# Patent

## Title
Adaptive frequency equalizer

## Abstract

An adaptive frequency equalization system providing an equalizer that has programmable taps that adjusts magnitude and phase of symbol information of a received signal and that provides equalized symbol information. The system includes a hard decision circuit that selects ideal symbol values using the equalized symbol information. A frequency response circuit determines frequency response update values using the ideal symbol values and the received signal. An adjust circuit updates stored frequency response information using the frequency response update values, and also updates the programmable taps of the equalizer using the stored frequency response information.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation of U.S. patent application Ser. No. 10/886,025 filed on Jul. 8, 2004, which is incorporated by reference in its entirety and which claims priority to Provisional Application No. 60/485,159 filed on Jul. 8, 2003 and entitled “Adaptive Frequency Equalizer.”


FIELD OF THE INVENTION
The present invention relates to wireless communications, and more particularly to an adaptive frequency equalizer for wireless communications to improve channel estimate determination.
DESCRIPTION OF RELATED ART
The typical environment in which Wireless Local Area Networks (WLANs) and the like are deployed is very noisy and not optimal for wireless communications. For example, most homes and work places include many electronic devices resulting in an electronically noisy environment that may interfere with communications, such as microwave ovens, garage door openers, radios, television sets, computer systems, etc. The communication medium between wireless devices may change constantly. Most environments include multiple reflective surfaces and corners, creating multipath noise. Also, movement of items or devices or the like, such as hands, bodies, jewelry, mouse pointers, etc. or activation of electronic devices, such as cooling fans or the like, affects the overall wireless communication path and potentially degrades wireless communication performance.
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 802.11 standard is a family of standards for wireless local area networks (WLAN) in the unlicensed 2.4 and 5 Gigahertz (GHz) bands. A radio configured in accordance with IEEE 802.11a or 802.11g standards employs Orthogonal Frequency Division Multiplexing (OFDM) modulation in which a stream of data is transmitted over multiple small frequency sub-channels. In the OFDM configuration, multiple sub-carrier signals are incorporated within each OFDM symbol. Data is incorporated on each data tone using a selected modulation scheme, such as Binary Phase Shift Keying (BPSK), Quadrature PSK (QPSK), 16 Quadrature Amplitude Modulation (QAM), and/or 64 QAM. Each of the modulation schemes employs a corresponding constellation map with variable constellation points corresponding to a corresponding variable number of bits for achieving the various data rates. For example, BPSK is used for 6 or 9 Mbps, QPSK is used for 12 or 18 Mbps, 16 QAM is used for 24 or 36 Mbps, and 64 QAM is used for 48 or 54 Mbps. The encoding process employs a quadrature generation technique and provides in phase (I) and quadrature (Q) signals on respective I and Q channels.
Commonly, a short training period is included at the start of each transmission, including Short Syncs and two Long Syncs (LS) appended at the front end of each transmitted frame. The Long Syncs provide a reference amplitude and phase for each of the active sub-channels. The Long Syncs may be averaged together to reduce the noise in the received reference values. After the Long Syncs have been received, each sub-channel received symbol is multiplied by the inverse of the reference amplitude and the conjugate of the reference phase (when expressed as a complex unit vector) for that sub-channel. This removes most of the amplitude and phase distortion that has occurred between the transmitter and the receiver.
Optimum soft-decisions should be Signal-to-Noise Ratio (SNR) weighted. The Long Syncs have been used to generate LLR (log likelihood ratio) weights to correctly weight soft-decisions going into an error-correcting decoder, such as a Viterbi decoder or the like. Given a flat noise floor, the use of LLR weights translates into a signal-power weighting. These LLR weights have been the signal power determined in each sub-channel of the Long Syncs. Using the LLR weights improves soft-decisions and reduces transmission errors.
A first problem is that the received reference values are usually degraded by noise, which is an unavoidable consequence of radio transmission. The reference information provided during the training phase (e.g., in the Long Syncs) is known by the receiver, so that a significant amount of this noise can be determined. A second problem, however, is that the signal amplitude and phase distortion may change over time, from the start of transmission of each frame to the end of the frame, making the initial channel estimate information obsolete and inaccurate towards the end of each frame. Both of these problems increase the probability of error when receiving a frame, due to both signal equalization errors and soft-decision weighting errors.
Legacy radios were designed with several assumptions. The channel was assumed to be relatively stable. The frames were bursty in nature and relatively short, so that it was assumed that the wireless channel did not significantly change over the duration of each frame. The initial channel estimate information determined at the start of each frame was assumed to be sufficiently accurate for that frame. Presently, however, there is a greater emphasis on mobility and/or accuracy. Mobility results in a changing environment that could result in significant changes in the channel during each frame. Even in a stable environment, improved accuracy can improve transmission speed and enable a higher transmission rate with a lower packet error rate (PER). It is desired to improve channel estimation to enable mobile application and/or higher transmission rates.



BRIEF DESCRIPTION OF THE DRAWINGS
The benefits, features, and advantages of the present invention will become better understood with regard to the following description, and accompanying drawings in which:
FIG. 1 is a block diagram of an exemplary adaptive frequency equalizer configured in accordance with an embodiment of the present invention;
FIG. 2 is a graph diagram of a constellation map according to 64 QAM;
FIG. 3 is a block diagram of an LMS-structured adaptive frequency equalizer; and
FIG. 4 is a chart of simulated PER performance comparing a legacy equalizer with an adaptive frequency equalizer using adaptive LLR weighting according to embodiments of the present invention.



DETAILED DESCRIPTION THE INVENTION
The following description is presented to enable one of ordinary skill in the art to make and use the present invention as provided within the context of a particular application and its requirements. Various modifications to the preferred embodiment will, however, be apparent to one of ordinary skill in the art, and the general principles defined herein may be applied to other embodiments. Therefore, the present invention is not intended to be limited to the particular embodiments shown and described herein, but is to be accorded the widest scope consistent with the principles and novel features herein disclosed.
A system and method of adaptively updating equalizer values while a transmission is being received according to embodiments of the present invention provides improved channel estimation without modifications to the signal format. Accurate reference values are obtained and updated throughout the duration of each transmission. The noise level in the reference values is also reduced. The improved reference values reduce the number of errors in the received transmission. Existing circuits employed during the initial Long Sync calculations are further used to update the reference values, thereby reducing additional hardware.
The LMS weight factors are also adaptively updated and employed in the soft-decision process throughout the duration of each transmitted frame. Adaptive soft-decision weighting is particular advantageous when signal distortion varies during each transmission, which is common in real-world environments and situations. Mobile wireless communications, for example, are significantly improved.
FIG. 1 is a block diagram of an exemplary adaptive frequency equalizer 100 configured in accordance with an embodiment of the present invention. A radio frequency (RF) signal incorporating a transmitted frame is received by way of antenna 102 and is processed through a radio 101, which converts the RF frame signal into a received baseband signal RS. The received OFDM signal is provided to one input of a multiplier 103, which receives a carrier offset frequency at its other input. The multiplier 103 removes any residual nominal carrier offset frequency in the RS signal. Although only one multiplier is shown, the carrier offset frequency is a phase rotation that is applied equally across a vector of all sub-channels. The output of the multiplier 103 is a preequalization signal vector FEQINPUT, which is provided to an input of an equalizer 105 having multiple taps programmed by a vector of sub-channel reference values (1/FREQRESP). The equalizer 105 is a frequency domain equalizer (FEQ) as known to those of ordinary skill in the art with programmable complex taps. The taps are programmed with real or complex tap coefficients. The equalizer 105 is shown as a multiplier symbol, which represents multiple complex multiplier taps, one for each subchannel of the OFDM symbol. Initially, the 1/FREQRESP reference values are derived from the Long Sync training periods. As described further below, the 1/FREQRESP reference values are further adapted or otherwise updated throughout the duration of the received frame. The output of the equalizer 105 is a post-equalization signal vector FEQOUTPUT, which incorporates received sub-channel symbols that should be near replicas of the transmitted symbols after equalization.
The FEQOUTPUT signal vector is then demodulated using standard techniques. As shown, for example, the FEQOUTPUT signal vector is provided to a soft decision block 107, which generates soft decision information (SD) provided to a decoder 109, such as a Viterbi decoder or the like. The decoder 109 outputs a data signal (DS) comprising the transmitted information. The soft decision block 107 employs LLR weights to determine the SD information, where the LLR weights are initially derived from the Long Sync training periods. As described below, the LLR weights are further adapted or otherwise updated throughout the duration of the received frame.
The functions used to adaptively update the 1/FREQRESP reference values are shown just under the main signal path. The two input signal vectors, including the pre-equalization signal vector FEQINPUT and the post-equalization signal vector FEQOUTPUT are used for adaptation. The FEQOUTPUT signal vector is provided to a hard decision (HD) block 111, which outputs ideal HD values for each subchannel of each OFDM symbol. The ideal HD values are also referred to as the IDEAL(FEQOUTPUT) values. The HD block 111 determines the nearest ideal symbol value represented by the FEQOUTPUT signal vector, which is a complex number, and outputs corresponding ideal symbol values. In the embodiment shown, the HD values are each 6 bits for 65 QAM including a 3-bit real value and a 3-bit imaginary value. FIG. 2 is a graph diagram of a constellation map 200 according to 64 QAM. Since each constellation point has a real or imaginary value of 1, 3, 5 or 7 (4 values total), only three signed bits are needed for the real and imaginary values. Any binary numeric representation scheme may be employed (e.g., 2's complement) as known to those of ordinary skill in the art. In one embodiment, the HD block 111 makes the hard decision determinations by determining which constellation point sub-sector in which each FEQOUTPUT signal vector value falls. For example, a FEQOUTPUT signal vector value falling within a sub-sector 201 of the constellation map 200 is assigned the ideal complex value 5-j3 as being the closest constellation point. The HD values are provided to a conjugate block 113, which outputs the conjugate of each HD value to one input of a multiplier 115, having another input receiving the FEQINPUT signal vector. The multiplier 115 combines the HD value conjugate with the FEQINPUT signal vector and provides the result to an input of another multiplier 117, which receives a SCALE value at its other input. The multiplier 117 multiplies the output of multiplier 115 with the SCALE value and provides the result to one input of an adder 119, which receives the output of another multiplier 121 at its input. The adder 119 adds the outputs of the multipliers 117 and 121 together and provides FREQRESP adjust values to the input of a FREQRESP block 125. Each FREQRESP adjust value is added to a corresponding FREQRESP reference value stored in the FREQRESP block 125 to generate a new and updated FREQRESP reference value. In this manner, an accumulative process is used to adaptively update the FREQRESP reference values throughout the duration of each frame.
The FREQRESP reference values from the FREQRESP block 125 are provided to one input of a multiplier 121, which receives corresponding values from a block 123. The HD values from HD block 111 are provided to the input of block 123, which calculates a value (1−IDEAL(FEQOUTPUT)−*CONJ(IDEAL(FEQOUTPUT))*SCALE), or 1−SCALE*|HD|2 for each HD input (where CONJ is the conjugate operation), and where each output is a real value. An output of block 123 is provided to the other input of multiplier 121, which multiplies together corresponding values from blocks 123 and 125 and provides the result to the other input of the adder 119. In the embodiment shown, SCALE is a real value (not complex) that controls how fast the target FREQRESP responds to changes in a value FREQRESPESTIMATE. SCALE may be a static value or it may be varied over time to optimize performance. SCALE is typically between 1 and 0, and can be a negative power of 2 (e.g., 1/32, 1/64, etc.), which simplifies the multiplication into a bit shift. In one embodiment, the multiplier 117 is a shift register that reduces the digital output of multiplier 115 by shifting one or more times.
Since the ideal HD values are known, once SCALE is selected, the full set of values stored in block 123 may be determined. For 64 QAM, block 123 stores 64 values, each corresponding to a constellation point shown in the constellation map 200. 16 QAM uses the inner 4×4 matrix, and QPSK uses the inner 2×2 matrix. BPSK uses +/−1+j0 only. Pilot tones may be treated as BPSK or as 1+j0 if scrambling has been removed. The block 123 may be implemented in hardware as a lookup table (LUT) in which each HD value from HD block 111 operates as an address to access the corresponding value output from the lookup table. If SCALE is predetermined and static, the lookup table may be hardwired or otherwise stored with permanent values. If SCALE is programmable or otherwise varied during operation, then the lookup table may be programmed once SCALE is determined. Once the values for 64 QAM are determined and stored, the 16 QAM and QPSK values are also determined as subsets, and BPSK is only two values +1 or −1. Thus, the particular data rate does not have to be known before-hand.
A block 131 represents the logic and/or circuitry used to generate initial FREQRESP reference values determined from the Long Sync training periods of the frame. The initial FREQRESP reference values are stored into the FREQRESP block 125, and inverted by an inverter block (INVERT) 127 to generate initial 1/FREQRESP reference values used to initially program the equalizer 105. As each subsequent OFDM symbol is processed, the FREQRESP reference values stored in the FREQRESP block 125 are adaptively updated by the values output from the adder 119. The updated FREQRESP reference values are inverted by inverter block 127 providing updated 1/FREQRESP reference values, which are used to update the equalizer 105. In this manner, the initial channel estimate programmed into the equalizer 105 as determined by the Long Sync training periods is continuously updated throughout the duration of each frame. In this manner, the channel estimate becomes more accurate for a relatively stable channel or adapts to changes in the channel.
A dashed line 133 identifies the additional hardware to perform the adaptive process. The inversion process is already used in legacy systems to convert the Long Syncs into the 1/FREQRESP equalizer values, so that the hardware used to implement the inverter 119 is reused. Similar hardware previously used to store the initial 1/FREQRESP reference values is used to implement the FREQRESP block 125 to store the initial and adaptively updated FREQRESP reference values. The filtering process performed by the adaptive frequency equalizer 100 occurs before inversion, which provides improved noise reduction. The FREQRESP reference values tend to be significantly smaller values than the 1/FREQRESP reference values, where the averaging of larger numbers tends to increase noise and decrease accuracy. Therefore, the use of FREQRESP values results in maximum performance.
The updated FREQRESP reference values from the FREQRESP block 125 are provided to a power calculation block 129, which generates the LLR weights used by the soft decision block 107. In legacy systems, the LLR weights calculated from the Long Syncs were used throughout the remaining portion of the frame. Since the FREQRESP reference values are adaptively updated, the LLR weights are also adaptively updated to improve the soft decision process. LLR weight adaptation is beneficial in real-world situations in which signal distortion varies during any particular transmission.
The adaptation process calculates new FREQRESP reference value estimates by estimating what the values should have been to convert the FEQINPUT value into an ideal FEQOUTPUT value as illustrated by the following equation 1:

1/FREQRESPESTIMATE=IDEAL(FEQOUTPUT)/FEQINPUT  (1)

where IDEAL(FEQOUTPUT) signifies the ideal symbol value nearest to FEQOUTPUT, and all values are complex. Equation 1 simplifies to following equation 2:

FREQRESPESTIMATE=FEQINPUT/IDEAL(FEQOUTPUT)  (2)

Then the FREQRESPESTIMATE is filtered into the current FREQRESP reference values using a filter coefficient that is weighted by the ideal FEQOUTPUT power. The weighting places more emphasis on estimates calculated from higher-powered symbols, which provides better accuracy than un-weighted estimates. The weighted filtering is described according to the following equation 3:

FREQRESP=FREQRESP+(FREQRESPESTIMATE31 FREQRESP)*SCALE*(IDEAL(FEQOUTPUT)*CONJG(IDEAL(FEQOUTPUT))  (3)

using SCALE as previously described. SCALE may be varied over time to optimize performance.
Equation 3 can be simplified for hardware by substituting for FREQRESPESTIMATE and recognizing that the inverse of a complex number “c” is 1/c=CONJ(c)/(c*CONJ(c)). First, substitute as illustrated by the following equation 4:

FREQRESP=FREQRESP+(FEQOUTPUT/IDEAL(FEQOUTPUT)−FREQRESP)*SCALE*(IDEAL(FEQOUTPUT)*CONJ(IDEAL(FEQOUTPUT))  (4)

Then substitute for 1/IDEAL(FEQOUTPUT) as shown by the following equation 5:

FREQRESP=FREQRESP+(FEQINPUT*CONJ(IDEAL(FEQOUTPUT))/(IDEAL(FEQOUTPUT)*CONJ(IDEAL(FEQOUTPUT)))−FREQRESP)*SCALE*(IDEAL(FEQOUTPUT)*CONJ(IDEAL(FEQOUTPUT))  (5)

Finally, simplify as illustrated by the following equation 6:

FREQRESP=FREQRESP+(FEQINPUT*CONJ(IDEAL(FEQOUTPUT))*SCALE−FREQRESP*IDEAL(FEQOUTPUT)*CONJ(IDEAL(FEQOUTPUT))*SCALE  (6)

And as illustrated by the following equation (7):

FREQRESP=FREQRESP*(1−IDEAL(FEQOUTPUT)*CONJ(IDEAL(FEQOUTPUT))*SCALE)+(FEQINPUT*CONJ(IDEAL(FEQOUTPUT))*SCALE

It is appreciated that division has been eliminated. Also, the component “1−(IDEAL(FEQOUTPUT)*CONJ(IDEAL(FEQOUTPUT))” has relatively few values, since IDEAL(FEQOUTPUT) takes on only the few ideal symbol values. This makes it amenable to implementation as a lookup table as previously described, which reduces hardware implementation complexity.
An advantage of the present invention is that additional signal information, other than the Long Sync training periods, is used to update the 1/FREQRESP equalizer values. This results in more accurate values, and fewer transmission errors. If the signal distortion is changing, the continuously updated equalizer values can track the signal changes, providing appropriate and up-to-date equalizer values throughout the transmission duration. This can reduce transmission errors, particularly when long transmissions are used.
FIG. 3 is a block diagram of a Least Means Squared (LMS)-structured adaptive frequency equalizer 300. The primary signal path from the radio 101 to the decoder 109 is substantially the same, where the same reference numbers are used for similar components. FEQOUTPUT is provided to the HD block 111 as before, which outputs the HD values. In this case, the FEQOUTPUT is subtracted from the HD values by an adder 301, and the result is multiplied by the conjugate of FEQOUTPUT by a multiplier 303. FEQOUTPUT is provided to a conjugate block 304, which provides CONJ(FEQINPUT) to the multiplier 303. The output of multiplier 303 is multiplied by SCALE at a multiplier 305, and the result is added to current 1/FREQRESP values stored in a 1/FREQRESP block 309. The updated result is stored back in the /FREQRESP block 309 to adaptively update the 1/FREQRESP reference values. The 1/FREQRESP reference values are provided to an inverter 311, which provides corresponding FREQRESP values to a power calculation block 313 to generate the LLR weights used in the soft decision operation. Since the 1/FREQRESP reference values are adaptively updated, the LLR weights may also be adaptively updated to improve transmission.
The adaptive frequency equalizer 100 has at least two performance advantages over the LMS-structured adaptive frequency equalizer 300. The filtering of the LMS adaptive frequency equalizer 300 may be expressed according to the following equation 8:

1/FREQRESP=(1/FREQRESP)*(1−FEQINPUT*CONJ(FEQINPUT)*SCALE)+(IDEAL(FEQOUTPUT)*CONJ(FEQINPUT)*SCALE  (8)

whereas the filtering of the equalizer 100 is expressed in equation 7, repeated as follows:

FREQRESP=FREQRESP*(1−IDEAL(FEQOUTPUT)*CONJ(IDEAL(FEQOUTPUT))*SCALE)+(FEQINPUT*CONJ(IDEAL(FEQOUTPUT))*SCALE  (7)

A major difference has been highlighted in bold type. LMS filtering is weighted by noisy FEQINPUT powers. The filtering employed by the adaptive frequency equalizer 100 is weighted by the noise-free IDEAL(FEQOUTPUT) powers. This difference results in lower noise in the reference estimates when compared to LMS estimates, and translates into reduced transmission errors.
Second, the LMS structure can be seen to be averaging values of IDEAL(FEQOUTPUT)/FEQINPUT. At small values of FEQINPUT, due to added noise, the value of this ratio may vary widely, with large numbers that may dominate when averaged with near-normal values. There is also the possibility of a divide-by-zero problem. The adaptive frequency equalizer 100 averages values of FEQINPUT/IDEAL(FEQOUTPUT). If noise brings FEQINPUT close to zero value, the value of this ratio will be close to zero. Its importance diminishes when averaged with near-normal values. The resulting average then inverts nicely into a value with less noise than the LMS method, which correspondingly reduces transmission errors.
FIG. 4 is a chart of simulated Packet Error Rate (PER) performance comparing legacy equalizer and LLR weighting configurations with adaptive equalizer and adaptive LLR weighting according to embodiments of the present invention. The chart shows simulation results comparing non-adaptive equalization according to prior art, adaptive equalization using the adaptive frequency equalizer 100 both with and without LLR weight adaptation, and the LMS adaptive frequency equalizer 300. All plots are at a data rate of 54 megabits per second (Mbps). A first plot 401 with star-shaped points illustrates the non-adaptive legacy approach. The second plot 403 with open square points illustrates the legacy case with the addition of adaptive LLR weights. The third plot 405 with triangle points illustrates the LMS adaptive equalizer approach without LLR weight adaptation. The fourth plot 407 with closed square points illustrates the approach employed by the adaptive frequency equalizer 100 without LLR weight adaptation. The fifth plot 409 with diamond points illustrates the approach employed by the adaptive frequency equalizer 100 using LLR weight adaptation.
For the same 10% PER, the prior art implementation required an energy per bit (Eb) over one-sided Noise spectral density (No) ratio (Eb/No) of about 23.6 decibels (dB). The adaptive frequency equalizer 100 required an Eb/No of only 21.7 dB as shown by plot 409 (including LLR weight adaptation), which provides an improvement in performance of 1.9 dB. The LMS adaptive frequency equalizer 300 required an Eb/No of 22.7 dB as shown by plot 405, just about splitting the difference between the other two implementations. Two additional simulations were performed, including plot 403 in which only the LLR weights used in the soft-decisions (“adapt LLR only”) were updated, which showed no improvement in this particular simulation. The other plot 407 in which only the equalizer values (“adapt FEQ only”) were updated using the adaptive frequency equalizer 100 without LLR weight adaptation, which achieved nearly all of the improvement of the full implementation (FEQ and LLR adaptation). The simulations appear to show that performance is not too sensitive to the LLR soft-decision weightings. The illustrated simulations, however, did not vary the signal distortion during a single transmission. Such signal distortion variations, which occurs in real-world environments, places more importance on the soft-decision weights. In this manner, the LLR adaptation improves performance.
Although a system and method according to the present invention has been described in connection with various embodiments, it is not intended to be limited to the specific form set forth herein, but on the contrary, it is intended to cover such alternatives, modifications, and equivalents, as can be reasonably included within the spirit and scope of the invention.

## Claims

1. An adaptive frequency equalization system, comprising:
an equalizer with programmable taps configured to adjust magnitude and phase of symbol information of a received signal and to provide equalized symbol information, wherein soft decision information is generated based at least on the equalized symbol information and log likelihood ratio (LLP) weights;
a hard decision circuit configured to select ideal symbol values using said equalized symbol information;
a frequency response circuit configured to determine frequency response update values based on at least said ideal symbol values; and
an adjust circuit configured to update stored frequency response information using said frequency response update values, and to update said programmable taps of said equalizer using said stored frequency response information.

2. A method comprising:
receiving, via an antenna, a signal including a frame;
converting the signal into a pre-equalization signal;
receiving the pre-equalization signal at an equalizer having multiple taps programmed by a vector of sub-channel reference values, wherein the vector of sub-channel reference values are initially derived from one or more long synch training periods, and are subsequently updated during the duration of the received frame;
outputting a post-equalization signal from the equalizer; and
demodulating the post-equalization signal,
wherein the vector of sub-channel reference values are updated based on the pre-equalization signal and the post-equalization signal, and
wherein demodulating the post-equalization signal includes generating soft decision information based at least on the post-equalization signal and log likelihood ratio (LLR) weights.

3. The method of claim 2, wherein converting the signal into a pre-equalization signal comprises converting the signal into a baseband signal and removing any residual carrier offset frequency from the baseband signal.

4. The method of claim 2, wherein the equalizer comprises a frequency domain equalizer.

5. The method of claim 2, wherein the LLR weights are initially derived from one or more long synch training periods, and are subsequently updated during the duration of the received frame.

6. The method of claim 2, further comprising receiving the post-equalization signal at a hard decision circuit and outputting ideal values for each sub-channel from the hard decision circuit.

7. The method of claim 6, wherein the hard decision circuit is configured to determine a nearest ideal symbol value represented by the post-equalization signal, and output the ideal symbol values based thereon.

8. The method of claim 6, further comprising receiving the ideal values for each sub-channel at a conjugate circuit and outputting one or more conjugates to a multiplier, wherein the multiplier is configured to also receive the pre-equalization signal.

9. The method of claim 8, further comprising:
combining, at the multiplier, the one or more conjugates and the pre-equalization signal;
outputting, from the multiplier, one or more results to a second multiplier which scales the one or more results; and
outputting, from the second multiplier, one or more scaled results to an adder which is coupled to a third multiplier and which is configured to add the one or more scaled results and the input from the third multiplier.

10. The method of claim 9, further comprising outputting one or more results from the adder to a frequency response unit which is configured to add the one or more results to corresponding values stored in the frequency response unit and thereby generate updated sub-channel reference values.

11. The method of claim 10, further comprising outputting the updated sub-channel reference values to the equalizer.

12. The method of claim 10, further comprising generating one or more log likelihood ratio (LLR) weights based on the updated sub-channel reference values.

13. The method of claim 10, wherein the third multiplier is configured to receive the updated sub-channel reference values from the frequency response unit and also receive a modified version of the ideal values output from the hard decision circuit.

14. The method of claim 13, wherein the modified version of the ideal values output from the hard decision circuit are determined by accessing a lookup table.

15. A system, comprising:
an antenna configured to receive a signal including a frame;
a radio in conjunction with a multiplier configured to convert the signal into a pre-equalization signal;
an equalizer configured to receive the pre-equalization signal, wherein the equalizer includes multiple taps programmed by a vector of sub-channel reference values, and wherein the vector of sub-channel reference values are initially derived from one or more long synch training periods and are subsequently updated during the duration of the received frame; and
a demodulator configured to demodulate a post-equalization signal output from the equalizer,
wherein the vector of sub-channel reference values are updated based on the pre-equalization signal and the post-equalization signal, and
wherein the demodulator is configured to generate soft decision information based at least on the post-equalization signal and log likelihood ratio (LLR) weights in order to demodulate the post-equalization signal output from the equalizer.

16. The system of claim 15, wherein the radio is configured to convert the signal into a baseband signal and the multiplier is configured to remove any residual carrier offset frequency from the baseband signal in order to convert the signal into a pre-equalization signal.

17. The system of claim 15, wherein the equalizer comprises a frequency domain equalizer.

18. The system of claim 15, wherein the LLR weights are initially derived from one or more long synch training periods, and are subsequently updated during the duration of the received frame.

19. The system of claim 15, further comprising a hard decision circuit configured to receive the post-equalization signal and output ideal values for each sub-channel.

20. The system of claim 19, wherein the hard decision circuit is further configured to determine a nearest ideal symbol value represented by the post-equalization signal and output the ideal symbol values based thereon.

21. The system of claim 19, further comprising a conjugate circuit configured to receive the ideal values for each sub-channel and output one or more conjugates to a multiplier, wherein the multiplier is configured to also receive the one or more conjugates and combine the one or more conjugates with the pre-equalization signal.

22. The system of claim 21, further comprising:
a second multiplier configured to receive one or more results from the multiplier and scale the one or more results; and
an adder configured to receive one or more scaled results from the second multiplier and add the one or more scaled results to an input from a third multiplier.

23. The system of claim 22, further comprising a frequency response unit configured to receive one or more results from the adder, and add the one or more results from the adder to corresponding values stored in the frequency response unit and thereby generate updated sub-channel reference values.

24. The system of claim 23, wherein the equalizer is configured to receive the updated sub-channel reference values.

25. The system of claim 23, wherein one or more log likelihood ratio (LLR) weights are generated based on the updated sub-channel reference values.

26. The system of claim 23, wherein the third multiplier is configured to receive the updated sub-channel reference values from the frequency response unit and also receive a modified version of the ideal values output from the hard decision circuit.

27. The system of claim 26, wherein the modified version of the ideal values output from the hard decision circuit are determined by accessing a lookup table.