Abstract:
A system including a control module and a correlation module. The control module partitions a total number of subcarriers, in a received signal, into a predetermined number of bands. The correlation module generates a plurality of correlation values for a plurality of preamble sequences. A correlation value for a preamble sequence is generated by correlating symbols in each band with corresponding symbols in the preamble sequence to generate correlations for each band, adding the correlations generated for a respective band to generate a sum for each band, and adding the sums generated for all the bands. The control module select a largest correlation value from the plurality of correlation values and determine that one of the preamble sequences is detected in the received signal in response to the largest correlation value being greater than or equal to a predetermined threshold.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 11/717,405, filed Mar. 13, 2007, which is a continuation of U.S. patent application Ser. No. 11/648,735, filed Dec. 29, 2006, which application claims the benefit of U.S. Provisional Application No. 60/783,300, filed on Mar. 17, 2006, U.S. Provisional Application No. 60/792,508, filed on Apr. 17, 2006, U.S. Provisional Application No. 60/809,733, filed on May 31, 2006, and U.S. Provisional Application No. 60/826,392, Sep. 21, 2006. The disclosures of the above applications are incorporated herein by reference in their entirety. 
    
    
     FIELD 
     The present disclosure relates to communication systems, and more particularly to detecting preamble sequences in systems using orthogonal frequency domain multiplexing (OFDM). 
     BACKGROUND 
     The background description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent it is described in this background section, as well as aspects of the description which may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure. 
     Referring now to  FIG. 1 , a typical communication system  10  comprises an information source  12 , a transmitter  13 , a communication channel  20 , a receiver  27 , and a destination  28 . The transmitter  13  comprises a source encoder  14 , a channel encoder  16 , and a modulator  18 . The receiver  27  comprises a demodulator  22 , a channel decoder  24 , and a source decoder  26 . 
     The information source  12  may be an analog source such as a sensor that outputs information as continuous waveforms or a digital source such as a computer that outputs information in a digital form. The source encoder  14  converts the output of the information source  12  into a sequence of binary digits (bits) called an information sequence u. The channel encoder  16  converts the information sequence u into a discrete encoded sequence v called a codeword. The modulator  18  transforms the codeword into a waveform of duration T seconds that is suitable for transmission. 
     The waveform output by the modulator  18  is transmitted via the communication channel  20 . Typical examples of the communication channel  20  are telephone lines, wireless communication channels, optical fiber cables, etc. Noise, such as electromagnetic interference, inter-channel crosstalk, etc., may corrupt the waveform. 
     The demodulator  22  receives the waveform. The demodulator  22  processes each waveform and generates a received sequence r that is either a discrete (quantized) or a continuous output. The channel decoder  24  converts the received sequence r into a binary sequence u′ called an estimated information sequence. The source decoder  26  converts u′ into an estimate of the output of the information source  12  and delivers the estimate to the destination  28 . The estimate may be a faithful reproduction of the output of the information source  12  when u′ resembles u despite decoding errors that may be caused by the noise. 
     Communication systems use different modulation schemes to modulate and transmit data. For example, a radio frequency (RF) carrier may be modulated using techniques such as frequency modulation, phase modulation, etc. In wireline communication systems, a transmitted signal generally travels along a path in a transmission line between a transmitter and a receiver. In wireless communication systems, however, a transmitted signal may travel along multiple paths. This is because the transmitted signal may be reflected and deflected by objects such as buildings, towers, airplanes, cars, etc., before the transmitted signal reaches a receiver. Each path may be of different length. Thus, the receiver may receive multiple versions of the transmitted signal. The multiple versions may interfere with each other causing inter symbol interference (ISI). Thus, retrieving original data from the transmitted signal may be difficult. 
     To alleviate this problem, wireless communication systems often use a modulation scheme called orthogonal frequency division multiplexing (OFDM). In OFDM, a wideband carrier signal is converted into a series of independent narrowband sub-carrier signals that are adjacent to each other in frequency domain. Data to be transmitted is split into multiple parallel data streams. Each data stream is modulated using a sub-carrier. A channel over which the modulated data is transmitted comprises a sum of the narrowband sub-carrier signals, which may overlap. 
     When each sub-carrier closely resembles a rectangular pulse, modulation can be easily performed by Inverse Discrete Fourier Transform (IDFT), which can be efficiently implemented as an Inverse Fast Fourier Transform (IFFT). When IFFT is used, the spacing of sub-carriers in the frequency domain is such that when the receiver processes a received signal at a particular frequency, all other signals are nearly zero at that frequency, and ISI is avoided. This property is called orthogonality, and hence the modulation scheme is called orthogonal frequency division multiplexing (OFDM). 
     Referring now to  FIGS. 2A-2C , a wireless communication system  50  may comprise base stations BS 1 , BS 2 , and BS 3  (collectively BS) and one or more mobile stations (MS). Each BS may comprise a processor  30 , a medium access controller (MAC)  32 , a physical layer (PHY) module  34 , and an antenna  36  as shown in  FIG. 2B . Similarly, each MS may comprise a processor  40 , a medium access controller (MAC)  42 , a physical layer (PHY) module  44 , and an antenna  46  as shown in  FIG. 2C . The PHY modules  34  and  44  may comprise radio frequency (RF) transceivers (not shown) that transmit and receive data via antennas  36  and  46 , respectively. Each BS and MS may transmit and receive data while the MS moves relative to the BS. 
     Specifically, each BS may transmit data using orthogonal frequency division multiplexing access (OFDMA) system. Each BS may transmit data typically in three segments: SEG 1 , SEG 2 , and SEG 3 . The MS, which moves relative to each BS, may receive data from one or more base stations depending on the location of the MS relative to each BS. For example, the MS may receive data from SEG  3  of BS 1  and SEG  2  of BS 2  when the MS is located as shown in  FIG. 2A . 
     Relative motion between MS and BS may cause Doppler shifts in signals received by the MS. This can be problematic since systems using OFDMA are inherently sensitive to carrier frequency offsets (CFO). Therefore, pilot tones are generally used for channel estimation refinement. For example, some of the sub-carriers may be designated as pilot tones for correcting residual frequency offset errors. 
     Additionally, the PHY module  34  of each BS typically adds a preamble to a data frame that is to be transmitted. Specifically, the PHY module  34  modulates and encodes the data frame comprising the preamble at a data rate specified by the MAC  34  and transmits the data frame. When the PHY module  44  of the MS receives the data frame, the PHY module  44  uses the preamble in the data frame to detect a beginning of packet transmission and to synchronize to a transmitter clock of the BS. 
     According to the I.E.E.E. standard 802.16e, which is incorporated herein by reference in its entirety, a first symbol in the data frame transmitted by the BS is a preamble symbol from a preamble sequence. The preamble sequence typically contains an identifier called IDcell, which is a cell ID of the BS, and segment information. The BS selects the preamble sequence based on the IDcell and the segment number of the BS. Each BS may select different preamble sequences. Additionally, each BS may select preamble sequences that are distinct among the segments of that BS. 
     The BS modulates multiple sub-carriers with the selected preamble sequence. Thereafter, the BS performs IFFT, adds a cyclic prefix, and transmits a data frame. The MS uses the cyclic prefix to perform symbol timing and fractional carrier frequency synchronization. Unless the MS knows the preamble sequence, however, the MS cannot associate itself to a particular segment of a particular BS. 
     SUMMARY 
     A system comprises a differential demodulation module and a correlation module. The differential demodulation module differentially demodulates modulated signals to generate differentially demodulated signals. The correlation module correlates the differentially demodulated signals with derived preamble sequences and generates correlation values. 
     In another feature, the modulated signals include sub-carriers that are modulated using orthogonal frequency domain multiplexing (OFDM). 
     In another feature, every P th  one of the sub-carriers is modulated with a preamble bit, where P is an integer greater than or equal to 1. 
     In another feature, every P th  one of the sub-carriers has substantially the same channel phase. 
     In another feature, each one of the correlation values has a real part and an imaginary part. 
     In another feature, the system further comprises a control module that selects one of the correlation values having a largest real part and that detects a preamble sequence in the modulated signals upon determining that the largest real part is greater than or equal to a predetermined threshold. The predetermined threshold is based on the signal strength of the modulated signals. The control module identifies a segment of a base station that transmitted the modulated signals based on the preamble sequence. 
     In another feature, every P th  one of the sub-carriers has substantially the same differential channel phase. 
     In another feature, the system further comprises a control module that selects a largest correlation value from the correlation values and that detects a preamble sequence in the modulated signals upon determining that a magnitude of the largest correlation value is greater than or equal to a predetermined threshold. The predetermined threshold is based on the signal strength of the modulated signals. The control module identifies a segment of a base station that transmitted the modulated signals based on the preamble sequence. 
     In another feature, the differential demodulation module generates the differentially demodulated signals by multiplying a Q th  one of the modulated signals by a complex conjugate of a (Q+P) th  one of the modulated signals, where Q is an integer greater than or equal to 1. 
     In another feature, the derived preamble sequences are derived from preamble sequences, and wherein each of the preamble sequences is different from others of the preamble sequences. 
     In another feature, each bit of one of the derived preamble sequences has a first state when a corresponding bit and a bit adjacent to the corresponding bit in a corresponding one of the preamble sequences have opposite states, and the each bit has a second state when the corresponding bit and the bit adjacent to the corresponding bit have the same state. 
     In another feature, the derived preamble sequences are stored in one of the correlation module and the control module. The derived preamble sequences have a cross-correlation value that is less than or equal to a predetermined cross-correlation threshold. The predetermined cross-correlation threshold is less than approximately 0.2 for an orthogonal frequency domain multiplexing (OFDM) system using a 1024 fast Fourier transform (FFT) mode. 
     In another feature, the modulated signals include a fractional carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. 
     In another feature, the modulated signals include an integer carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. The correlation module correlates the derived preamble sequences with the differentially demodulated signals having the integer CFO. 
     In another feature, the modulated signals include a linearly increasing phase offset generated by a symbol timing offset. 
     In another feature, the control module calculates a symbol timing offset by multiplying a phase angle of the largest correlation value by (N/2πP), where N is a number of sub-carriers in an N fast Fourier transform (FFT) mode, and where N is an integer greater than 1. N is one of 128, 512, 1024, and 2048. 
     In another feature, a physical layer module (PHY) comprises the system and further comprises a transceiver module that communicates with the differential demodulation module and that receives the modulated signals. 
     In another feature, a network device comprises the PHY and further comprises at least one antenna that communicates with the transceiver module. 
     In still other features, a method comprises differentially demodulating modulated signals, generating differentially demodulated signals from the modulated signals, correlating the differentially demodulated signals with derived preamble sequences, and generating correlation values based on the correlating. 
     In another feature, the method further comprises differentially demodulating sub-carriers that are included in the modulated signals and that are modulated using orthogonal frequency domain multiplexing (OFDM), wherein every P th  one of the sub-carriers is modulated with a preamble bit, where P is an integer greater than or equal to 1. 
     In another feature, the method further comprises differentially demodulating the sub-carriers, wherein the every P th  one of the sub-carriers has substantially the same channel phase. 
     In another feature, the method further comprises determining a real part and an imaginary part of each one of the correlation values. 
     In another feature, the method further comprises selecting one of the correlation values having a largest real part and detecting a preamble sequence in the modulated signals upon determining that the largest real part is greater than or equal to a predetermined threshold. The method further comprises determining the predetermined threshold based on the signal strength of the modulated signals. The method further comprises identifying a segment of a base station that transmitted the modulated signals based on the preamble sequence. 
     In another feature, the method further comprises differentially demodulating the sub-carriers, wherein the every P th  one of the sub-carriers has substantially the same differential channel phase. 
     In another feature, the method further comprises selecting a largest correlation value from the correlation values and detecting a preamble sequence in the modulated signals upon determining that a magnitude of the largest correlation value is greater than or equal to a predetermined threshold. The method further comprises determining the predetermined threshold based on the signal strength of the modulated signals. The method further comprises identifying a segment of a base station that transmitted the modulated signals based on the preamble sequence. 
     In another feature, the method further comprises generating the differentially demodulated signals by multiplying a Q th  one of the modulated signals by a complex conjugate of a (Q+P) th  one of the modulated signals, where Q is an integer greater than or equal to 1. 
     In another feature, the method further comprises deriving the derived preamble sequences from preamble sequences, wherein each of the preamble sequences is different from others of the preamble sequences, and wherein the derived preamble sequences have a cross-correlation value that is less than or equal to a predetermined cross-correlation threshold. The method further comprises determining that the predetermined cross-correlation threshold is less than approximately 0.2 for an orthogonal frequency domain multiplexing (OFDM) method using a 1024 fast Fourier transform (FFT) mode. 
     In another feature, the method further comprises generating each bit of one of the derived preamble sequences having a first state when a corresponding bit and a bit adjacent to the corresponding bit in a corresponding one of the preamble sequences have opposite states, and generating the each bit having a second state when the corresponding bit and the bit adjacent to the corresponding bit have the same state. 
     In another feature, the method further comprises storing the derived preamble sequences. 
     In another feature, the method further comprises differentially demodulating the modulated signals having a fractional carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. 
     In another feature, the method further comprises differentially demodulating the modulated signals having an integer carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. The method further comprises correlating the derived preamble sequences with the differentially demodulated signals having the integer CFO. 
     In another feature, the method further comprises differentially demodulating the modulated signals having a linearly increasing phase offset generated by a symbol timing offset. 
     In another feature, the method further comprises calculating a symbol timing offset by multiplying a phase angle of the largest correlation value by (N/2πP), where N is a number of sub-carriers in an N fast Fourier transform (FFT) mode, and where N is an integer greater than 1. N is one of 128, 512, 1024, and 2048. 
     In still other features, a system comprises differential demodulation means for differentially demodulating modulated signals to generate differentially demodulated signals and correlation means for correlating the differentially demodulated signals with derived preamble sequences and generating correlation values. 
     In another feature, the modulated signals include sub-carriers that are modulated using orthogonal frequency domain multiplexing (OFDM). 
     In another feature, every P th  one of the sub-carriers is modulated with a preamble bit, where P is an integer greater than or equal to 1. 
     In another feature, every P th  one of the sub-carriers has substantially the same channel phase. 
     In another feature, each one of the correlation values has a real part and an imaginary part. 
     In another feature, the system further comprises control means for selecting one of the correlation values having a largest real part and detecting a preamble sequence in the modulated signals upon determining that the largest real part is greater than or equal to a predetermined threshold. The predetermined threshold is based on the signal strength of the modulated signals. The control means identifies a segment of a base station that transmitted the modulated signals based on the preamble sequence. 
     In another feature, every P th  one of the sub-carriers has substantially the same differential channel phase. 
     In another feature, the system further comprises control means for selecting a largest correlation value from the correlation values and detecting a preamble sequence in the modulated signals upon determining that a magnitude of the largest correlation value is greater than or equal to a predetermined threshold. The predetermined threshold is based on the signal strength of the modulated signals. The control means identifies a segment of a base station that transmitted the modulated signals based on the preamble sequence. 
     In another feature, the differential demodulation means generates the differentially demodulated signals by multiplying a Q th  one of the modulated signals by a complex conjugate of a (Q+P) th  one of the modulated signals, where Q is an integer greater than or equal to 1. 
     In another feature, the derived preamble sequences are derived from preamble sequences, and wherein each of the preamble sequences is different from others of the preamble sequences. 
     In another feature, each bit of one of the derived preamble sequences has a first state when a corresponding bit and a bit adjacent to the corresponding bit in a corresponding one of the preamble sequences have opposite states, and the each bit has a second state when the corresponding bit and the bit adjacent to the corresponding bit have the same state. 
     In another feature, the derived preamble sequences are stored in one of the correlation means and the control means. 
     In another feature, the derived preamble sequences have a cross-correlation value that is less than or equal to a predetermined cross-correlation threshold. The predetermined cross-correlation threshold is less than approximately 0.2 for an orthogonal frequency domain multiplexing (OFDM) system using a 1024 fast Fourier transform (FFT) mode. 
     In another feature, the modulated signals include a fractional carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. 
     In another feature, the modulated signals include an integer carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. The correlation means correlates the derived preamble sequences with the differentially demodulated signals having the integer CFO. 
     In another feature, the modulated signals include a linearly increasing phase offset generated by a symbol timing offset. 
     In another feature, the control means calculates a symbol timing offset by multiplying a phase angle of the largest correlation value by (N/2πP), where N is a number of sub-carriers in an N fast Fourier transform (FFT) mode, and where N is an integer greater than 1. N is one of 128, 512, 1024, and 2048. 
     In another feature, a physical layer means (PHY) for communicating comprises the system and further comprises transceiver means for communicating with the differential demodulation means and receiving the modulated signals. 
     In another feature, a network device comprises the PHY means and further comprises at least one antenna means for communicating with the transceiver means. 
     In still other features, a computer program executed by a processor comprises differentially demodulating modulated signals, generating differentially demodulated signals from the modulated signals, correlating the differentially demodulated signals with derived preamble sequences, and generating correlation values based on the correlating. 
     In another feature, the computer program further comprises differentially demodulating sub-carriers that are included in the modulated signals and that are modulated using orthogonal frequency domain multiplexing (OFDM), wherein every P th  one of the sub-carriers is modulated with a preamble bit, where P is an integer greater than or equal to 1. 
     In another feature, the computer program further comprises differentially demodulating the sub-carriers, wherein the every P th  one of the sub-carriers has substantially the same channel phase. 
     In another feature, the computer program further comprises determining a real part and an imaginary part of each one of the correlation values. 
     In another feature, the computer program further comprises selecting one of the correlation values having a largest real part and detecting a preamble sequence in the modulated signals upon determining that the largest real part is greater than or equal to a predetermined threshold. The computer program further comprises determining the predetermined threshold based on the signal strength of the modulated signals. The computer program further comprises identifying a segment of a base station that transmitted the modulated signals based on the preamble sequence. 
     In another feature, the computer program further comprises differentially demodulating the sub-carriers, wherein the every P th  one of the sub-carriers has substantially the same differential channel phase. 
     In another feature, the computer program further comprises selecting a largest correlation value from the correlation values and detecting a preamble sequence in the modulated signals upon determining that a magnitude of the largest correlation value is greater than or equal to a predetermined threshold. The computer program further comprises determining the predetermined threshold based on the signal strength of the modulated signals. The computer program further comprises identifying a segment of a base station that transmitted the modulated signals based on the preamble sequence. 
     In another feature, the computer program further comprises generating the differentially demodulated signals by multiplying a Q th  one of the modulated signals by a complex conjugate of a (Q+P) th  one of the modulated signals, where Q is an integer greater than or equal to 1. 
     In another feature, the computer program further comprises deriving the derived preamble sequences from preamble sequences, wherein each of the preamble sequences is different from others of the preamble sequences, and wherein the derived preamble sequences have a cross-correlation value that is less than or equal to a predetermined cross-correlation threshold. The computer program further comprises determining that the predetermined cross-correlation threshold is less than approximately 0.2 for an orthogonal frequency domain multiplexing (OFDM) computer program using a 1024 fast Fourier transform (FFT) mode. 
     In another feature, the computer program further comprises generating each bit of one of the derived preamble sequences having a first state when a corresponding bit and a bit adjacent to the corresponding bit in a corresponding one of the preamble sequences have opposite states, and generating the each bit having a second state when the corresponding bit and the bit adjacent to the corresponding bit have the same state. 
     In another feature, the computer program further comprises storing the derived preamble sequences. 
     In another feature, the computer program further comprises differentially demodulating the modulated signals having a fractional carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. 
     In another feature, the computer program further comprises differentially demodulating the modulated signals having an integer carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. The computer program further comprises correlating the derived preamble sequences with the differentially demodulated signals having the integer CFO. 
     In another feature, the computer program further comprises differentially demodulating the modulated signals having a linearly increasing phase offset generated by a symbol timing offset. 
     In another feature, the computer program further comprises calculating a symbol timing offset by multiplying a phase angle of the largest correlation value by (N/2πP), where N is a number of sub-carriers in an N fast Fourier transform (FFT) mode, and where N is an integer greater than 1. N is one of 128, 512, 1024, and 2048. 
     In still other features, a system comprises a correlation module and a control module. The correlation module correlates modulated signals with a plurality of preamble sequences and generates correlation values. The control module selects a largest correlation value from the correlation values and detects one of the preamble sequences in the modulated signals upon determining that a magnitude of the largest correlation value is greater than or equal to a first predetermined threshold. The first predetermined threshold is based on the signal strength of the modulated signals. 
     In another feature, each of the preamble sequences is different from others of the preamble sequences. The preamble sequences are stored in one of the correlation module and the control module. 
     In another feature, the control module identifies a segment of a base station that transmitted the modulated signals based on the one of the preamble sequences. 
     In another feature, the modulated signals include sub-carriers that are modulated using orthogonal frequency domain multiplexing (OFDM). The sub-carriers have a common channel gain and a random channel phase. Every P th  one of the sub-carriers is modulated with a preamble bit, where P is an integer greater than or equal to 1. 
     In another feature, the preamble sequences have a cross-correlation value of less than or equal to a second predetermined threshold. The second predetermined threshold is less than approximately 0.2 for an orthogonal frequency domain multiplexing (OFDM) system using a 1024 fast Fourier transform (FFT) mode. 
     In another feature, the modulated signals include a fractional carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. 
     In another feature, the modulated signals include an integer carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. 
     In another feature, a physical layer module (PHY) comprises the system and further comprises a transceiver module that communicates with the correlation module and the control module and that receives the modulated signals. 
     In another feature, a network device comprises the PHY and further comprises at least one antenna that communicates with the transceiver module. 
     In another feature, the control module divides N of the sub-carriers into L bands when a channel gain of the sub-carriers is not substantially the same for all of the sub-carriers, where N and L are integers greater than or equal to 1, and where each of the L bands includes N/L of the sub-carriers. 
     In another feature, the correlation module correlates symbols in every P th  one of the N/L sub-carriers in each of the L bands with corresponding symbols in each of the preamble sequences and generates intra-band correlation values for each band for each of the preamble sequences, where P is an integer greater than or equal to 1. 
     In another feature, the control module generates a band correlation value for each of the L bands and for each of the preamble sequences by adding the intra-band correlation values. The control module further generates a magnitude of each of the band correlation value. The control module further generates the correlation values by adding the magnitude of each of the band correlation value for each of the preamble sequences. 
     In still other features, a method comprises, correlating modulated signals with a plurality of preamble sequences, generating correlation values based on the correlating, selecting a largest correlation value from the correlation values, and detecting one of the preamble sequences in the modulated signals upon determining that a magnitude of the largest correlation value is greater than or equal to a first predetermined threshold. The method further comprises determining the first predetermined threshold based on the signal strength of the modulated signals. 
     In another feature, the method further comprises storing the preamble sequences, wherein each of the preamble sequences is different from others of the preamble sequences. 
     In another feature, the method further comprises identifying a segment of a base station that transmitted the modulated signals based on the one of the preamble sequences. 
     In another feature, the method further comprises receiving the modulated signals that include sub-carriers that are modulated using orthogonal frequency domain multiplexing (OFDM), wherein every P th  one of the sub-carriers is modulated with a preamble bit, where P is an integer greater than or equal to 1, and wherein the sub-carriers have a common channel gain and a random channel phase. 
     In another feature, the method further comprises correlating the modulated signals with the preamble sequences having a cross-correlation value of less than or equal to a second predetermined threshold. The method further comprises determining that the second predetermined threshold is less than approximately 0.2 for an orthogonal frequency domain multiplexing (OFDM) method using a 1024 fast Fourier transform (FFT) mode. 
     In another feature, the method further comprises receiving the modulated signals having a fractional carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. 
     In another feature, the method further comprises receiving the modulated signals having an integer carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. 
     In another feature, the method further comprises dividing N of the sub-carriers into L bands when a channel gain of the sub-carriers is not substantially the same for all of the sub-carriers, where N and L are integers greater than or equal to 1, and where each of the L bands includes N/L of the sub-carriers. 
     In another feature, the method further comprises correlating symbols in every P th  one of the N/L sub-carriers in each of the L bands with corresponding symbols in each of the preamble sequences and generating intra-band correlation values for each band for each of the preamble sequences, where P is an integer greater than or equal to 1. 
     In another feature, the method further comprises generating a band correlation value for each of the L bands and for each of the preamble sequences by adding the intra-band correlation values, generating a magnitude of each of the band correlation value, and generating the correlation values by adding the magnitude of each of the band correlation value for each of the preamble sequences. 
     In still other features, a system comprises correlation means for correlating modulated signals with a plurality of preamble sequences and generating correlation values. The system further comprises control means for selecting a largest correlation value from the correlation values and detecting one of the preamble sequences in the modulated signals upon determining that a magnitude of the largest correlation value is greater than or equal to a first predetermined threshold. The first predetermined threshold is based on the signal strength of the modulated signals. 
     In another feature, each of the preamble sequences is different from others of the preamble sequences. The preamble sequences are stored in one of the correlation means and the control means. 
     In another feature, the control means identifies a segment of a base station that transmitted the modulated signals based on the one of the preamble sequences. 
     In another feature, the modulated signals include sub-carriers that are modulated using orthogonal frequency domain multiplexing (OFDM). The sub-carriers have a common channel gain and a random channel phase. Every P th  one of the sub-carriers is modulated with a preamble bit, where P is an integer greater than or equal to 1. 
     In another feature, the preamble sequences have a cross-correlation value of less than or equal to a second predetermined threshold. The second predetermined threshold is less than approximately 0.2 for an orthogonal frequency domain multiplexing (OFDM) system using a 1024 fast Fourier transform (FFT) mode. 
     In another feature, the modulated signals include a fractional carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. 
     In another feature, the modulated signals include an integer carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. 
     In another feature, a physical layer means (PHY) for communicating comprises the system and further comprises transceiver means for communicating with the correlation means and the control means and that receives the modulated signals. 
     In another feature, a network device comprises the PHY means and further comprises at least one antenna means for communicating with the transceiver means. 
     In another feature, the control means divides N of the sub-carriers into L bands when a channel gain of the sub-carriers is not substantially the same for all of the sub-carriers, where N and L are integers greater than or equal to 1, and where each of the L bands includes N/L of the sub-carriers. 
     In another feature, the correlation means correlates symbols in every P th  one of the N/L sub-carriers in each of the L bands with corresponding symbols in each of the preamble sequences and generates intra-band correlation values for each band for each of the preamble sequences, where P is an integer greater than or equal to 1. 
     In another feature, the control means generates a band correlation value for each of the L bands and for each of the preamble sequences by adding the intra-band correlation values. The control means further generates a magnitude of each of the band correlation value. The control means further generates the correlation values by adding the magnitude of each of the band correlation value for each of the preamble sequences. 
     In still other features, a computer program executed by a processor comprises correlating modulated signals with a plurality of preamble sequences, generating correlation values based on the correlating, selecting a largest correlation value from the correlation values, and detecting one of the preamble sequences in the modulated signals upon determining that a magnitude of the largest correlation value is greater than or equal to a first predetermined threshold. The computer program further comprises determining the first predetermined threshold based on the signal strength of the modulated signals. 
     In another feature, the computer program further comprises storing the preamble sequences, wherein each of the preamble sequences is different from others of the preamble sequences. 
     In another feature, the computer program further comprises identifying a segment of a base station that transmitted the modulated signals based on the one of the preamble sequences. 
     In another feature, the computer program further comprises receiving the modulated signals that include sub-carriers that are modulated using orthogonal frequency domain multiplexing (OFDM), wherein every P th  one of the sub-carriers is modulated with a preamble bit, where P is an integer greater than or equal to 1, and wherein the sub-carriers have a common channel gain and a random channel phase. 
     In another feature, the computer program further comprises correlating the modulated signals with the preamble sequences having a cross-correlation value of less than or equal to a second predetermined threshold. The computer program further comprises determining that the second predetermined threshold is less than approximately 0.2 for an orthogonal frequency domain multiplexing (OFDM) computer program using a 1024 fast Fourier transform (FFT) mode. 
     In another feature, the computer program further comprises receiving the modulated signals having a fractional carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. 
     In another feature, the computer program further comprises receiving the modulated signals having an integer carrier frequency offset (CFO) that generates a phase error that is substantially the same in each one of the modulated signals. 
     In another feature, the computer program further comprises dividing N of the sub-carriers into L bands when a channel gain of the sub-carriers is not substantially the same for all of the sub-carriers, where N and L are integers greater than or equal to 1, and where each of the L bands includes N/L of the sub-carriers. 
     In another feature, the computer program further comprises correlating symbols in every P th  one of the N/L sub-carriers in each of the L bands with corresponding symbols in each of the preamble sequences and generating intra-band correlation values for each band for each of the preamble sequences, where P is an integer greater than or equal to 1. 
     In another feature, the computer program further comprises generating a band correlation value for each of the L bands and for each of the preamble sequences by adding the intra-band correlation values, generating a magnitude of each of the band correlation value, and generating the correlation values by adding the magnitude of each of the band correlation value for each of the preamble sequences. 
     In still other features, the systems and methods described above are implemented by a computer program executed by one or more processors. The computer program can reside on a computer readable medium such as but not limited to memory, non-volatile data storage and/or other suitable tangible storage mediums. 
     Further areas of applicability of the present disclosure will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the disclosure, are intended for purposes of illustration only and are not intended to limit the scope of the disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure will become more fully understood from the detailed description and the accompanying drawings, wherein: 
         FIG. 1  is a functional block diagram of an exemplary communication system according to the prior art; 
         FIG. 2A  is a schematic representation of an exemplary wireless communication system comprising three base stations and a mobile station according to the prior art; 
         FIG. 2B  is a functional block diagram of an exemplary base station utilized in the system of  FIG. 2A ; 
         FIG. 2C  is a functional block diagram of an exemplary mobile station utilized in the system of  FIG. 2A ; 
         FIG. 3  is a schematic representation of an exemplary wireless communication system comprising three base stations and a mobile station; 
         FIG. 4  is a table showing preamble sequences used by base stations of  FIG. 3  to transmit data; 
         FIG. 5A  is a functional block diagram of an exemplary preamble detection system according to the present disclosure; 
         FIG. 5B  is a graph showing normalized cross-correlation between preamble sequences of  FIG. 4 ; 
         FIG. 5C  is a graph showing normalized cross-correlation between preamble sequences of  FIG. 4  when integer carrier frequency offset is present; 
         FIG. 5D  is a graph showing variation in channel gain relative to sub-carrier frequency in a highly frequency-selective channel; 
         FIG. 6A  is a functional block diagram of an exemplary preamble detection system according to the present disclosure; 
         FIG. 6B  is a graph showing normalized cross-correlation between preamble sequences derived from the preamble sequences shown in  FIG. 4 ; 
         FIG. 6C  is a graph showing normalized cross-correlation between derived preamble sequences when integer carrier frequency offset is present; 
         FIGS. 7A-7B  depict a flowchart of an exemplary method for preamble detection according to the present disclosure; 
         FIG. 8  is a flowchart of an exemplary method for preamble detection when sub-carriers have substantially similar channel phase; 
         FIG. 9  is a flowchart of an exemplary method for preamble detection when sub-carriers have an unknown differential similar channel phase; 
         FIG. 10A  is a functional block diagram of a vehicle control system; and 
         FIG. 10B  is a functional block diagram of a cellular phone. 
     
    
    
     DETAILED DESCRIPTION 
     The following description is merely exemplary in nature and is in no way intended to limit the disclosure, its application, or uses. For purposes of clarity, the same reference numbers will be used in the drawings to identify similar elements. As used herein, the term module, circuit and/or device refers to an Application Specific Integrated Circuit (ASIC), an electronic circuit, a processor (shared, dedicated, or group) and memory that execute one or more software or firmware programs, a combinational logic circuit, and/or other suitable components that provide the described functionality. As used herein, the phrase at least one of A, B, and C should be construed to mean a logical (A or B or C), using a non-exclusive logical or. It should be understood that steps within a method may be executed in different order without altering the principles of the present disclosure. 
     Referring now to  FIG. 3 , a wireless communication system  100  may comprise base stations BS 1 , BS 2 , and BS 3  (collectively BS) and one or more mobile stations (MS). Generally, one MS may communicate with up to three adjacent base stations. Each BS may transmit data that is modulated using an orthogonal frequency division multiplexing access (OFDMA) system. 
     Specifically, each BS may transmit data in three segments: SEG 1 , SEG 2 , and SEG 3 . The MS, which may move relative to each BS, may receive data from one or more base stations depending on the location of the MS relative to each BS. For example, the MS may receive data from SEG  3  of BS 1 , SEG  2  of BS 2 , and/or SEG  1  of BS 3  when the MS is located as shown. 
     When a receiver in the MS is turned on (i.e., when the MS is powered up), the MS may associate with an appropriate segment of a corresponding BS depending on the location of the MS. The MS, however, can process data in a frame transmitted by a BS only if the MS can correctly detect a preamble sequence in the frame. Specifically, the MS can perform frame synchronization and retrieval of a cell ID (IDcell) and a segment number of the BS from the frame if the MS can detect the preamble sequence in the frame. 
     Referring now to  FIG. 4 , OFDMA systems may use 1024 and 512 sub-carriers to modulate and transmit data. OFDMA systems using 1024 and 512 sub-carriers are generally referred to as OFDMA systems having 1024 and 512 FFT modes, respectively. Additionally, I.E.E.E. 802.16e supports 128 FFT and 2048 FFT modes. 
     A total of 114 preamble sequences exist for OFDMA systems that use fast Fourier transforms (FFT) to modulate 1024 and 512 sub-carriers. Each preamble sequence is unique. That is, each preamble sequence is distinct from another preamble sequence and is identified by an index number. The index number may be referred to as preamble sequence index. Each preamble sequence is 284 and 143 bits long for 1024 and 512 FFT modes, respectively. 
     Since one MS may typically communicate with up to three base stations, each BS modulates every third sub-carrier. That is, each BS modulates one of every three sub-carriers. Additionally, each BS uses only one bit of the total bits in a preamble sequence when modulating every third sub-carrier. For example, in 1024 FFT mode, the BS may use bit numbers  1 ,  2 ,  3 , . . . , etc., of the 284 bits in a preamble sequence to modulate sub-carrier numbers  1 ,  4 ,  7 , . . . , etc., of the 1024 sub-carriers, respectively. 
     Each BS may use the same set of sub-carriers. Each segment in a BS, however, uses distinct sub-carriers at least for preamble purposes. For example, for each BS, segment  1  (SEG 1 ) may use sub-carriers  0 ,  3 ,  6 ,  9 , . . . , etc.; segment  2  (SEG 2 ) may use sub-carriers  1 ,  4 ,  7 ,  10 , . . . , etc.; and segment  3  (SEG 3 ) may use sub-carriers  2 ,  5 ,  8 ,  11 , . . . , etc. 
     Consequently, the MS receives distinct signals from each BS. For example, the MS may receive signals from SEG 2  of BS 2  on sub-carriers  1 ,  4 ,  7 ,  10 , . . . , etc., from SEG 1  of BS 3  on sub-carriers  0 ,  3 ,  6 ,  9 , . . . , etc., and from SEG  3  of BS 1  on sub-carriers  2 ,  5 ,  8 ,  11 , . . . , etc. Thus, the signals received by the MS may not interfere with each other since their sub-carriers are distinct. 
     A set of sub-carriers for segment n may be mathematically expressed as follows.
 
PreambleCarrierSet n   =n+ 3 k  
 
where 0≦k≦283 for 1024 FFT mode and 0≦k≦142 for 512 FFT mode. Additionally, there may be 86 guard sub-carriers on the left and right ends of the spectrum in 1024 FFT mode. In the 512 FFT mode, there may be 42 guard sub-carriers on the left end and 41 guard sub-carriers on the right end.
 
     Typically, when the receiver in the MS is turned on, the MS initially performs symbol timing and carrier frequency synchronization before the MS can detect a preamble sequence. The MS may perform these tasks using a cyclic prefix in the data frame. Thereafter, the MS determines whether a first symbol in the frame is a preamble symbol. If the first symbol is a preamble symbol, then the MS determines which preamble sequence is present in the frame. Once the MS determines the preamble sequence, the MS can associate with a corresponding segment of an appropriate BS. 
     Symbols in preamble sequences (i.e., preamble symbols) typically have higher energy than data symbols. For example, the energy of the preamble symbols is typically 8/3 times (i.e., 4.26 dB higher than) the energy of data symbols. This is useful in distinguishing preamble symbols from data symbols. 
     Additionally, the preamble sequences are almost orthogonal. That is, a cross-correlation between any two preamble sequences is very small. For example, the cross-correlation is typically less than 0.2. This is useful in distinguishing individual preamble sequences from one another. As shown in the table in  FIG. 4 , if the MS detects a preamble sequence having an index 0, then the MS associates with segment 0 of BS having cell ID 0, and so on. 
     Referring now to  FIGS. 5A-5D , a system  150  for detecting a preamble sequence in a mobile station (MS) may be implemented in a physical layer (PHY) module  152  of the MS. The system  150  comprises a correlation module  154  and a control module  156 . The correlation module  154  receives an input signal transmitted by a base station (BS). The input signal may be mathematically expressed as follows.
 
 Y[k]=H[k]X   i   [k]+Z[k] 
 
where k is sub-carrier index, i is preamble sequence index, Y[k] is received signal (i.e., input signal), H[k] is channel gain, Xi[k] is transmit signal, and Z[k] is noise.
 
     When a preamble bit (i.e., a preamble symbol) in a preamble sequence is 0, the corresponding transmit signal Xi[k] is 1. When a preamble bit in a preamble sequence is 1, the corresponding transmit signal Xi[k] is −1. That is, when a preamble bit in a preamble sequence is 1, the phase of the sub-carrier in the transmit signal Xi[k] is shifted by π relative to the phase of the sub-carrier when a preamble bit in a preamble sequence is 0. 
     The system  150  detects a preamble sequence in the input signal as follows. The correlation module  154  correlates the input signal with preamble sequences. The preamble sequences may be stored in memory in the correlation module  154  or the control module  156 . Based on the output of the correlation module  154 , the control module  156  initially determines whether a first symbol in the input signal is a preamble symbol or a data symbol. If the first symbol is a preamble symbol, then the control module  156  determines an index i of the preamble sequence. Based on the index of the preamble sequence detected, the control module  156  determines which segment transmitted the preamble sequence. Accordingly, the MS associates with that segment. 
     When all k sub-carriers have a common channel gain H (i.e., when H[k] is independent of k) and when all k sub-carriers have random channel phase, the k sub-carriers are referred to as “almost flat frequency channels.” For almost flat frequency channels, the input signal may be mathematically expressed as follows.
 
 Y[k]=H[k]X   i   [k]+Z[k]≈HX   i   [k]+Z[k] 
 
     A cross-correlation between different preamble sequences is given by the following formula. 
                 max     i   ,     j   ≠   i         ⁢     {              ∑     k   ∈     P     s   ⁡     (   i   )             ⁢         X   i     ⁡     [   k   ]       ⁢       X   j   *     ⁡     [   k   ]                    ∑     k   ∈     P     s   ⁡     (   i   )             ⁢              X   i     ⁡     [   k   ]            2         }       ≈     0.1620   ⁢           ⁢   for   ⁢           ⁢   1024   ⁢           ⁢   F   ⁢           ⁢   F   ⁢           ⁢   T           
where Ps=set of pilot sub-carriers for segment s except left most pilot sub-carrier, and s(i)=segment number for a preamble sequence index i.  FIG. 5B  shows cross-correlation values normalized by
 
               ∑     k   ∈     P     s   ⁡     (   0   )             ⁢              X   0     ⁡     [   k   ]            2           
for 1024 FFT mode.
 
     Since the cross-correlation between different preamble sequences is small, the correlation module  154  correlates the input signal with the preamble sequences as follows. 
               C   j     =       ∑     k   ∈     P     s   ⁡     (   j   )             ⁢       Y   ⁡     [   k   ]       ⁢       X   j   *     ⁡     [   k   ]                 
The correlation module  154  performs the correlation for all k sub-carriers and j preamble sequences. Thus, in 1024 FFT mode, the correlation module  154  performs correlation for all 114 preamble sequences.
 
     The correlation module  154  generates correlation values and outputs the correlation values to the control module  156 . The control module  156  selects a largest correlation value from the correlation values. The control module  156  calculates a magnitude of the largest correlation value. The control module  156  calculates the magnitude because all sub-carriers have random channel phase, i.e., because sub-carrier channels are almost frequency flat channels. This is mathematically expressed as follows. 
     
       
         
           
             
               i 
               ^ 
             
             = 
             
               
                 argmax 
                 j 
               
               ⁢ 
               
                 { 
                 
                    
                   
                     C 
                     j 
                   
                    
                 
                 } 
               
             
           
         
       
     
     The control module  156  compares the magnitude of the largest correlation value to a predetermined threshold. The predetermined threshold is a function of signal strength of the input signal. If the magnitude of the largest correlation value is greater than or equal to the predetermined threshold, the control module  156  determines that a preamble sequence is detected in the input signal. 
     Thereafter, the control module  156  determines which segment transmitted the preamble sequence that the control module  156  detected in the input signal. The input signal may be a sum of up to three signals that may be transmitted by three different segments of three different base stations. This is mathematically expressed as follows. 
               Y   ⁡     [   k   ]       =         ∑     s   =   0     2     ⁢       H   ⁡     [     k   ,   s     ]       ⁢       X     i   ⁡     (   s   )         ⁡     [   k   ]           +     Z   ⁡     [   k   ]               
where i(s)=preamble sequence index used for segment s, X i(s) [k]=preamble OFDMA symbol of segment s, and H[k,s]=channel gain corresponding to the segment s.
 
     The control module  156  determines which segment transmitted the preamble sequence implicitly when the control module  156  detects the preamble sequence. This is because each preamble sequence is unique as identified by a unique preamble sequence index number, and each segment transmits a unique preamble sequence using distinct sub-carriers. 
     Thus, when the control module  156  detects the preamble sequence by selecting the largest correlation value, the control module  156  implicitly selects the segment having maximum channel gain. Thus, when the control module  156  detects the preamble sequence, the control module  156  implicitly detects which segment transmitted the preamble sequence. 
     Occasionally, the input signal may comprise a carrier frequency offset (CFO). The CFO may be fractional or integer. An input signal comprising fractional CFO may be mathematically expressed as follows.
 
 Y[k]=C (ε,0) H[k]X[k]+I (ε, k )+ Z[k] 
 
where ε=ΔfNT represents normalized CFO. Fractional CFO introduces Inter-carrier interference (ICI) as given by the following equation.
 
               I   ⁡     (     ɛ   ,   k     )       =       ∑     r   =   1       N   -   1       ⁢       C   ⁡     (     ɛ   ,   r     )       ⁢     H   ⁡     [       (     (     k   -   r     )     )     N     ]       ⁢     X   ⁡     [       (     (     k   -   r     )     )     N     ]                 
where N equals total number of sub-carriers (e.g., N=1024 in 1024 FFT mode), and
 
     
       
         
           
             
               C 
               ⁡ 
               
                 ( 
                 
                   ɛ 
                   , 
                   r 
                 
                 ) 
               
             
             = 
             
               
                 
                   sin 
                   ⁡ 
                   
                     ( 
                     
                       π 
                       ⁡ 
                       
                         ( 
                         
                           ɛ 
                           - 
                           r 
                         
                         ) 
                       
                     
                     ) 
                   
                 
                 
                   N 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     sin 
                     ⁡ 
                     
                       ( 
                       
                         
                           π 
                           ⁡ 
                           
                             ( 
                             
                               ɛ 
                               - 
                               r 
                             
                             ) 
                           
                         
                         / 
                         N 
                       
                       ) 
                     
                   
                 
               
               ⁢ 
               
                 ⅇ 
                 
                   
                     - 
                     
                       jπ 
                       ⁡ 
                       
                         ( 
                         
                           ɛ 
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                         ) 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       1 
                       - 
                       
                         1 
                         / 
                         N 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     Additionally, the fractional CFO decreases signal to noise ratio (SNR) of the input signal. This is mathematically expressed as follows. 
               E   ⁡     [     SNR   ⁡     (     ɛ   ,   k     )       ]       ≈                C   ⁡     (     ɛ   ,   0     )            2     ⁢     SNR   0             (     1   -            C   ⁡     (     ɛ   ,   0     )            2       )     ⁢     SNR   0       +   1             
where SNR 0  represents average SNR in absence of CFO. SNR decreases as CFO increases.
 
     Since fractional CFO introduces ICI and attenuates the input signal, the fractional CFO adversely affects preamble sequence detection in system  150 . The fractional CFO, however, does not affect the preamble sequence detection significantly. This is because the fractional CFO adds a phase error that is common to all sub-carriers, which does not change the frequency selectivity of the channels. 
     On the other hand, when the CFO is an integer I, a phase error θ introduced by the integer CFO may be common to all k sub-carriers. In that case, the input signal may be mathematically expressed as follows.
 
 Y[k]=e   jθ   H [(( k−l )) N   ]X   i [(( k−l )) N   ]+Z [(( k−l )) N ]
 
     Specifically, the integer CFO causes a cyclic shift of the input signal in the frequency domain. In other words, the integer CFO rotates the input signal in the frequency domain. Accordingly, the correlation module  154  correlates preamble sequences with a shifted version of the input signal as given by the following equation. 
     
       
         
           
             
               C 
               
                 j 
                 , 
                 m 
               
             
             = 
             
               
                 ∑ 
                 
                   k 
                   ∈ 
                   
                     P 
                     
                       s 
                       ⁡ 
                       
                         ( 
                         j 
                         ) 
                       
                     
                   
                 
               
               ⁢ 
               
                 
                   Y 
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                     [ 
                     
                       
                         ( 
                         
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                       N 
                     
                     ] 
                   
                 
                 ⁢ 
                 
                   
                     X 
                     j 
                     * 
                   
                   ⁡ 
                   
                     [ 
                     k 
                     ] 
                   
                 
               
             
           
         
       
     
     Consequently, the control module  156  detects the preamble sequence by selecting a maximum correlation value according to the following equation. 
               (       i   ^     ,     l   ^       )     =       argmax     (     j   ,   m     )       ⁢     {          C     j   ,   m            }               FIG. 5C  shows maximum correlation values normalized by
 
     
       
         
           
             
               ∑ 
               
                 k 
                 ∈ 
                 
                   P 
                   
                     s 
                     ⁡ 
                     
                       ( 
                       0 
                       ) 
                     
                   
                 
               
             
             ⁢ 
             
               
                 
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                       X 
                       0 
                     
                     ⁡ 
                     
                       [ 
                       k 
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                 2 
               
               . 
             
           
         
       
     
     Occasionally, the channel may not be almost frequency flat. That is, the sub-carriers in a channel may not have a common channel gain H. In other words, H[k] may not be independent of k. In that case, the channel gain may vary with frequency of sub-carriers as shown in  FIG. 5D . Such a channel is called highly frequency selective channel. In a highly frequency selective channel, the variation in channel gain significantly changes the phase of sub-carriers and distorts the correlation between transmitted and expected preamble sequences. Consequently, the system  150  cannot reliably detect correct preamble sequences by correlating all of the sub-carriers with each of the preamble sequences. 
     However, the system  150  can estimate a preamble sequence index by partitioning the channel into bands, wherein the channel may be relatively frequency flat, and then correlating on a per-band basis. Specifically, the control module  156  partitions the total number of sub-carriers into a predetermined number of bands. If N denotes a total number of sub-carriers in a channel, the control module  156  divides the channel in to L bands, each comprising N/L consecutive sub-carriers as shown in  FIG. 5D . For example, in 1024 FFT mode, the control module  156  may divide the 1024 sub-carriers into 16 bands, each comprising 64 successive sub-carriers. Thus, band 1 may include sub-carriers 1-64, band 2 may include sub-carriers 65-128, . . . , and band 16 may include sub-carriers 961-1024. 
     Assuming that the channel gain does not vary significantly among the sub-carriers within individual bands although the channel gain varies across the bands, the correlation module  154  performs correlation on a per-band basis. Specifically, the correlation module  154  correlates symbols in modulated sub-carriers in a band with corresponding symbols in a preamble sequence and generates correlation values for the band, which may be called intra-band correlation values. The control module  156  adds the intra-band correlation values and generates a magnitude of a sum of the intra-band correlation values, which may be called a band correlation value. 
     Thus for a preamble sequence, the control module  156  generates L band correlation values. The control module  156  adds the L band correlation values to generate a correlation value for the preamble sequence. Thus, the correlation module  154  performs correlation for all i preamble sequences, and the control module  156  generates i correlation values. The effect of variation in channel gain on the phase of sub-carriers and the consequent distortion in correlation is minimized by correlating on a per-band basis and by generating correlation values based on band correlation values. 
     The control module  156  selects a largest correlation value from the i correlation values. This is mathematically expressed as follows. 
               i   ^     =       argmax   i     ⁢     {       ∑     l   =   0       L   -   1       ⁢            ∑     k   =     l   ⁡     (     N   /   L     )               (     l   +   1     )     ⁢     (     N   /   L     )       -   1       ⁢       Y   ⁡     [   k   ]       ⁢       X   i   *     ⁡     [   k   ]                  }             
The control module  156  compares the largest correlation value to a predetermined threshold. The predetermined threshold is a function of signal strength of the input signal. If the largest correlation value is greater than or equal to the predetermined threshold, the control module  156  determines that a preamble sequence is detected in the input signal. Since each preamble sequence is unique, the control module  156  determines which segment transmitted the preamble sequence implicitly when the control module  156  detects the preamble sequence.
 
     Referring now to  FIG. 6A , a system  160  for detecting a preamble sequence in a mobile station (MS) may be implemented in a physical layer (PHY) module  162  of the MS. The system  160  comprises a differential demodulation module  164 , a correlation module  166 , and a control module  168 . The differential demodulation module  164  receives an input signal transmitted by a base station (BS). The input signal may be mathematically expressed as follows.
 
 Y[k]=H[k]X   i   [k]+Z[k] 
 
where k is sub-carrier index, i is preamble sequence index, Y[k] is received input signal, H[k] is channel gain, Xi[k] is transmit signal, and Z[k] is noise.
 
     Adjacent modulated sub-carriers (i.e., sub-carriers 1, 4, 7, etc.) may have similar channel phase or an unknown differential channel phase that is common to all k sub-carriers. The unknown differential channel phase may be caused by presence of a symbol timing offset, which in turn may be caused by improper symbol timing synchronization. When adjacent modulated sub-carriers have similar channel phase, the channel phase difference between adjacent modulated sub-carriers is nearly zero. 
     On the other hand, when adjacent modulated sub-carriers have an unknown differential channel phase that is common to all k sub-carriers, the channel phase difference between adjacent modulated sub-carriers may be non-zero. When adjacent modulated sub-carriers have similar channel phase or unknown differential channel phase common to all sub-carriers, the sub-carriers are generally referred to as “moderately frequency selective channels.” 
     The differential demodulation module  164  performs a differential demodulation operation on the input signal and generates a differentially demodulated signal. Specifically, the differential demodulation module  164  multiplies a modulated sub-carrier by a complex conjugate of an adjacent modulated sub-carrier located three sub-carriers apart. 
     When the adjacent modulated sub-carriers have similar channel phase, the differentially demodulated signal can be mathematically expressed as follows.
 
 M[k]=Y*[k− 3 ]Y[k]=H[k]H*[k− 3 ]D   i   [k]+{tilde over (Z)}[k]≈|H[k]H*[k− 3 ]|D   i   [k]+{tilde over (Z)}[k] 
 
where Y[k−3] denotes a complex conjugate of a modulated sub-carrier that is three sub-carriers apart from the modulated sub-carrier Y[k]. The complex conjugate is indicated by asterisk or “*”. Since the adjacent modulated sub-carriers have similar channel phase, the channel phase difference between the adjacent modulated sub-carriers is nearly zero. That is,
 
∠( H[k]H*[k− 3])≈0
 
     The correlation module  166  or the control module  168  stores XOR&#39;ed versions of preamble sequences in memory. XOR&#39;ed versions of preamble sequences may also be referred to as derived preamble sequences. An XOR&#39;ed or derived preamble sequence is generated by XORing adjacent bits in the preamble sequence. For example, if one of the 114 preamble sequences in 1024 FFT mode includes bits B 1 , B 2 , B 3 , . . . , B 284 , then an XOR&#39;ed version of that preamble sequence includes bits X 1 , X 2 , X 3 , . . . , X 284 , where X 1 =B 1 xorB 2 , X 2 =B 2 xorB 3 , etc. The derived preamble sequences may be mathematically expressed as follows.
 
 D   i   [k]=X   i   [k]X   i   *[k −3]
 
where the asterisk (i.e., “*”) denotes a complex conjugate. Actually performing complex conjugate operations to generate complex conjugates, however, is unnecessary since complex conjugates of 1 and −1 are 1 and −1, respectively. That is, 1*=1, and (−1)*=−1.
 
     A cross-correlation between the derived preamble sequences is given by the following formula. 
                 max     i   ,     j   ≠   i         ⁢     {         ∑     k   ∈     P     s   ⁡     (   i   )             ⁢         D   i     ⁡     [   k   ]       ⁢       D   j   *     ⁡     [   k   ]               ∑     k   ∈     P     s   ⁡     (   i   )             ⁢              D   i     ⁡     [   k   ]            2         }       ≈     0.1731   ⁢           ⁢   for   ⁢           ⁢   1024   ⁢           ⁢   FFT             FIG. 6B  shows cross-correlation values normalized by
 
               ∑     k   ∈     P     s   ⁡     (   0   )             ⁢              D   0     ⁡     [   k   ]            2           
for 1024 FFT mode.
 
     Since the cross-correlation between the derived preamble sequences is small, the correlation module  166  correlates the differentially demodulated input signals with the derived preamble sequences as follows. 
               C   j     =       ∑     k   ∈     P     s   ⁡     (   j   )             ⁢       M   ⁡     [   k   ]       ⁢       D   j   *     ⁡     [   k   ]                 
The correlation module  166  performs the correlation for all k sub-carriers and j preamble sequences. Thus, in the 1024 FFT mode, the correlation module  166  performs the correlation for all modulated 114 preamble sequences. Since the values of D j [k] (reference to complex conjugate by “*” omitted) are either 1 or −1, effectively M[k]D j [k]=±M[k].
 
     The correlation module  166  generates correlation values and outputs the correlation values to the control module  168 . The correlation values are complex numbers, which have real and imaginary parts. The imaginary parts of the correlation values represent noise in the input signal. The control module  168  disregards the imaginary parts since ∠(H[k]H*[k−3])≈0. 
     The control module  168  selects a correlation value having a largest real part. This is mathematically expressed as follows. 
               i   ^     =       argmax   j     ⁢     {     Re   ⁢     {     C   j     }       }             
The control module  168  compares the largest real part to a predetermined threshold. The predetermined threshold is a function of signal strength of the input signal. If the largest real part is greater than or equal to the predetermined threshold, the control module  168  determines that a preamble sequence is detected in the input signal. As in system  150 , the control module  168  implicitly determines which segment transmitted the preamble sequence when the control module  168  detects the preamble sequence.
 
     On the other hand, when the adjacent modulated sub-carriers have an unknown differential channel phase θ that is common to all k sub-carriers, the demodulated signal generated by the demodulation module  164  is given by the following equation.
 
 M[k]=H[k]H*[k− 3 ]D   i   [k]+{tilde over (Z)}[k]≈e   jθ   |H[k]H*[k− 3 ]|D   i   [k] 
 
where ∠(H[k]H*[k−3])≈θ is not zero.
 
     Since the cross-correlation between the derived preamble sequences is small, the correlation module  166  performs correlation and generates correlation values similar to when the adjacent modulated sub-carriers have similar channel phase. However, because ∠(H[k]H*[k−3])≈θ is not zero, the control module  168  calculates magnitude of the largest correlation value instead of selecting real part of the largest correlation value. That is, the control module  168  does not disregard the imaginary part of the largest correlation value. This is mathematically expressed as follows. 
     
       
         
           
             
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     The control module  168  compares the magnitude of the largest correlation value to a predetermined threshold. The predetermined threshold is a function of signal strength of the input signal. If the magnitude of the largest correlation value is greater than or equal to the predetermined threshold, the control module  168  determines that a preamble sequence is detected in the input signal. As in system  150 , the control module  168  implicitly determines which segment transmitted the preamble sequence when detecting the preamble sequence. 
     As in system  150 , the preamble sequence detection in system  160  is not affected by a fractional CFO present in the input signal. When an integer CFO is present in the input signal, the differential demodulation module  164  differentially demodulates the input signal having the integer CFO. The correlation module  166  correlates derived preamble sequences with differentially demodulated input signal having the integer CFO. The control module  168  performs preamble detection according to the channel phase of adjacent modulated sub-carriers.  FIG. 6C  shows maximum correlation values normalized by 
     
       
         
           
             
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     Occasionally, the input signal may have a small symbol timing offset due to improper symbol timing synchronization, which is performed when the MS is powered up. The symbol timing offset may cause inter-symbol interference (ISI). Additionally, the symbol timing offset may cause an inter-carrier interference (ICI). The input signal having a symbol timing offset can be mathematically expressed as follows. 
               Y   ⁡     [   k   ]       =         exp   ⁡     (       j   ⁢           ⁢   2   ⁢   π   ⁢           ⁢   τ   ⁢           ⁢   k     N     )       ⁢     H   ⁡     [   k   ]       ⁢       X   i     ⁡     [   k   ]         +     I   ⁡     (     τ   ,   k     )       +     Z   ⁡     [   k   ]               
where τ represents symbol timing offset and I(τ,k) represents ISI and ICI.
 
     Specifically, the symbol timing offset introduces an extra phase offset among the sub-carriers. The phase offset may increase linearly as the sub-carrier index k increases. In that case, system  160  may perform better than system  150 . Additionally, the extra phase offset introduced by the symbol timing offset appears in the differentially demodulated signal generated by the differential demodulation module  164 . Therefore, system  160  utilizing magnitude of a largest correlation value may perform better than system  160  utilizing largest real part of a correlation value. 
     The differentially demodulated signal with the extra phase offset is mathematically expressed as follows. 
               M   ⁡     [   k   ]       =         exp   ⁡     (       j   ⁢           ⁢   6   ⁢   π   ⁢           ⁢   τ     N     )       ⁢     H   ⁡     [   k   ]       ⁢       H   *     ⁡     [     k   -   3     ]       ⁢       D   i     ⁡     [   k   ]         +       Z   ′     ⁡     [   k   ]               
If the linearly increasing phase offset is too large, the control module  168  calculates magnitude of the largest correlation value instead of selecting a largest real part of a correlation value.
 
     In system  160  utilizing magnitude of the largest correlation value, the control module  168  estimates symbol timing offset as follows. After calculating a magnitude of a largest correlation value, the control module  168  measures a phase of the correlation value having the largest magnitude. The control module  168  calculates symbol timing offset by multiplying the phase of the correlation value having the largest magnitude by a ratio of N to 3*2π. Mathematically, this may be expressed as follows. 
               C   j     =       ∑     k   ∈     P     s   ⁡     (   j   )             ⁢       M   ⁡     [   k   ]       ⁢       D   j   *     ⁡     [   k   ]                         i   ^     =       argmax   j     ⁢     {          C   j          }                     τ   ^     =       N     6   ⁢   π       ⁢   ∠   ⁢           ⁢     C   i             
where ∠C î  is the phase angle of the correlation value having the largest magnitude, and N is total number of sub-carriers in an FFT mode (e.g., N=1024 in 1024 FFT mode). Additionally, the multiplier 3 is used to multiply 2π since every third sub-carrier is modulated. Thus, the multiplier may be P when every P th  sub-carrier is modulated, where P is an integer greater than or equal to 1.
 
     Referring now to  FIGS. 7A-7B , a method  200  for detecting a preamble sequence begins at step  202 . A correlation module  154  receives an input signal having signals modulated using orthogonal frequency division multiplexing (OFDM) in step  203 . A control module  156  determines whether a channel is almost frequency flat in step  204 . If true, a control module  156  determines in step  206  if an integer carrier frequency offset (CFO) is present in the input signal. If the integer CFO is absent, the correlation module  154  correlates the signals with preamble sequences in step  208 . If the integer CFO is present, however, the correlation module  154  correlates the signals shifted by the integer CEO with preamble sequences in step  210 . 
     The control module  156  selects in step  212  a largest correlation value from the correlation values generated by the correlation module  154 . The control module  156  checks if a magnitude of the largest correlation value exceeds a predetermined threshold in step  214 . If false, the control module  156  determines in step  216  that no preamble sequence is detected in the input signal, and the method  200  ends in step  218 . 
     If true, however, the control module  156  determines that a preamble sequence is detected in the input signal in step  220 . Since each preamble sequence is unique and since each segment of each base station transmits using distinct sub-carriers, the control module  156  implicitly determines in step  224  which segment of a base station transmitted the detected preamble sequence. The method  200  ends in step  218 . 
     If, however, the result of step  203  is false, the control module  156  divides the channel into L bands in step  226 . The correlation module  154  correlates on a per-band basis and generates intra-band correlation values in step  228 . The control module  156  adds the intra-band correlation values and generates a magnitude of a sum of the intra-band correlation values to generate a band correlation value in step  230 , thereby generating L band correlation values for each preamble sequence. 
     The control module  156  adds the band correlation values for a preamble sequence to generate a correlation value for the preamble sequence in step  232 , thereby generating i correlation values for i preamble sequences in step  232 . Steps starting at step  212  are performed thereafter. 
     Referring now to  FIG. 8 , a method  250  for detecting a preamble sequence when moderately frequency selective channels have substantially the same channel phase begins at step  252 . A differential demodulation module  164  receives an input signal having signals modulated using orthogonal frequency division multiplexing (OFDM) in step  254 . The differential demodulation module  164  differentially demodulates the signals in step  256 . 
     A control module  168  determines in step  258  if an integer carrier frequency offset (CFO) is present in the input signal. If the integer CFO is absent, a correlation module  166  correlates the differentially demodulated signals with derived preamble sequences in step  260 . If the integer CFO is present, however, the correlation module  166  correlates in step  264  the derived preamble sequences with the differentially demodulated signals that include the shift caused by the integer CFO. 
     The control module  168  selects in step  266  a largest real part of correlation values generated by the correlation module  166 . The control module  168  checks if the largest real part is greater than or equal to a predetermined threshold in step  268 . If false, the control module  168  determines in step  270  that no preamble sequence is detected in the input signal, and the method  250  ends in step  272 . 
     If true, however, the control module  168  determines that a preamble sequence is detected in the input signal in step  274 . Since each preamble sequence is unique and since each segment of each base station transmits using distinct sub-carriers, the control module  168  implicitly determines in step  276  which segment of a base station transmitted the detected preamble sequence. The method  250  ends in step  272 . 
     Referring now to  FIG. 9 , a method  350  for detecting a preamble sequence when moderately frequency selective channels have substantially the same differential channel phase begins at step  352 . A differential demodulation module  164  receives an input signal having signals modulated using orthogonal frequency division multiplexing (OFDM) in step  354 . The differential demodulation module  164  differentially demodulates the signals in step  356 . 
     A control module  168  determines in step  358  if an integer carrier frequency offset (CFO) is present in the input signal. If the integer CFO is absent, a correlation module  166  correlates the differentially demodulated signals with derived preamble sequences in step  360 . If the integer CFO is present, however, the correlation module  166  correlates in step  364  the derived preamble sequences with the differentially demodulated signals that include the shift caused by the integer CFO. 
     The control module  168  selects in step  366  a largest correlation value from the correlation values generated by the correlation module  166 . The control module  168  checks if a magnitude of the largest correlation value is greater than or equal to a predetermined threshold in step  368 . If false, the control module  168  determines in step  370  that no preamble sequence is detected in the input signal, and the method  350  ends in step  372 . 
     If true, however, the control module  168  determines that a preamble sequence is detected in the input signal in step  374 . Since each preamble sequence is unique and since each segment of each base station transmits using distinct sub-carriers, the control module  168  implicitly determines in step  376  which segment of a base station transmitted the detected preamble sequence. The method  350  ends in step  372 . 
     Although every third sub-carrier is modulated as described in the systems and methods disclosed in this disclosure, skilled artisans can appreciate that the systems and methods disclosed herein may be implemented by modulating every P th  sub-carrier, where P is an integer greater than 1. Thus, if P=2, the systems and methods disclosed herein may be implemented by modulating every other (i.e., alternate) sub-carrier, etc. 
     Referring now to  FIGS. 10A-10B , various exemplary implementations incorporating the teachings of the present disclosure are shown. For example, the teachings of the present disclosure may be implemented in communication systems based on WiMAX standards, which provide mobile wireless connectivity without the need for a direct line-of-sight with a base station. The WiMAX standards “Stage 2 Verification And Validation Readiness Draft,” Release 1 dated Aug. 8, 2006 and “Stage 3 Verification And Validation Readiness Draft” Release 1 dated Aug. 8, 2006 are incorporated herein by reference in their entirety. 
     Referring now to  FIG. 10A , the teachings of the disclosure may be implemented in a WiMAX interface  452  of a vehicle  446 . The vehicle  446  may include a vehicle control system  447 , a power supply  448 , memory  449 , a storage device  450 , and the WiMAX interface  452  and associated antenna  453 . The vehicle control system  447  may be a powertrain control system, a body control system, an entertainment control system, an anti-lock braking system (ABS), a navigation system, a telematics system, a lane departure system, an adaptive cruise control system, etc. 
     The vehicle control system  447  may communicate with one or more sensors  454  and generate one or more output signals  456 . The sensors  454  may include temperature sensors, acceleration sensors, pressure sensors, rotational sensors, airflow sensors, etc. The output signals  456  may control engine operating parameters, transmission operating parameters, suspension parameters, etc. 
     The power supply  448  provides power to the components of the vehicle  446 . The vehicle control system  447  may store data in memory  449  and/or the storage device  450 . Memory  449  may include random access memory (RAM) and/or nonvolatile memory such as flash memory, phase change memory, or multi-state memory, in which each memory cell has more than two states. The storage device  450  may include an optical storage drive, such as a DVD drive, and/or a hard disk drive (HDD). The vehicle control system  447  may communicate externally using the WiMAX interface  452 . 
     Referring now to  FIG. 10B , the teachings of the disclosure can be implemented in a WiMAX interface  468  of a cellular phone  458 . The cellular phone  458  includes a phone control module  460 , a power supply  462 , memory  464 , a storage device  466 , and a cellular network interface  467 . The cellular phone  458  may include the WiMAX interface  468  and associated antenna  469 , a microphone  470 , an audio output  472  such as a speaker and/or output jack, a display  474 , and a user input device  476  such as a keypad and/or pointing device. 
     The phone control module  460  may receive input signals from the cellular network interface  467 , the WiMAX interface  468 , the microphone  470 , and/or the user input device  476 . The phone control module  460  may process signals, including encoding, decoding, filtering, and/or formatting, and generate output signals. The output signals may be communicated to one or more of memory  464 , the storage device  466 , the cellular network interface  467 , the WiMAX interface  468 , and the audio output  472 . 
     Memory  464  may include random access memory (RAM) and/or nonvolatile memory such as flash memory, phase change memory, or multi-state memory, in which each memory cell has more than two states. The storage device  466  may include an optical storage drive, such as a DVD drive, and/or a hard disk drive (HDD). The power supply  462  provides power to the components of the cellular phone  458 . 
     Those skilled in the art can now appreciate from the foregoing description that the broad teachings of the disclosure can be implemented in a variety of forms. Therefore, while this disclosure includes particular examples, the true scope of the disclosure should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, the specification and the following claims.