or more pilot signals on one or more subcarrier signals. 
     In some implementations, the generating a first estimated input signal includes performing channel equalization using the time-invariant channel response. 
     In some implementations, the generating the first time-varying channel response includes performing a least-mean-squared technique. 
     In some implementations, the generating a second estimated input signal includes performing channel equalization using the first time-varying channel response. 
     According to an aspect of the described systems and techniques, a method includes: receiving a communications signal comprising one or more pilot signals on one or more subcarrier signals; estimating a time-invariant channel response based at least in part on the one or more pilot signals; generating a first estimated frequency-domain source signal based at least in part on the time-invariant channel response; generating a first estimated time-domain source signal based at least in part on the first estimated frequency-domain source signal; estimating a time-varying time-domain channel response using a least-mean-squared technique; generating a time-varying frequency-domain channel response based at least in part on the time-varying time-domain channel response; and generating a second estimated frequency-domain source signal based at least in part on the time-varying frequency domain channel response. 
     In some implementations, the generating a first estimated time-domain source signal includes performing a one-dimensional Inverse Fast Fourier Transform technique; and the generating a time-varying frequency-domain channel response includes performing a two-dimensional Fast Fourier Transform technique. 
     According to an aspect of the described systems and techniques, an apparatus includes an input configured to obtain a communications signal of a channel, and a channel equalizer configured to remove, in the frequency domain, channel effects from the communications signal using one or more time-varying time-domain channel response estimates. 
     In some implementations, the channel equalizer includes: a first equalization unit configured to perform a time-invariant equalization and to be responsive to a time-invariant channel response; an estimation unit configured to generate a time-varying channel response and to be responsive to an output of the first equalization unit; and a second equalization unit configured to perform a time-varying equalization and to be responsive to an output of the estimation unit. 
     In some implementations, the apparatus also includes a first decision unit responsive to an output of the second equalization unit. 
     In some implementations, the channel equalizer also includes a second decision unit responsive to an output of the first equalization unit. 
     In some implementations, the estimation unit includes a least-mean-squared unit. 
     In some implementations, the channel equalizer also includes an initial response estimator configured to estimate the time-invariant channel response based on one or more pilot signals. 
     In some implementations, the channel equalizer also includes: a one-dimensional Fast Fourier Transform unit; a one-dimensional Inverse Fast Fourier Transform unit; and a two-dimensional Fast Fourier Transform unit. 
     In some implementations, the input configured to obtain the communications signal is configured to receive the communications signal of the channel. 
     According to an aspect of the described systems and techniques, an apparatus includes a means for obtaining a communications signal of a channel and a means for removing, in the frequency domain, channel effects from the communications signal, the means for removing comprising a means for generating, in the time domain, one or more time-varying channel response estimates. 
     In some implementations, the means for removing channel effects also includes: a means for estimating a time-invariant channel response based at least in part on the communications signal; a means for generating a first estimated signal based at least in part on the time-invariant channel response; and a means for generating a second estimated signal based at least in part on a first time-varying channel response. Also, the means for generating one or more time-varying channel response estimates can include a means for generating the first time-varying channel response based at least in part on the first estimated signal. 
     In some implementations, the means for obtaining the communications signal includes a means for receiving the communications signal. 
     In some implementations, the means for removing channel effects also includes a means for generating a second time-varying channel response based at least in part on the second estimated input signal and a means for generating a third estimated input signal based at least in part on the second time-varying channel response. 
     In some implementations, the means for removing channel effects also includes a means for iteratively generating additional time-varying channel responses and additional estimated input signals until a final estimated input signal is determined to be acceptable based at least in part on one of the generated additional estimated input signals. 
     In some implementations, the means for estimating a time-invariant channel response includes a means for receiving one or more pilot signals on one or more subcarrier signals. 
     In some implementations, the means for generating a first estimated input signal includes a means for performing channel equalization using the time-invariant channel response. 
     In some implementations, the means for generating the first time-varying channel response includes a means for performing a least-mean-squared technique. 
     In some implementations, the means for generating a second estimated input signal includes a means for performing channel equalization using the first time-varying channel response. 
     According to an aspect of the described systems and techniques, an apparatus includes: a means for receiving a communications signal comprising one or more pilot signals on one or more subcarrier signals; a means for estimating a time-invariant channel response based at least in part on the one or more pilot signals; a means for generating a first estimated frequency-domain source signal based at least in part on the time-invariant channel response; a means for generating a first estimated time-domain source signal based at least in part on the first estimated frequency-domain source signal; a means for estimating a time-varying time-domain channel response using a least-mean-squared technique; a means for generating a time-varying frequency-domain channel response based at least in part on the time-varying time-domain channel response; and a means for generating a second estimated frequency-domain source signal based at least in part on the time-varying frequency domain channel response. 
     In some implementations, the means for generating a first estimated time-domain source signal includes a means for performing a one-dimensional Inverse Fast Fourier Transform technique and the means for generating a time-varying frequency-domain channel response includes a means for performing a two-dimensional Fast Fourier Transform technique. 
     According to an aspect of the described systems and techniques, a system includes an antenna configured to obtain a communications signal of a channel and a channel equalizer configured to remove, in the frequency domain, channel effects from the communications signal using one or more time-varying time-domain channel response estimates. 
     In some implementations of the system, the channel equalizer includes: a first equalization unit configured to perform a time-invariant equalization and to be responsive to a time-invariant channel response; an estimation unit configured to generate a time-varying channel response and to be responsive to an output of the first equalization unit; and a second equalization unit configured to perform a time-varying equalization and to be responsive to an output of the estimation unit. 
     In some implementations, the system also includes a first decision unit responsive to an output of the second equalization unit. 
     In some implementations of the system, the channel equalizer also includes a second decision unit responsive to an output of the first equalization unit. 
     In some implementations of the system, the estimation unit includes a least-mean-squared unit. 
     In some implementations of the system, the channel equalizer also includes an initial response estimator configured to estimate the time-invariant channel response based on one or more pilot signals. 
     In some implementations of the system, the channel equalizer also includes: a one-dimensional Fast Fourier Transform unit; a one-dimensional Inverse Fast Fourier Transform unit; and a two-dimensional Fast Fourier Transform unit. 
     In some implementations of the system, the antenna configured to obtain the communications signal is configured to receive the communications signal of the channel. 
     The described systems and techniques can result in one or more of the following advantages. Channel effects acting on a transmitted signal can be reduced or removed. Examples of channel effects that may be, reduced or removed include Doppler effects and other time-varying channel effects. 
     The described systems and techniques can be implemented in electronic circuitry, computer hardware, firmware, software, or in combinations of them, such as the structural means disclosed in this specification and structural equivalents thereof. This can include a program operable to cause one or more machines (e.g., a signal processing device) to perform operations described. Thus, program implementations can be realized from a disclosed method, system, or apparatus, and apparatus implementations can be realized from a disclosed system, program, or method. Similarly, method implementations can be realized from a disclosed system, program, or apparatus, and system implementations can be realized from a disclosed method, program, or apparatus. 
     For example, the disclosed embodiment(s) below can be implemented in various systems and apparatus, including, but not limited to, a special purpose programmable machine (e.g., a wireless access point, a router, a switch, a remote environment monitor), a mobile data processing machine (e.g., a wireless client, a cellular telephone, a personal digital assistant (PDA), a mobile computer, a digital camera), a general purpose data processing machine (e.g., a minicomputer, a server, a mainframe, a supercomputer), or combinations of these. 
     The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features, objects and advantages may be apparent from the description and drawings, and from the claims. 
    
    
     
       DRAWING DESCRIPTIONS 
         FIG. 1A  is a block diagram of a signal transmission and reception system. 
         FIG. 1B  is a diagram showing channel equalization in a signal (e.g., orthogonal frequency-division multiplexed (OFDM) signal) transmission and reception system. 
         FIG. 2  shows a system for channel equalization. 
         FIG. 3  shows a process for channel equalization. 
         FIGS. 4A-4E  show various exemplary implementations of the described systems and techniques. 
     
    
    
     Like reference symbols in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
       FIGS. 1A and 1B  depict a transmission and reception system. A source device  105  may transmit a signal (e.g., orthogonal frequency-division multiplexed (OFDM) signal) over a channel  125  to a receiver  145 . Receiver  145  may obtain the signal via input  143 . In some implementations, if the channel comprises wireless transmission, input  143  may be an antenna. In some implementations, e.g., transmission over a cable, input  143  may be an connector attached to the cable. In some implementations, e.g., transmission via satellite, input  143  may be a satellite reception dish. 
     A source device  105  may process a frequency-domain source signal X(k)  110  to be transmitted. Signal X(k)  110  may be modulated, e.g., by quadrature amplitude modulation techniques such as QAM16 (16-QAM) or QAM256 (256-QAM), or by other modulation techniques. Signal X(k) may be transformed into the time-domain using, for example, an Inverse Fast Fourier Transform (IFFT) unit  115 , resulting in a time-domain source signal x(n)  120 . 
     Time-domain source signal x(n)  120  may be sent over channel  125  and may be received at receiver  145 . Channel  125  may be a conventional radio frequency channel or it may be another transmission channel, e.g., cable, satellite, etc. Different channels may modify the signal by introducing different channel effects. For example, some channels may attenuate the signal. The received signal y(n)  130  arriving at receiver  145  may thus be different from the time-domain source signal x(n)  120 . 
     Components within receiver  145  may introduce noise into the system. Various noise components may be modeled in this description by adding a noise signal n(n)  135  to received signal y(n)  130 . Thus, the modeled received signal {tilde over (y)}(n)  140  at receiver  145  may be represented as
 
{tilde over ( y )}( n )= y ( n )+ n ( n ).  (1)
 
     The modeled received signal {tilde over (y)}(n)  140  may be transformed into frequency domain signal {tilde over (Y)}(k)  155 , for example by using a Fast Fourier Transform unit  150 . The receiver  145  may perform channel equalization  160  to compensate for channel effects, producing an equalized receive signal {tilde over (X)}(k)  165 . The equalized received signal {tilde over (X)}(k)  165  may then be processed by a decision block  170  (e.g., a Viterbi decoder). 
     Decision block  170  may be used to remove noise from the equalized received signal {tilde over (X)}(k)  165 . For example, suppose a transmitted binary signal consisted of two values, 0 volts and 1 volt. As a result of noise, the equalized received binary signal may comprise values other than exactly 0 and 1. Thus, for example, if 0.2 V were received, decision block  170  can be used to interpret/decode the received signal to be an intended value of 0. Similarly, if 0.8 V were received, decision block  170  can interpret/decode the received value to be the intended value of 1. Decision block  170  may be implemented using one or more of several algorithms, such as, in one implementation, using a slicer technique or a Viterbi algorithm. The decoded signal {circumflex over (X)}(k)  175  resulting from decision block  170  may be close to or identical to frequency-domain source signal X(k)  110 . 
     The channel equalization block  160  may be implemented in several ways. For example, assuming channel  125  has time-invariant channel effects, the impulse response for the channel may be represented as h(l). This may be represented in the frequency domain by H(k), which results from the N-point FFT of h(l): 
                         H   ⁡     (   k   )       =       ∑     n   =   0       N   -   1       ⁢           ⁢       h   ⁡     (   n   )       ·     w     k   ·   n             ,     
     ⁢     w   =     ⅇ         -   j     ·   2     ⁢     π   /   N             ⁢     
     ⁢       k   =   0     ,   1   ,       …   ⁢           ⁢   N     -   1               (   2   )               
Received signal y(n)  130  may then be represented in the frequency domain as:
 
 Y ( k )= X ( k )· H ( k ).  (3)
 
The frequency-domain representation {tilde over (Y)}(k)  155  of the modeled received signal {tilde over (y)}(n)  140  may then be represented as
 
 {tilde over (Y)} ( k )= X ( k )· H ( k )+ N ( k ).  (4)
 
     H(k) can be determined by transmitting a known pilot signal on a set of subcarriers. The pilot signal may be in either the time-domain or the frequency domain. In the frequency-domain, a particular frequency may contain the pilot signal, which may be specified by a standard, e.g., the Digital Video Broadcasting (DVB) standard from the European Telecommunications Standards Institute (ETSI). 
     Having determined H(k), channel equalization may be performed according to the following equation:
 
 {tilde over (X)} ( k )= {tilde over (Y)} ( k )/ H ( k ).  (5)
 
     In many applications, however, the channel cannot be considered to be time-invariant. For example, for a moving receiver  145  (e.g., in a car) the Doppler effect may cause channel effects for a wireless channel to be time-varying. Other factors, such as changes in electromagnetic field or changes in temperature may also cause time-varying channel effects. 
     For time-varying channels, the impulse response of the channel may be represented as h(n,l), where n represents time and/represents delay. 
     Because the channel effects are time-varying, the subcarriers are not orthogonal, and the system may be modeled as: 
                         Y   ~     ⁡     (   k   )       =         ∑     i   =   0       N   -   1       ⁢           ⁢       X   ⁡     (   i   )       ·       H   2     ⁡     (       k   -   i     ,   i     )           +     N   ⁡     (   k   )           ,           (   6   )               
where H 2 (k,i) is the 2-dimensional FFT of h(n,l) and can be represented as:
 
     
       
         
           
             
               
                 
                   
                     
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     Although H 2 (k,i) cannot be accurately estimated by pilot subcarriers, it may be estimated directly by estimating h(n,l). Equation (6) may be written in the time-domain as: 
     
       
         
           
             
               
                 
                   
                     
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     If x(n) is known, then a least-mean-squared (LMS) algorithm can be used to adaptively track h(n,l): 
                       h   ⁡     (       n   +   1     ,   l     )       =       h   ⁡     (     n   ,   l     )       +     μ   ·     (         y   ~     ⁡     (   n   )       -     y   ⁡     (   n   )         )     ·     x   ⁡     (     n   -   l     )             ,           ⁢     l   =   0     ,         …   ⁢           ⁢   L     -     1   ⁢           ⁢   where   ⁢           ⁢     y   ⁡     (   n   )           =       ∑     l   =   0     L     ⁢           ⁢       h   ⁡     (     n   ,   l     )       ·     x   ⁡     (     n   -   l     )                     (   9   )               
and where μ is the LMS step size.
 
       FIG. 2  shows a system for estimating the equalized received signal {tilde over (X)}(k)  165 . At  205 , {tilde over (Y)}(k)  155  is generated by taking the FFT of modeled received signal {tilde over (y)}(n). At  210 , {tilde over (H)}(k) is estimated based on pilot subcarriers in both the current and adjacent symbols. At  215 , if the channel is assumed to be time-invariant, {tilde over (X)}(k) may be estimated:
 
 {tilde over (X)} ( k )= {tilde over (Y)} ( k )/ {tilde over (H)} ( k ).  (10)
 
In some implementations, a time-varying channel equalization can be applied at  215  if a time-varying model is available. Such implementations may be useful in several technologies, including those related to WiMAX and the Institute of Electrical and Electronics Engineers, Inc., (IEEE) Standard 802.16(e).
 
     At  220 , a decision block generates {circumflex over (X)}(k) for example according to a slicer technique or a Viterbi algorithm. At  225 , the time-domain representation {circumflex over (x)}(n) may be generated by implementing IFFT({circumflex over (X)}(k)). 
     At  230 , h(n,l) may be estimated using {circumflex over (x)}(n) in the LMS algorithm of equation (9). At  235 , H 2 (k,i) may be generated by implementing the two-dimensional FFT of h(n,l). 
     At  240 , a time-varying channel equalization is performed using equation (6) based on the estimated time-varying transfer function H 2 (k,i) (calculated at  235 ), signal {circumflex over (X)}(k) (calculated at  220 ), and signal {tilde over (Y)}(k) (calculated at  205 ). The equalized signal may be represented {tilde over ({tilde over (X)}(k). 
     At  245 , signal {circumflex over ({circumflex over (X)}(k) is generated by implementing a decision procedure on equalized signal {tilde over ({tilde over (X)}(k). This decision procedure may be the same as or similar to the decision procedure implemented at  220 . 
     An iteration control  250 , determines whether to perform another iteration using {circumflex over ({circumflex over (X)}(k) (calculated at  245 ) as the input to the IFFT at  225 . In some implementations, {tilde over ({tilde over (X)}(k) (calculated at  240 ) may be used instead as the input to the IFFT at  225 . Because iterations may be costly in terms of both time and hardware, it may be sufficient to perform only one or two iterations. In some implementations, an LMS error may be calculated between particular signals of successive iterations (e.g., between equalized signals such as {tilde over ({tilde over (X)}(k), decision signals such as {circumflex over ({circumflex over (X)}(k), etc.). Iteration control  250  may continue iterations until a particular LMS error threshold is met. The resulting equalized signal generated at the end of the process may be a statistically close estimate of source signal  110 . 
     Some implementations need not perform all the operations depicted in  FIG. 2  or described herein. For example, in some implementations, the determination at iteration control  250  of whether to loop back in the process is not performed (i.e., single iteration systems). 
       FIG. 3  shows a process for channel equalization. At  310 , a communications signal of a channel may be obtained (e.g., by receiver  145 ). At  320 , a time-invariant channel response may be estimated based at least in part on the communications signal (e.g., by channel equalization unit  160 , unit  210 ). A first estimated signal may be generated based at least in part on the time-invariant channel response at  330  (e.g., by channel equalization unit  160 , unit  215 , unit  220 ). At  340 , a first time-varying channel response may be generated based at least in part on the first estimated signal (e.g., by channel equalization unit  160 , unit  230 ). At  350 , a second estimated signal may be generated based at least in part on the first time-varying channel response (e.g., by channel equalization unit  160 , unit  240 , unit  245 ). 
     At  360 , a determination may be made whether to perform another iteration of the process (e.g., by channel equalization unit  160 , iteration control  250 ). If another iteration is to be made, a second time-varying channel response may be generated at  340  (e.g., by channel equalization unit  160 , unit  230 ) based at least in part on the second estimated signal, and, at  350 , a third estimated signal may be generated (e.g., by channel equalization unit  160 , unit  240 , unit  245 ) based at least in part on the second time-varying channel response. 
     Some implementations may not perform some of the operations depicted in  FIG. 3  or described herein. For example, in some implementations, the determination at  360  of whether to loop back into the process is not performed (i.e., single iteration systems). 
       FIGS. 4A-4E  show various exemplary implementations of the described systems and techniques. Referring now to  FIG. 4A , the described systems and techniques (e.g., associated with receiver  100 ) can be implemented in a high definition television (HDTV)  420 . The described systems and techniques may be implemented in either or both signal processing and/or control circuits, which are generally identified in  FIG. 4A  at  422 , a WLAN (wireless local area network) interface  429  and/or mass data storage  427  of the HDTV  420 . The HDTV  420  receives HDTV input signals in either a wired or wireless format and generates HDTV output signals for a display  426 . In some implementations, signal processing circuit and/or control circuit  422  and/or other circuits (not shown) of the HDTV  420  may process data, perform coding and/or encryption, perform calculations, format data and/or perform any other type of HDTV processing that may be required. 
     The HDTV  420  may communicate with mass data storage  427  that stores data in a nonvolatile manner such as optical and/or magnetic storage devices. The mass data storage  427  may be a hard disk drive (HDD), such as a mini HDD that includes one or more platters having a diameter that is smaller than approximately 1.8″. The HDTV  420  may be connected to memory  428  such as random access memory (RAM), read only memory (ROM), low latency nonvolatile memory such as flash memory and/or other suitable electronic data storage. The HDTV  420  also may support connections with a WLAN via a WLAN network interface  429 . 
     Referring now to  FIG. 4B , the described systems and techniques may be implemented in a control system of a vehicle  430 , a WLAN interface  448  and/or mass data storage  446  of the vehicle control system. In some implementations, the described systems and techniques are implemented in a powertrain control system  432  that receives inputs from one or more sensors such as temperature sensors, pressure sensors, rotational sensors, airflow sensors and/or any other suitable sensors and/or that generates one or more output control signals such as engine operating parameters, transmission operating parameters, and/or other control signals. 
     The described systems and techniques may also be implemented in other control systems  440  of the vehicle  430 . The control system  440  may likewise receive signals from input sensors  442  and/or output control signals to one or more output devices  444 . In some implementations, the control system  440  may be part of an anti-lock braking system (ABS), a navigation system, a telematics system, a vehicle telematics system, a lane departure system, an adaptive cruise control system, a vehicle entertainment system such as a stereo, digital versatile disc (DVD), compact disc and the like. Still other implementations are contemplated. 
     The powertrain control system  432  may communicate with mass data storage  446  that stores data in a nonvolatile manner. The mass data storage  446  may include optical and/or magnetic storage devices for example hard disk drives HDD and/or DVDs. The HDD may be a mini HDD that includes one or more platters having a diameter that is smaller than approximately 1.8″. The powertrain control system  432  may be connected to memory  447  such as RAM, ROM, low latency nonvolatile memory such as flash memory and/or other suitable electronic data storage. The powertrain control system  432  also may support connections with a WLAN via a WLAN network interface  448 . The control system  440  may also include mass data storage, memory and/or a WLAN interface (all not shown). 
     Referring now to  FIG. 4C , the described systems and techniques can be implemented in a cellular phone  450  that may include a cellular antenna  451 . The described systems and techniques may be implemented in either or both signal processing and/or control circuits, which are generally identified in  FIG. 4C  at  452 , a WLAN interface  468  and/or mass data storage  464  of the cellular phone  450 . In some implementations, the cellular phone  450  includes a microphone  456 , an audio output  458  such as a speaker and/or audio output jack, a display  460  and/or an input device  462  such as a keypad, pointing device, voice actuation and/or other input device. The signal processing and/or control circuits  452  and/or other circuits (not shown) in the cellular phone  450  may process data, perform coding and/or encryption, perform calculations, format data and/or perform other cellular phone functions. 
     The cellular phone  450  may communicate with mass data storage  464  that stores data in a nonvolatile manner such as optical and/or magnetic storage devices for example hard disk drives HDD and/or DVDs. The HDD may be a mini HDD that includes one or more platters having a diameter that is smaller than approximately 1.8″. The cellular phone  450  may be connected to memory  466  such as RAM, ROM, low latency nonvolatile memory such as flash memory and/or other suitable electronic data storage. The cellular phone  450  also may support connections with a WLAN via a WLAN network interface  468 . 
     Referring now to  FIG. 4D , the described systems and techniques can be implemented in a set top box  480 . The described systems and techniques may be implemented in either or both signal processing and/or control circuits, which are generally identified in  FIG. 4D  at  484 , a WLAN interface  496  and/or mass data storage  490  of the set top box  480 . The set top box  480  receives signals from a source  482  such as a broadband source and outputs standard and/or high definition audio/video signals suitable for a display  488  such as a television and/or monitor and/or other video and/or audio output devices. The signal processing and/or control circuits  484  and/or other circuits (not shown) of the set top box  480  may process data, perform coding and/or encryption, perform calculations, format data and/or perform any other set top box function. 
     The set top box  480  may communicate with mass data storage  490  that stores data in a nonvolatile manner. The mass data storage  490  may include optical and/or magnetic storage devices for example hard disk drives HDD and/or DVDs. The HDD may be a mini HDD that includes one or more platters having a diameter that is smaller than approximately 1.8″. The set top box  480  may be connected to memory  494  such as RAM, ROM, low latency nonvolatile memory such as flash memory and/or other suitable electronic data storage. The set top box  480  also may support connections with a WLAN via a WLAN network interface  496 . 
     Referring now to  FIG. 4E , the described systems and techniques can be implemented in a media player  400 . The described systems and techniques may be implemented in either or both signal processing and/or control circuits, which are generally identified in  FIG. 4E  at  404 , a WLAN interface  416  and/or mass data storage  410  of the media player  400 . In some implementations, the media player  400  includes a display  407  and/or a user input  408  such as a keypad, touchpad and the like. In some implementations, the media player  400  may employ a graphical user interface (GUI) that typically employs menus, drop down menus, icons and/or a point-and-click interface via the display  407  and/or user input  408 . The media player  400  further includes an audio output  409  such as a speaker and/or audio output jack. The signal processing and/or control circuits  404  and/or other circuits (not shown) of the media player  400  may process data, perform coding and/or encryption, perform calculations, format data and/or perform any other media player function. 
     The media player  400  may communicate with mass data storage  410  that stores data such as compressed audio and/or video content in a nonvolatile manner. In some implementations, the compressed audio files include files that are compliant with MP3 (Moving Picture experts group audio layer  4 ) format or other suitable compressed audio and/or video formats. The mass data storage may include optical and/or magnetic storage devices for example hard disk drives HDD and/or DVDs. The HDD may be a mini HDD that includes one or more platters having a diameter that is smaller than approximately 1.8″. The media player  400  may be connected to memory  414  such as RAM, ROM, low latency nonvolatile memory such as flash memory and/or other suitable electronic data storage. The media player  400  also may support connections with a WLAN via a WLAN network interface  416 . Still other implementations in addition to those described above are contemplated. 
     A number of implementations have been described. Nevertheless, it will be understood that various modifications can be made without departing from the spirit and scope of the disclosure. For example, one or more of the receivers described above can be embodied in a number of different ways. A receiver may be embodied as part of an integrated circuit on a single piece of silicon, where one or many circuits can be formed on a single silicon substrate, and other digital components used for the communication can also be formed on the substrate. In addition, however, a receiver can be embodied as discrete components, e.g., defined using hardware definition language, or by a suitably programmed digital signal processor, or in software executed by a general purpose processor. The processor can be configured to simulate the results of the receiver, e.g., as part of a simulation program such as MATLAB™. 
     In addition, other modifications are possible. For example, it should be understood that the described systems and techniques can analogously be used for other kinds of channel equalization. Moreover, while portions of the implementations have been described as being done in the digital domain, it should be understood that these portions could also be implemented in the analog domain. Also, various operations depicted in a flowchart or other figure can be skipped or performed out of order and still provide desirable results. Accordingly, all such modifications and other implementations are within the scope of the following claims.