Patent Publication Number: US-6700866-B1

Title: Methods and apparatus for use in obtaining frequency synchronization in an OFDM communication system

Description:
RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Application No. 60/140,552, filed Jun. 23, 1999 and entitled “An OFDM Pilot-Based Synchronization Procedure,” which is incorporated herein in its entirety. 
     This following applications, assigned to the Assignee of the current invention, and being filed concurrently, contain material related to the subject matter of this application, and are incorporated herein by reference: 
     by J. Heinonen et al., entitled “Methods and Apparatus for Use in Obtaining Frequency Synchronization in an OFDM Communication System,” Ser. No. 09/594,886, filed Jun. 14, 2000; 
     by J. Heinonen et al., entitled “Apparatus and Method for Synchronization in a Multiple Carrier Communication System by Observing a Plurality of Synchronization Indicators,” Ser. No. 09/593,215, filed Jun. 14, 2000; 
     by J. Heinonen et al., entitled “Apparatus and Method for Synchronization in a Multiple Carrier Communication System by Observing Energy Within a Guard Band,” Ser. No. 09/593,449, filed Jun. 14, 2000 now U.S. Pat. No. 6,389,087, and 
     by J. Heinonen et al., entitled “Apparatus and Method for Synchronization in a Multiple Carrier Communication System by Observing a Phase-Frequency Relationship of a Plurality of Pilot Signals,” Ser. 09/593,547, filed Jun. 14, 2000. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to the field of orthogonal frequency division multiplexing (OFDM) communication systems, and more particularly to the field of frequency synchronization in OFDM communication systems. 
     2. Description of the Related Art 
     Orthogonal frequency division multiplexing (OFDM) is a robust technique for efficiently transmitting data over a channel. This technique uses a plurality of sub-carrier frequencies (sub-carriers) within a channel bandwidth to transmit the data. These sub-carriers are arranged for optimal bandwidth efficiency compared to more conventional transmission approaches, such as frequency division multiplexing (FDM), which waste large portions of the channel bandwidth in order to separate and isolate the sub-carrier frequency spectra and thereby avoid inter-carrier interference (ICI). By contrast, although the frequency spectra of OFDM sub-carriers overlap significantly within the OFDM channel bandwidth, OFDM nonetheless allows resolution and recovery of the information that has been modulated onto each sub-carrier. Also, OFDM is much less susceptible to inter-symbol interference (ISI) from the use of a guard time between successive bursts. 
     Although OFDM exhibits several advantages, prior art implementations of OFDM also exhibit several difficulties and practical limitations. The most important difficulty with implementing OFDM transmission systems is that of achieving timing and frequency synchronization between the transmitter and the receiver. In order to properly receive an OFDM signal that has been transmitted across a channel and demodulate the symbols from the received signal, an OFDM receiver must determine the exact timing of the beginning of each symbol within a data frame. Prior art methods utilize a “cyclic prefix,” which is generally a repetition of part of a symbol acting to prevent inter-symbol interference (ISI) between consecutive symbols. If correct timing is not known in prior art receivers, the receiver will not be able to reliably remove the cyclic prefixes and correctly isolate individual symbols before computing the FFT of their samples. In this case, sequences of symbols demodulated from the OFDM signal will generally be incorrect, and the transmitted data bits will not be accurately recovered. 
     Equally important but perhaps more difficult than achieving proper symbol timing is the issue of determining and correcting for carrier frequency offset, the second major aspect of OFDM synchronization. Ideally, the receive carrier frequency, f.sub.cr, should exactly match the transmit carrier frequency, f.sub.ct. If this condition is not met, however, the mismatch contributes to a nonzero carrier frequency offset, DELTA.f.sub.c, in the received OFDM signal. OFDM signals are very susceptible to such carrier frequency offset which causes a loss of orthogonality between the OFDM sub-carriers and results in inter-carrier interference (ICI) and a severe increase in the bit error rate (BER) of the recovered data at the receiver. In general, prior art synchronization methods are computationally intensive. 
     Accordingly, there is an existing need to provide alternatives to synchronization in OFDM communication systems. More particularly, there is an existing need to provide alternatives to frequency synchronization that are less computationally intensive than the prior art. 
     SUMMARY OF THE INVENTION 
     Methods and apparatus for use in obtaining frequency synchronization in a multicarrier modulated system utilizing a frequency band of orthogonal narrowband carriers are described. The frequency synchronization described herein relates to the use of a coarse frequency correction process, a fine frequency correction process, and an overarching iterative process that makes use of both the coarse and fine frequency correction processes. 
     The iterative method involves the steps of performing a coarse frequency correction process which is operative to adjust receiver frequency so that a pilot tone signal is within a predetermined frequency range and, after performing the coarse frequency correction process, performing a fine frequency correction process which is operative to adjust receiver frequency so that the pilot tone signal is substantially aligned with a pilot tone reference within the predetermined frequency range. From performing the coarse frequency correction process, receiver frequency is adjusted so that the pilot tone signal is within the predetermined frequency range. However, the pilot tone signal may be outside a Nyquist sampling frequency range which undesirably causes an alias pilot tone signal to be within the Nyquist sampling frequency range. Assuming this condition, from performing the fine frequency correction process, receiver frequency is adjusted so that the alias pilot tone signal is substantially aligned with the pilot tone reference and the pilot tone signal is undesirably shifted outside the predetermined frequency range. 
     To eliminate any such result, the method further involves, after performing the coarse and the fine frequency correction processes, performing the coarse frequency correction process again and, after performing the coarse frequency correction process again, performing the fine frequency correction process again. From performing the coarse frequency correction process again, receiver frequency is adjusted so that the pilot tone signal is within both the predetermined frequency range and the Nyquist sampling frequency range. From performing the fine frequency correction process again, receiver frequency is adjusted so that the pilot tone signal is substantially aligned with the pilot tone reference. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is an illustrative representation of a wireless communication system, such as a fixed wireless system, utilizing OFDM communication methods. 
     FIG. 2 is a schematic block diagram of a receiver unit of the wireless communication system of FIG.  1 . 
     FIG. 3 is an illustrative representation of a set of pilot tones for use in the wireless communication system of FIG.  1 . 
     FIG. 4 is a flowchart describing a general method for use in obtaining synchronization in the wireless communication system of FIG.  1 . 
     FIG. 5 is an illustrative representation of a set of frequency bands utilized in the wireless communication system of FIG.  1 . 
     FIG. 6 is an illustrative representation of the set of frequency bands of FIG. 5, where frequency alignment ranges are defined for use in a coarse frequency correction process. 
     FIG. 7 is a block diagram representation of functional components for use in the coarse frequency correction process. 
     FIGS. 8A and 8B form a flowchart which describes a method for use in obtaining frequency synchronization and, more particularly, the coarse frequency correction process. 
     FIGS. 9 and 10 show an illustrative example of the application of the coarse frequency correction process where no frequency error exists. 
     FIGS. 11 and 12 show an illustrative example of the application of the coarse frequency correction process where frequency error does exist. 
     FIG. 13 is a flowchart describing a method for use in obtaining frequency synchronization and, more particularly, a fine frequency correction process. 
     FIG. 14 is a block diagram representation of functional components for use in the fine frequency correction process. 
     FIG. 15 is a graph showing an example of processing related to a summation function in the fine frequency correction process. 
     FIG. 16 is a schematic block diagram of a digital signal processing apparatus for use in frequency synchronization. 
     FIG. 17 is a flowchart describing a method for use in obtaining frequency synchronization, which preferably includes the coarse and the fine frequency correction processes described herein. 
     FIGS. 18A,  18 B,  18 C, and  18 D are illustrative graphs which describe an example of the method of FIG.  17 . 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 is an illustrative representation of a wireless communication system  100  which utilizes orthogonal frequency division multiplexing (OFDM) or OFDM-like communication methodologies. Wireless communication system  100  includes at least one base unit  106  having one or more antennas  108 , and a plurality of remote units  102  (“RUs” or “receiver units”), such as remote unit  104 . Base unit  106  and remote units  102  communicate via radio frequency (RF) signals, such as RF signals  110  between base unit  106  and remote unit  104 . Wireless communication system  100  can make use of a number of different communication techniques, such as frequency division multiplie access (FDMA), time division multiple access (TDMA), or time division duplex (TDD). Preferably, wireless communication system  100  is a fixed wireless system (FWS), where base unit  106  provides telephone and high-speed data communication to each one of a number of fixed-location subscribers equipped with an RU. 
     FIG. 2 is a schematic block diagram of receiver unit  104  of wireless communication system  100 . As shown, receiver unit  104  has electronic circuitry which includes diversity antennas  204  and  206  coupled to an airlink physical interface  202 , a field programmable gate array (FPGA)  208 , two Fast Fourier Transform (FFT) application-specific integrated circuits (ASICs)  210 , an airlink digital signal processor (DSP)  212 , a time generator FPGA  214 , an audio coder DSP  216 , a controller  220 , a telco interface  222 , and power supply circuitry  224 . Airlink physical interface  202  has a two-branch radio frequency (RF) receiver with two analog-to-digital (A/D) converters, and a single branch RF transmitter with a digital-to-analog (D/A) converter. FFT ASICs  210  and FPGA  208  provide a frequency-to-time/time-to-frequency domain translation engine for OFDM waveforms. Airlink DSP  212  performs airlink physical layer processing and audio coder DSP performs the OFDM vocoder functions. Time generation FPGA  214 . provides a serial time division multiplex (TDM) interface along with hardware support for RF control. Telco inteface  222  has a subscriber link interface circuit to provide an interface to a customer&#39;s telephone wiring. Controller  220  provides control for most of these devices, and power supply circuitry  224  provides electrical power for operation of the devices. Preferably, airlink and audio coder DSPs  212  and  216  utilize DSPs provided by Texas Instruments and controller  220  utilizes an MC68360 Quad Integrated Communications Controller (QUICC) CPU provided by Motorola, Inc. 
     Referring ahead to FIG. 4, a flowchart  400  describing a general stage (step  402 ), a receiver unit performs time slot acquisition (step  404 ). Following the time slot acquisition process, the receiver unit performs a frequency acquisition (step  406 ). The bulk of frequency and timing errors are eliminated in the “acquisition mode” of steps  404  and  406 . After some degree of time and frequency have been found, the receiver unit performs frequency tracking (step  408 ) and fine time acquisition (step  410 ). In the “tracking mode” of steps  408  and  410 , any residual errors are eliminated on a continual basis. Timeslot acquisition utilizes time samples, whereas the other processes operate in the frequency domain. The present invention described herein relates to obtaining frequency synchronization in the context described in relation to the flowchart of FIG. 4 (step  406 ). In addition to occurring at RU power up, the frequency acquisition process may occur upon a detected loss of lock. 
     A set of pilot tones, which may be referred to as RU Synchronization Pilots or RSPs, is utilized to achieve frequency synchronization. Referring back to FIG. 3, an illustrative representation of a set of pilot tones  300  transmitted from a base unit and intended for receipt by a receiver unit are shown. The set of pilot tones  300  includes a set of simulcast pilot tones  302  and a set of time-keyed pilot tones  306 . As shown in FIG. 3, the set of simulcast pilot tones  302  are separated in frequency into first and second subsets of simulcast pilot tones  302  and  304 . The set of time-keyed pilot tones  306  are positioned in frequency between the first and second subsets  302  and  304 . While the set of simulcast pilot tones  302  are broadcast every time slot, the set of time-keyed pilot tones are broadcast once every  1280  time slots ( 480  milliseconds). In the embodiment shown, there are eight pilot tones in the set of simulcast pilot tones  302  and nine pilot tones in the set of time-keyed pilot tones  306 . 
     FIG. 5 is an illustrative representation of a frequency band having a set of to merely as frequency bands. In this embodiment, each one of frequency bands  500  is reserved for the transmission of tones by a single base unit and for reception by a single receiver unit. The set of frequency bands  500  shown in FIG. 5 include a frequency band of interest  502 , a lower adjacent frequency band  504 , and an upper adjacent frequency band  506 . For clarity, only portions of the lower and upper adjacent frequency bands  504  and  506  are shown. Also, although the frequency bands are shown as having active pilot and traffic tones (indicated by upward-pointing arrows), this is only the case when communication is actually occurring between the base and receiver units. Traffic tones are tones which may bear user voice or data. 
     Pilot tones and traffic tones are communicated within each one of frequency bands  500 . Pilot tones are arranged in frequency as described in relation to FIG. 3, where the simulcast pilot tones are utilized for the frequency synchronization to be described. In FIG. 5, the pilot tones are represented by arrows that are solid and of the same height, while traffic tones (e.g., traffic tones  508 ) are represented by arrows that are dotted and of varying height. The amplitude and phase of pilot tones remain relatively constant over time, while the amplitude and phase of traffic tones vary over time. Adjacent pilot tones are separated by a frequency gap f g  that is different from a frequency gap f int  (i.e., a “guard band”) between adjacent frequency bands. For example, two adjacent pilot tones of lower adjacent frequency band  504  are separated by a frequency gap  510 , and lower adjacent frequency band  504  and frequency band of interest  502  are separated by a frequency gap  512 . As apparent, f g &gt;f int . 
     In the preferred embodiment, the entire frequency band of FIG. 5 is 5 MHz wide, where each frequency band has a bandwidth f band =1 MHz and each tone has a 3125 Hz bandwidth (one FFT tone bin width). The frequency gap f g  between adjacent pilot tones is 56.25 kHz (18 tone bins) and the frequency gap f int  between adjacent frequency bands is 46.875 kHz (15 tone bins). In addition, eighteen traffic tones (18 tone bins) are positioned in between adjacent pilot tones. 
     One objective in frequency synchronization is to eliminate sufficient error so that a frequency tracking mechanism (e.g., a phase-locked loop (PLL)) can lock a minimal amount of time. The frequency synchronization process described herein includes a coarse frequency synchronization process and a fine frequency synchronization process, executed in an iterative fashion. In the preferred coarse frequency synchronization process described, receiver frequency is corrected to within a predetermined frequency range corresponding to single tone bin. In the preferred fine frequency synchronization process described, receiver frequency is corrected so that a received pilot tone is substantially aligned with a predefined pilot tone reference within the predetermined frequency band. In the preferred embodiment, one FFT bin width is equal to 3125 Hz, the coarse frequency correction process is operative to reduce any error exceeding 3125 Hz (a single tone bin), and the fine frequency correction process is operative to reduce any residual error less than or equal to one-half of 3125 Hz (one-half of a tone bin). The present invention relates more particularly to the overarching process involving both the coarse and the fine frequency correction processes. 
     FIGS. 6-12 are drawings that relate to the coarse frequency synchronization process. FIG. 6 is, more particularly, an illustrative representation of the set of frequency bands  500  of FIG. 5, where “frequency alignment ranges” defined for use in the coarse frequency synchronization process are shown. A frequency alignment range  602  (also denoted by the letter A and T A ) corresponds to a lower edge of the frequency band of interest  502 . A frequency alignment range  604  (also denoted by the letter B and T B ) corresponds to an upper edge of the frequency band of interest  502 . Frequency alignment range  602  may be referred to as the lower frequency alignment range and frequency alignment range  604  may be referred to the upper frequency alignment range. Frequency alignment range  602  corresponds to a lower edge portion of the frequency band of interest  502 , an upper edge portion of lower adjacent frequency band  504 , and the guard band in between those portions. Similarly, frequency alignment range  604  covers an upper edge portion of the frequency band of interest  502 , a lower edge portion of upper adjacent frequency band  506 , and the guard band in between those portions. 
     Each frequency range of importance, such as frequency band of interest  502  and frequency alignment ranges  602  and  604 , is associated with a set of tone bins that stores tone values generated from received tones that are believed to be within that frequency range. For example, a primary set of tone bins or tone values in the DSP is assigned to what is believed to be frequency band of interest  502 , a first set of tone bins or tone values in the DSP is assigned to what is believed to be frequency alignment range  602 , and a second set of tone bins or tone values in the DSP is assigned to what is believed to be frequency alignment range  604 . As apparent, the tone bins assigned to frequency alignment ranges  602  and  604  overlap with the tone bins assigned to frequency band of interest  502 . Only when frequency is correctly synchronized does a set of tone bins assigned to a frequency range actually correspond to tone values from tones received within that frequency range. When frequency is not synchronized, the set of tone bins assigned to the frequency range does not store tone values corresponding to that frequency range, but rather a shifted set of tone bins stores those tone values. An important object of the coarse frequency correction process is to correctly align a set of tone bins with frequency band of interest  502 . 
     Being predefined and fixed during synchronization, frequency alignment ranges  602  and  604  of FIG. 6 are sized f A  and f B  to accommodate a maximum allowable frequency error. In the embodiment described, f A  and f B  are each the same size, 175 kHz, to tolerate a maximum error of 87.5 kHz. The centers of the frequency alignment ranges  602  and  604  are separated by spacing that is equal to the spacing between the outermost pilot tones selected for frequency synchronization. Where the selected pilot tones are positioned on the outermost edge of the frequency band of interest, as in the described embodiments, the centers of frequency alignment ranges  602  and  604  are separated by spacing that is equal to the bandwidth of the frequency band of interest, f band . Frequency alignment ranges  602  and  604  also have a pilot tone reference associated therewith. The location of the pilot tone reference is predefined within frequency alignment range  602  or  604 . In the embodiment described, the pilot tone reference location is in the center of a frequency alignment range. More particularly, a tone bin corresponding to a center of the frequency alignment range is assigned as the pilot tone reference location. 
     Reference will now be made to FIGS. 8A and 8B which are flowcharts that describe a method for use in obtaining frequency synchronization in an OFDM communication system. More particularly, FIGS. 8A and 8B describe a method for use in obtaining coarse frequency synchronization. The method is performed after time has been adjusted to place the OFDM waveform inside the appropriate processing interval. 
     Beginning at a start block  800  of FIG. 8A, a current set of tones associated with a first frequency range is received in a current time slot (step  802 ). The current set of tones received include those tones associated with a lower edge portion of a frequency band of interest, such as frequency alignment range  602  of FIG. 6. A set of current tone values is generated from the current set of tones and stored in a first set of tone bins (step  804 ). Next, complex conjugate multiplication is performed between a previous set of tone values and the current set of tone values from the first set of tone bins, to thereby compute a first set of tone values (step  806 ). The previous set of tone values are tone values that were generated from a set of tones received in a previous time slot for the first frequency range. By performing this process, tones associated with the first frequency range that vary in phase over time (i.e., traffic tones) are suppressed. 
     Continuing with the flowchart of FIG. 8A, processes similar to steps  802 - 806  are applied in steps  808 - 812  to an upper edge portion of the frequency band of interest, such as frequency alignment range  604  of FIG.  6 . These steps may be performed substantially at the same time as steps  802 - 806 . A current set of tones associated with a second frequency range is received in a current time slot (step  808 ). The current tones received include those tones associated with an upper edge portion of the frequency band of interest, such as frequency alignment range  604  of FIG. 6. A set of current tone values are generated from the current set of tones and stored in a second set of tone bins (step  810 ). Next, complex conjugate multiplication is performed between a previous set of tone values and the current set of tone values, to thereby compute a second set of tone values (step  812 ). The previous set of tone values are tone values that were generated from a set of tones received in a previous time slot for the second frequency range. By performing this process, tones of the second frequency range that vary in phase over time (i.e., traffic tones) are suppressed. The current sets of tone values then become the previous sets of tone values (step  814 ), and the method repeats starting again at step  802 . The results of the method (i.e., first and second sets of tone values associated with the first and second frequency ranges, respectively) are passed through a connector  816  to the flowchart of FIG.  8 B. 
     In the preferred embodiment, results from step  806  and results from step  812  of FIG. 8A are averaged over some predetermined time interval to generate the first and the second sets of tone values. Basically, the averaging is a filtering function. More particularly, the results from steps  806  and  812  are averaged over multiple time slots to mitigate the effects of fading. For example, the averaging may be performed over 50-100 time slots. Although many suitable techniques may be utilized, an equation below describes one way in which averaging may be performed 
     
       
           x   (k,i) =(α−1) y   (k,i)   *y   (k−1,i)   +αx   (k−1,i) , 
       
     
     where 
     X (k, i)  is a “smoothed” tone i magnitude squared at a time k; 
     x (k−1, i)  is a “smoothed” tone i magnitude squared at a time k−1; 
     y (k, i)  is a complex tone i at time k; 
     y (k−1, i)  is a complex tone i at time k−1; and 
     α is a “smoothing” constant (or “forgetting factor”) &lt;1. 
     Continuing with the method in FIG. 8B via connector  816 , complex conjugate multiplication between the first and the second sets of tone values is performed to generate a plurality of conjugated values (step  818 ). Mathematically, the cross correlation may be described by 
     
       
           Z   [A,B]   =T   A   T   B * 
       
     
     where T A  and T B  are tones (pilot and traffic tones) within the A and B intervals (see FIG.  6 ); and Z [A, B]  is an N-long array of multiplication products where N is the number of tone bins within each interval. 
     Next, the absolute value is taken for each of the conjugated values (step  820 ), i.e., the absolute value of each element of Z [A, B] . A maximum value from the results is identified (step  822 ). Receiver frequency is then adjusted based on a location of the maximum value relative to a predetermined pilot tone location (step  824 ). More particularly, the frequency adjustment in step  824  is based on a difference between the maximum value location and the predetermined pilot location. The receiver frequency is shifted by a difference in tone bin locations between the tone bin corresponding to the maximum value and the tone bin corresponding to the pilot tone reference. The method ends after step  824 , but could be repeated using next first and second sets of tone values (step  826 ). 
     Thus, a simple means of suppressing traffic tones is performed by applying the correlation on power spectra computed using phase-differentials of FFT outputs. By applying this process, magnitudes of traffic tones end up being small relative to the pilot tones in order to reduce false correlation peaks. Multiplying the current set of pilot tones with the complex conjugate of the previous slot&#39;s pilot tones eliminates time-constant phases in the pilot tones. Only phases that vary in time are left in the results. For the pilot tones, the time-varying phases are predominantly due to frequency error, which results in a constant phase difference from timeslot to timeslot. Traffic tones will experience varying phase difference between timeslots and average out to values small relative to those of the pilot tones. 
     Referring back to FIG. 7, a block diagram representation of functional components for use in obtaining frequency synchronization is shown. These functional components are associated with the coarse frequency correction process and the methods described in relation to FIGS. 8A and 8B. The functional components are shown organized in three sections: a functional block  702 , a functional block  704 , and a functional block  706 . Functional block  702  includes a complex conjugate multiplication function  710  (e.g., steps  802 - 812  of FIG. 8A) and an averaging function  716 . In the embodiment shown, complex conjugate multiplication function  710  includes a multiplication function, a delay function, and a conjugation function. Functional block  702  is operative so that complex conjugate multiplication is performed between received tone values from a current time slot at a line  708  and received tone values from a previous time slot. A set of conjugated values is output at a point  712 , and a number of these results are averaged by averaging function  716 . 
     Functional block  704  has a complex conjugation function  718  which operates so that complex conjugate multiplication is performed between a lower edge of the frequency band of interest (e.g., frequency alignment range  602  of FIG. 6) and an upper edge of the frequency band of interest (e.g., frequency alignment range  604  of FIG.  6 ). More particularly, complex conjugate multiplication is performed between tone values from a set of tone bins assigned to the lower frequency alignment range and tone values from a set of tone bins assigned to the upper frequency alignment range. Functional component block  706  includes a magnitude function  720 , which computes the absolute value of the output values of functional component block  704 . The output of magnitude function  720  is coupled to a peak locator function  722 , which identifies or locates the maximum value or peak from the output values of magnitude function  720 . An output  724  of peak locator function  722  is utilized to shift frequency according to the relative location of the identified peak. More specifically, receiver frequency will be shifted by a difference in tone bin locations between the tone bin corresponding to the maximum value and the tone bin corresponding to the pilot tone reference. 
     FIG. 9 is an illustrative representation of the sets of frequency bands and the frequency alignment ranges in a case where frequency error in excess of a single tone bin does not exist. As shown in FIG. 9, a pilot tone reference is located in a center of each one of the lower and upper frequency alignment ranges. FIG. 10 is associated with FIG.  9  and shows results of the complex conjugate multiplication between the lower and upper frequency alignment ranges. As shown in FIGS. 9 and 10, the pilot tone reference aligns with the outermost received pilot tone within the frequency band of interest. 
     FIG. 11 is an illustrative representation of the sets of frequency bands and the frequency alignment ranges in the case where frequency error in excess of a single tone bin does exist. FIG. 12 is associated with FIG.  11  and shows results of the complex conjugate multiplication between the lower and upper frequency alignment ranges. As shown in FIGS. 11 and 12, the pilot tone reference does not align with the outermost received pilot tones within the frequency band of interest. Frequency is shifted according to a relative location of the identified peak. That is, the tone bin assignment will shift by a difference in tone bin locations between the tone bin corresponding to the maximum value and the tone bin corresponding to the pilot tone reference. Thus, frequency error is reduced to within a single tone bin. 
     Thus, a coarse frequency synchronization process with several advantages has been described. Channel equalization and compensation processes are not required in the receiver for purposes of frequency synchronization. The method is simple in concept and in realization: it requires relatively few arithmetic calculations, which is an important consideration when using fixed-point DSPs. In a typical application of correlation, sidelobes due to the uniform spacing of embedded pilots lead to multiple peaks which can make identification of frequency error difficult, and this problem is exacerbated when the frequency band of interest has adjacent frequency bands. On the other hand, the method described herein is reliable because it results in a single peak. No template for correlation is required, nor is a priori information such as the spacing between pilot tones needed. 
     FIGS. 13-15 are drawings that relate to a fine frequency correction process. This fine frequency correction process may be referred to as a phase-differential frequency correction process. The fine frequency correction process is operative to adjust receiver frequency so that the pilot tone signal is substantially aligned with a pilot tone reference within the predetermined frequency range. More particularly, this method is capable of estimating a frequency error of less than or equal to one-half of an FFT tone bin. 
     Referring more particularly to FIG. 13, a flowchart describing a method for use in obtaining frequency synchronization in an OFDM communication is shown. This method makes use of all eight simulcast tones  302  described in relation to FIG.  3 . Beginning at a start block  1300  of FIG. 13, a current set of tones from a current time slot is received (step  1302 ). A current set of tone values is computed for the current set of tones (step  1304 ) and stored in a set of tone bins associated with the frequency band of interest (e.g., frequency band  502  of FIG.  5 ). Next, complex conjugation is performed between the current set of tone values and a previous set of tone values to generate a plurality of conjugated values (step  1306 ). The previous set of tone values are tone values that were computed from tones of the frequency band of interest received in a previous time slot. The current and the previous sets of tones received include the simulcast pilot tones (e.g., simulcast pilot tones  302  of FIG. 3) in the frequency band of interest for the current and the previous time slots. 
     The plurality of conjugated values from the complex conjugate multiplication is summed (step  1308 ) and an arctangent function on the sum is performed to compute a difference in phase between the current and the previous sets of tones (step  1310 ). A difference in frequency is then computed based on a quotient of the difference in phase over a difference in time between the time slots (step  1312 ). A frequency adjustment signal is then varied in accordance with the computed difference in frequency, and receiver frequency is adjusted in accordance with the frequency adjustment signal (step  1314 ). The method ends after step  1314 . Preferably, averaging is performed over a period of time using multiple values in step  1306  (on results of the complex conjugation, using new tone values as in step  1316 ) or using multiple values in step  1308  (on results of the summation). 
     FIG. 14 is an illustrative representation of functional components related to the method described in relation to FIG.  13 . Functional block  1404  includes a multiplication function, a delay function, and a conjugation function, which are functionally connected to perform the complex conjugate multiplication between a set of pilot tone values in the current time slot and the set of pilot tone values from the previous time slot. As shown in this embodiment, the eight simulcast pilot tones are input at line  1402  to functional block  1404  for such processing. The results from functional block  1404  are fed into a summation function  1408 , and the results from the summation are fed into an arctangent function  1410 . The frequency adjustment signal is provided at an output  1412  of arctangent function  1410 . Preferably, averaging is performed with an averaging function over a period of time using multiple values from functional block  1404  (on results of the complex conjugation) or using multiple values from functional block  1408  (on results of the summation). 
     A graph  1500  of FIG. 15 illustrates an example of processing related to summation function  1408  of FIG.  14 . Each vector of a plurality of vectors  1502  represents a vector sum of a single pilot tone (conjugated as described) with a running cumulative sum of other pilot tones (conjugated as described). The sum of the plurality of vectors  1502  results in a final vector  1504 , which represents the final vector summation. An angle  1506  of final vector  1504  is found by performing an arctangent function on final vector  1504 . Angle  1506  is the difference in phase between the sets of tones. The difference in frequency can be computed in a number of ways and is based on a quotient of the difference in phase over the difference in time between time slots of the received tones. 
     Alternatively, the method may involve performing an arctangent function on each one of the plurality of conjugated values, and averaging results from performing the arctangent function on each one of the conjugated values to compute the difference in phase. Also alternatively, the method may involve weighting each of the plurality of conjugated values with a signal-to-noise ratio (SNR) associated therewith, and summing the plurality of weighted conjugated values to compute the results of the complex conjugate multiplication used in performing the arctangent function. 
     As described in the fine frequency correction process of FIGS. 13-16, the pilot phase change between successive bursts as a function of time yields a frequency estimate. Consider an RSP represented by RSP(f k , t 0 )=A k e j     θ     (t0)  at time to and by RSP(f k , t 1 )=A k e j     θ     (t1)  at time t 1 . Here, A k  is the complex FFT bin value at frequency k and θ is the time-varying phase error. The frequency error ω e  can be computed as the difference of the phase angles of the tones divided by t 1 −t 0 , represented simply as 
     
       
         ω e =(θ t1 −θ t0 )/(t 1 −t 0 ). 
       
     
     In the preferred embodiment, the time interval is the burst transmit period, t 1 −t 0 =375 microseconds, where an OFDM packet time comprises 320 microseconds and a guard time comprises 55 microseconds. The above equation for ω e  is, however, only valid when the frequency error is less than the Nyquist sampling rate. If the frequency error is greater than the Nyquist frequency, aliasing of the estimate occurs. In the embodiment described, the phase is sampled with a frequency of 1/375×10 −6  Hz and therefore f NYQUIST =1/(2*375×10 −6 )=1333 Hz. To resolve the frequency ambiguity in the event the actual frequency error exceeds the 1333 Hz Nyquist frequency, the method described in relation to FIGS. 17 and 18 is employed (described below). 
     FIG. 17 is a flowchart describing another method for use in obtaining frequency synchronization in an OFDM communication system. This method makes use of both coarse and fine frequency correction processes in an iterative fashion. Beginning at a start block  1700 , a coarse frequency correction process is performed (step  1702 ). The coarse frequency correction process is operative to adjust receiver frequency so that a pilot tone signal is within a predetermined frequency range. Preferably, the predetermined frequency range corresponds to a single FFT tone bin. After performing the coarse frequency correction process, a fine frequency correction process is performed (step  1704 ). The fine frequency correction process is operative to adjust receiver frequency so that the pilot tone signal is substantially aligned with a pilot tone reference within the predetermined frequency range. Preferably, the frequency error is reduced by the fine frequency correction process to be less than or equal to one-half of a single FFT tone bin. 
     From performing the coarse frequency correction process in step  1702 , receiver frequency is adjusted so that the pilot tone signal is within the predetermined frequency range. However, because the Nyquist sampling frequency range within the predetermined frequency range gives rise to a phase ambiguity, the determined pilot tone location may be incorrect. Such a pilot tone may be considered an “aliased” pilot tone. An example illustration of this condition is shown in FIG.  18 A. FIG. 18A shows a predetermined frequency range  1802  corresponding to a tone bin width, a Nyquist sampling frequency range  1804  within predetermined frequency range  1802 , a pilot tone reference  1806  corresponding to a center of predetermined frequency range  1806 , a pilot tone signal  1808  within predetermined frequency range  1802  but outside Nyquist sampling frequency range  1804 , and an alias pilot tone signal  1810  within both predetermined frequency range  1802  and Nyquist sampling frequency range  1804 . Due to such a condition, from performing the fine frequency correction process in step  1704 , receiver frequency is actually adjusted so that the alias pilot tone signal is substantially aligned with the pilot tone reference and the pilot tone signal is shifted outside the predetermined frequency range. This is an undesirable condition. An example illustration of this undesirable condition is shown in FIG. 18B, which is based on the condition in FIG.  18 A. Note how the tone placement relative to the reference frequency is now 2×1333 Hz=2666 Hz away. 
     To eliminate any such condition, additional steps are performed as further described in relation to FIG.  17 . After performing the coarse and the fine frequency correction processes in steps  1702  and  1704 , the coarse frequency correction process is performed again (step  1702 ) after determining that a second iteration needs to be performed (step  1706 ). After performing the coarse frequency correction process again, the fine frequency correction process is performed again (step  1704 ). From performing the coarse frequency correction process again in step  1702 , receiver frequency is adjusted so that the pilot tone signal is within both the predetermined frequency range and the Nyquist sampling frequency range. An example of this condition is shown in FIG. 18C, which is based on the condition shown in FIG.  18 B. Note that the tone is now within 3125 Hz−(2*1333 Hz)=459 Hz from the reference position, well within the range of the fine frequency correction process. From performing the fine frequency correction process again in step  1704 , receiver frequency is adjusted so that the pilot tone signal is substantially aligned with the pilot tone reference. An example of the desired result is shown in FIG. 18D, which is based on the condition shown in FIG.  18 C. Here, the frequency error is reduced to less than one-half of a tone bin. 
     Correct frequency synchronization is thereby achieved by the iterative processing of FIG.  17 . The processes in steps  1702  and  1704  may be repeated as many times as necessary or desired for frequency synchronization. Although other suitable coarse and fine correction processes may be utilized, the coarse frequency correction process is preferably that process described in relation to FIGS. 6-12 and the fine frequency correction process is preferably that process described in relation to FIGS. 13-16. 
     Referring back to FIG. 16, a schematic block diagram of a digital signal processing apparatus  1600  is shown. Digital signal processing apparatus  1600  may be referred to as a frequency control device, and is used in connection with the inventive methods described herein. The digital signal processing apparatus  1600  includes a digital signal processor (DSP)  1602 , a digital-to-analog converter (DAC)  1604 , and a voltage-controlled oscillator (VCO)  1606 . As apparent, DSP  1602  executes many of the method steps described herein with processor instructions embedded in memory. DSP  1602  has an output coupled to an input of DAC  1604 , which has an output coupled to an input of VCO  1606 . In the embodiment shown, DSP  1602  feeds a digital data signal (i.e., a digital value) to DAC  1604 . DAC  1604  converts the digital data signal to an analog signal, which is fed to the input of VCO  1604 . The voltage level at the input of VCO  1604  determines the frequency of an analog signal generated by VCO  1606  at an output  1610 . Preferably, VCO  1606  is a 32 MHz VCXO. 
     More specifically, frequency error estimates are generated and DSP  1602  makes a corrective change to VCO  1606 , which changes the appropriate RF and intermediate frequencies (IF). The VCO frequency operating point is changed by altering its voltage input, which is generated when DSP  1602  writes a value y to DAC  1604 . The VCO frequency change Δω is modeled by 
     
       
         Δω=uK 0   
       
     
     where u is the input control voltage to VCO  1606  and K 0  is a gain factor  1608  of VCO  1606 . The value of u is determined by y which is computed in DSP  1602 . Conversion from the digital domain (y) to the analog domain (u) is achieved through a scaling factor β, which maps the computed digital value within the voltage range of DAC  1604 . The DAC scaling factor is β=2 15 /4.64 volts; i.e., the DAC outputs a maximum voltage of 4.64 volts for a corresponding input value of 2 15 . The value that is written to the DAC  1604  is based on 
     
       
           y =(Δωβ)/( MK   0 ) 
       
     
     where Δω is the estimated frequency error computed by the phase detector, and M is the RF multiplication factor corresponding to the gain required to amplify the VCO frequency change at 32 MHz to the corresponding change in RF frequencies. The value of M depends on the frequency plan, but is approximately equal to 60 in the preferred embodiment. 
     Thus, the methods described herein involve the use of a coarse frequency correction process, a fine frequency correction process, and an overarching iterative process that makes use of both the coarse and fine frequency correction processes. The coarse frequency correction process involves the steps of generating a plurality of tone values for a plurality of tone bins, where the plurality of tone bins include a first set of tone bins assigned to a first frequency range and a second set of tone bins assigned to a second frequency range; performing complex conjugate multiplication between the tone values of the first and the second sets of tone bins; identifying a maximum value from results of the complex conjugate multiplication; and shifting receiver frequency based on a location of the maximum value relative to a predetermined pilot tone location. In this method, the first frequency range corresponds to a lower edge portion of a frequency band of interest, an upper edge portion of a lower adjacent frequency band, and a lower guard band in between the lower and the upper edge portions; and the second frequency range corresponds to an upper edge portion of the frequency band of interest, a lower edge portion of an upper adjacent frequency band, and an upper guard band in between the upper and lower edge portions. 
     The coarse frequency correction process may further involve shifting receiver frequency based on a difference between the location of the maximum value and the predetermined pilot tone location. In addition, the coarse frequency correction process may further involve taking absolute values of results from the complex conjugate multiplication to thereby provide the results used in identifying the maximum value. To ensure a single peak for frequency correction, the generating of the plurality of tone values for the plurality of tone bins may involve generating a first set of tone values based on tones received in a current time slot; retrieving a second set of tone values that were previously generated based on tones received in a previous time slot; and performing complex conjugate multiplication between the first and the second sets of tone values generated from the previous and current time slots to thereby suppress tones that vary in phase over time. In addition, the generating of the plurality of tone values for the plurality of tone bins may further involve repeating the generating of first and second sets of tone values and the performing of complex conjugate multiplication between first and second sets of tone values for additional previous and current time slots; and averaging results of the repeated generating and performing of complex conjugate multiplication between the first and second sets of tone values. 
     The fine frequency correction process involves the steps of receiving, in a first time slot, a first set of tones associated with a frequency range; computing a first set of tone values based on the first set of tones; receiving, in a second time slot, a second set of tones associated with the frequency range, the first and the second time slots being separated by a difference in time; computing a second set of tone values based on the second set of tones; performing complex conjugate multiplication between the first and the second set of tone values; performing an arctangent function on results from the complex conjugate multiplication to compute a difference in phase between the first and the second set of tones; and computing a difference in frequency based on a quotient of the difference in phase over the difference in time. The fine frequency correction process may further involve the steps of varying a frequency adjustment signal in accordance with the computed difference in frequency, and adjusting receiver frequency in accordance with the frequency adjustment signal. 
     In addition, the method may further involve summing a plurality of conjugated values to thereby provide the results from the complex conjugate multiplication used in performing the arctangent function. On the other hand, the method may further involve performing an arctangent function on each one of a plurality of conjugated values; and averaging results from performing the arctangent function on each one of the conjugated values to thereby compute the difference in phase. Also alternatively, the method may involve weighting each of a plurality of conjugated values with a signal-to-noise ratio (SNR) associated therewith; and summing the plurality of weighted conjugated values to compute the results of the complex conjugate multiplication used in performing the arctangent function. 
     The overarching iterative process involves both the coarse and fine frequency correction processes. The iterative method includes the steps of performing a coarse frequency correction process which is operative to adjust receiver frequency so that a pilot tone signal is within a predetermined frequency range and, after performing the coarse frequency correction process, performing a fine frequency correction process which is operative to adjust receiver frequency so that the pilot tone signal is substantially aligned with a pilot tone reference within the predetermined frequency range. From performing the coarse frequency correction process, receiver frequency is adjusted so that the pilot tone signal is within the predetermined frequency range. The pilot tone signal may be outside a Nyquist sampling frequency range which undesirably causes an alias pilot tone signal to be within the Nyquist sampling frequency range. Assuming this condition, from performing the fine frequency correction process, receiver frequency is adjusted so that the alias pilot tone signal is substantially aligned with the pilot tone reference and the pilot tone signal is undesirably shifted outside the predetermined frequency range. 
     The iterative processing eliminates any such result by, after performing the coarse and the fine frequency correction processes, performing the coarse frequency correction process again and, after performing the coarse frequency correction process again, performing the fine frequency correction process again. From performing the coarse frequency correction process again, receiver frequency is adjusted so that the pilot tone signal is within both the predetermined frequency range and the Nyquist sampling frequency range. From performing the fine frequency correction process again, receiver frequency is adjusted so that the pilot tone signal is substantially aligned with the pilot tone reference. 
     Put another way, the overarching process includes the steps of adjusting receiver frequency so that an alias pilot tone signal is substantially aligned with a pilot tone reference and a pilot tone signal is shifted outside a predetermined frequency range; performing a coarse frequency correction process which is operative to adjust receiver frequency so that the pilot tone signal is within the predetermined frequency range; and performing a fine frequency correction process which is operative to adjust receiver frequency so that the pilot tone signal is substantially aligned with the pilot tone reference within the predetermined frequency range. 
     It should be readily apparent and understood that the foregoing description is only illustrative of the invention and in particular provides preferred embodiments thereof. Various alternatives and modifications can be devised by those skilled in the art without departing from the true spirit and scope of the invention. Accordingly, the present invention is intended to embrace all such alternatives, modifications, and variations which fall within the scope of the appended claims.