SYSTEM AND METHOD FOR FREQUENCY SYNCHRONIZATION OF DOPPLERSHIFTED SUBCARRIERS

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First Claim
1. A method for frequency synchronization in an OFDM communication system, comprising:
 receiving a first Orthogonal Frequency Division Multiplexing (OFDM) signal comprising a first plurality of Dopplershifted OFDM subcarriers;
receiving a second Orthogonal Frequency Division Multiplexing (OFDM) signal comprising a second plurality of Dopplershifted OFDM subcarriers of the subband;
calculating an autocorrelation for the first OFDM signal;
calculating a respective mutual correlation between the first OFDM signal and the second OFDM signal;
calculating an average frequency shift factor based on the autocorrelation and the mutual correlation;
calculating, for each Dopplershifted OFDM subcarrier of the first OFDM signal and the second OFDM signal, a frequency offset by multiplying the average frequency shift factor by a frequency index of the each subcarrier, the frequency offset for at least two Dopplershifted OFDM subcarriers of the subband being different from each other; and
compensating the frequency offset for said each Dopplershifted OFDM subcarrier for the frequency synchronization.
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Abstract
A method includes receiving an Orthogonal Frequency Division Multiplexing (OFDM) signal comprising a plurality of Dopplershifted OFDM subcarriers and determining frequencyshift data corresponding to the plurality of Dopplershifted OFDM subcarriers. The determining includes calculating frequencyshift data for each Dopplershifted OFDM subcarrier of the plurality of Dopplershifted OFDM subcarriers, thereby yielding a plurality of subcarrierspecific frequencyshift values and calculating an average of the plurality of subcarrierspecific frequencyshift values. The method further includes frequency shifting each subcarrier of the plurality of Dopplershifted OFDM subcarriers by a value based on the determined frequencyshift data multiplied by a frequency index of each subcarrier.
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14 Claims
 1. A method for frequency synchronization in an OFDM communication system, comprising:
receiving a first Orthogonal Frequency Division Multiplexing (OFDM) signal comprising a first plurality of Dopplershifted OFDM subcarriers; receiving a second Orthogonal Frequency Division Multiplexing (OFDM) signal comprising a second plurality of Dopplershifted OFDM subcarriers of the subband; calculating an autocorrelation for the first OFDM signal; calculating a respective mutual correlation between the first OFDM signal and the second OFDM signal; calculating an average frequency shift factor based on the autocorrelation and the mutual correlation; calculating, for each Dopplershifted OFDM subcarrier of the first OFDM signal and the second OFDM signal, a frequency offset by multiplying the average frequency shift factor by a frequency index of the each subcarrier, the frequency offset for at least two Dopplershifted OFDM subcarriers of the subband being different from each other; and compensating the frequency offset for said each Dopplershifted OFDM subcarrier for the frequency synchronization.  View Dependent Claims (2, 3, 4, 5)
 6. One or more nontransitory computerreadable storage media embodying logic when executed by a processor is configured to:
receiving a first Orthogonal Frequency Division Multiplexing (OFDM) signal comprising a first plurality of Dopplershifted OFDM subcarriers of a subband; receiving a second Orthogonal Frequency Division Multiplexing (OFDM) signal comprising a second plurality of Dopplershifted OFDM subcarriers of the subband; calculating an autocorrelation for the first OFDM signal; calculating a respective mutual correlation between the first OFDM signal and the second OFDM signal; calculating an average frequency shift factor based on the autocorrelation and the mutual correlation; calculate, for each Dopplershifted OFDM subcarrier of the first OFDM signal and the second OFDM signal, a frequency offset by multiplying the average frequency shift factor by a frequency index of the each subcarrier, the frequency offset for at least two Dopplershifted OFDM subcarriers of the subband being different from each other; and compensate the frequency offset for each said Dopplershifted OFDM subcarrier for the frequency synchronization.  View Dependent Claims (7, 8, 9, 10)
 11. A mobile system comprising:
an Orthogonal Frequency Division Multiplexing (OFDM) receiver configured to receive a first OFDM signal comprising a first plurality of Dopplershifted OFDM subcarriers of a subband and a second OFDM signal comprising a second plurality of Dopplershifted OFDM subcarriers of the subband; a subcarrier frequencyshift estimator interoperably coupled to the OFDM receiver, the subcarrier frequencyshift estimator configured to; calculating an autocorrelation for the first OFDM signal, calculating a respective mutual correlation between the first OFDM signal and the second OFDM signal, and calculating an average frequency shift factor based on the autocorrelation and the mutual correlation; and a frequency shift bank interoperably coupled to the OFDM receiver and the subcarrier frequencyshift estimator, the frequency shift bank configured to; calculate, for each Dopplershifted OFDM subcarrier of the first OFDM signal and the second OFDM signal, a frequency offset by multiplying the average frequency shift factor by a frequency index of the each subcarrier, the frequency offset for at least two Dopplershifted OFDM subcarriers of the subband being different from each other, and compensate the frequency offset for said each Dopplershifted OFDM subcarrier for the frequency synchronization.  View Dependent Claims (12, 13, 14)
1 Specification
This application is a continuation of U.S. application Ser. No. 16/117,215, filed on Aug. 30, 2018, which is a continuation of U.S. application Ser. No. 14/801,146, filed on Jul. 16, 2015, now issued as U.S. Pat. No. 10,091,044 on Oct. 2, 2018, which claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Application No. 62/025,650, filed July 17, 2014, entitled “System and Method for Frequency Synchronization of DopplerShifted Subcarriers”, which are herein incorporated by reference.
The present invention relates generally to wireless communications, and more particularly, but not by way of limitation, to systems and methods for frequency synchronization of Dopplershifted subcarriers.
A wireless communications system may use an Orthogonal Frequency Division Multiplexing (“OFDM”) transmission scheme. In a wireless communication system that employs an OFDM transmission scheme, a digital data stream is divided into multiple substreams and each substream is sent in parallel over a different subcarrier frequency. The subcarrier frequencies a re chosen such that the subcarriers are orthogonal to one another. Because the data is transmitted over multiple frequencies, systems that employ an OFDM transmission scheme (“OFDM systems”) may generally be considered to be in the category of multicarrier systems, as opposed to singlecarrier systems, in which data is transmitted on one carrier frequency.
One advantage of OFDM is the ability to efficiently transmit data over frequencyselective channels by employing Inverse Fast Fourier transform (“IFFT”) and Fast Fourier transform (“FFT”) algorithms. OFDM receivers can use digital signal processors and a relatively simple channelequalization method (e.g., a onetap multiplier for each tone) as opposed to more complex equalizers typically used by singlecarrier receivers. The orthogonality of OFDM subcarriers also increases spectral efficiency and enhances resilience to multipath fading. However, despite such advantages, OFDM systems may be more timingoffset sensitive than singlecarrier systems. Also, demodulation of a signal with carrierfrequency offset can cause a high biterror rate and may degrade performance of a symbol synchronizer in an OFDM system.
In one embodiment, a method includes receiving an Orthogonal Frequency Division Multiplexing (OFDM) signal comprising a plurality of Dopplershifted OFDM subcarriers and determining frequencyshift data corresponding to the plurality of Dopplershifted OFDM subcarriers. The determining includes calculating frequencyshift data for each Dopplershifted OFDM subcarrier of the plurality of Dopplershifted OFDM subcarriers, thereby yielding a plurality of subcarrierspecific frequencyshift values and calculating an average of the plurality of subcarrierspecific frequencyshift values. The method further includes frequency shifting each subcarrier of the plurality of Dopplershifted OFDM subcarriers by a value based on the determined frequencyshift data multiplied by a frequency index of each subcarrier.
In one embodiment, one or more nontransitory computerreadable storage media embodying logic when executed by a processor is configured to receive an Orthogonal Frequency Division Multiplexing (OFDM) signal comprising a plurality of Dopplershifted OFDM subcarriers and determine frequencyshift data corresponding to the plurality of Dopplershifted OFDM subcarriers. The determination includes calculation of frequencyshift data for each Dopplershifted OFDM subcarrier of the plurality of Dopplershifted OFDM subcarriers, thereby yielding a plurality of subcarrierspecific frequencyshift values and calculation of an average of the plurality of subcarrierspecific frequencyshift values. One or more nontransitory computerreadable storage media is further configured to frequency shift each subcarrier of the plurality of Dopplershifted OFDM subcarriers by a value based on the determined frequencyshift data multiplied by a frequency index of each subcarrier.
In one embodiment, a system includes an Orthogonal Frequency Division Multiplexing (OFDM) receiver configured to receive an OFDM signal comprising a plurality of Dopplershifted OFDM subcarriers and a subcarrier frequencyshift estimator interoperably coupled to the OFDM receiver, the subcarrier frequencyshift estimator is configured to determine frequencyshift data corresponding to the plurality of Dopplershifted OFDM subcarriers. The determination includes calculation of frequencyshift data for each Dopplershifted OFDM subcarrier of the plurality of Dopplershifted OFDM subcarriers, thereby yielding a plurality of subcarrierspecific frequencyshift values and calculation of an average of the plurality of subcarrierspecific frequencyshift values. The system further includes a frequency shift bank interoperably coupled to the OFDM receiver and the subcarrier frequencyshift estimator, wherein the frequency shift bank is configured to frequency shift each subcarrier of the plurality of Dopplershifted OFDM subcarriers by a value based on the determined frequencyshift data multiplied by a frequency index of each subcarrier.
A more complete understanding of the method and apparatus of the various embodiments may be obtained by reference to the following Detailed Description when taken in conjunction with the accompanying Drawings wherein:
Methods and systems have been proposed for OFDM timing and frequency synchronization. However, many frequencysynchronization schemes fail to accurately compensate for different amounts of Doppler shift that can be experienced among OFDM subcarriers in wireless communications. Like reference numerals correspond to like components throughout the following Detailed Description and accompanying Drawings.
where v is a velocity, for example, of a mobile station relative to a base station, c is the speed of light, and f is a radio frequency the mobile station receives. The amount of Doppler shift experienced by a particular subcarrier is thus seen to be proportional to the frequency of the subcarrier.
In
f_{κ}=κ+κ·δ (1A)
For example, consider a mobile station on a highspeed train moving toward a cellular tower or a base station at 400 km/hr. If the mobile station is on a Long Term Evolution (“LTE”) network, where the subcarrier spacing at a basestation transmitter is 15 kHz with primarysynchronizationsignal channel (“PSCH”) and secondarysynchronizationsignal channel (“SSCH”) consisting of 63 subcarriers with a central DC carrier, the amount of Doppler shift could amount to as much as +620 Hz for the 63rd subcarrier. Conversely, if the mobile station moves away from the base station at 400 km/hr, the 63rd subcarrier could experience as much as −620 Hz of Doppler shift.
In an OFDM system, the received signal samples r(n) affected by Doppler shift may be expressed as follows:
where there are 2K+1 subcarriers, S_{κ }is a modulation value for each subcarrier at an IFFT stage in the transmitter, H_{κ }is a transfer function of a channel at the Kth carrier frequency, N is the FFT size, κ is the carrier index, and a normalized frequencytocarrier spacing κ·δ denotes the normalized subcarrier frequency offset to the carrier spacing due to Doppler shift, and δ is a factor related to the velocity of the mobile station relative to the base station.
In a typical embodiment, the DSP 340 is operable to frequencysynchronize Dopplershifted OFDM subcarriers. To this end, a typical embodiment of the DSP 340 includes a subcarrier frequencyshift estimator (“SCFS estimator”) 350 operably coupled to the A/D converter 330, a cyclicprefix remover 360 operably coupled to the A/D converter 330, a serialtoparallel converter (“SPC”) 370 operably coupled to the cyclic prefix remover 360, and a frequencyshift bank 380 operably coupled to the SCFS estimator 350. The DSP 340 also includes a 2K+1 subcarrier and N point complex FFT processor 390 operably coupled to the frequencyshift bank 380 and the SPC 370. The DSP 340 also includes a paralleltoserial converter (“PSC”) 394 operably coupled to the FFT processor 390.
In a typical embodiment, the SCFS estimator 350 receives digitalsample data from the A/D converter 330, generates subcarrier frequencyoffset information related thereto, and provides the subcarrier frequencyoffset information to the frequencyshift bank 380. The cyclic prefix remover 360 removes cyclic prefixes from OFDM bit streams and selectively saves and discards the cyclic prefixes. The SPC 370 converts serial data into parallel data. In a typical embodiment, the frequency shift bank 380 receives the subcarrier frequencyoffset information from the SCFS estimator 350 and shifts corresponding OFDM subcarrier frequencies based on the subcarrier frequencyoffset information received from the SCFS estimator 350. The FFT processor 390 executes FFT algorithms, while the PSC 394 converts parallel data into serial data. Although exemplary components of the DSP 340 are described herein as logically distinct, in some embodiments, various components of the DSP 340 may be implemented with shared resources and may be implemented in hardware, software, firmware, or any suitable combination thereof, or in any other suitable manner.
When the OFDM signal expressed in Equation (2) is input, for example, into an FFT processor with a repeated period (e.g., a double OFDM symbol or an OFDM symbol plus a cyclic prefix), the result may be expressed as follows:
where
where R_{1q }and R_{2q }are FFT outputs of first and second (repeated) period for a qth subcarrier, respectively, at the receiver.
Further, in view of Equations (3), (4), and (5), in a typical embodiment, the SCFS estimator 350 applies the BPF 420 filter before the FFT processor 430, and the FFT processor 430 produces, to the qth subcarrier, the following:
Further, for an additive white Gaussian noise (“AWGN”) channel environment, Equations (6) and (7) may be expressed as:
Y_{1q}=R_{1q}+W_{1q} (9)
Y_{2q}=R_{2q}+ω_{2q}=R_{1q}e^{2πjqδ}+W_{2q} (10)
where W_{1q }and W_{2q }are additive white Gaussian noises within the first and second periods, respectively, on the qth subcarrier channel.
A maximum likelihood estimate {circumflex over (δ)} of a Doppler frequency shift factor δ at subcarrier channel q may be expressed as follows:
As such, in a typical embodiment, the SCFS estimator 350 calculates the maximum likelihood estimate {circumflex over (δ)}_{s }of an entiresystem Doppler frequency shift factor δ_{s }by averaging the maximum likelihood estimates of Doppler frequency shift factor {circumflex over (δ)} over all channels as follows:
In a typical embodiment, the SCFS estimator 350 calculates the frequency offset of each subcarrier, based, for example, on a discrete Fourier transform (“DFT”) of each subcarrier channel on first repeat period Y_{1q }and second repeat period Y_{2q }by multiplying the average maximum likelihood estimate of the Doppler frequency shift factor {circumflex over (δ)}_{s }by κ, where κ is the subcarrier channel index.
In a typical embodiment, the SCFS estimator 350 provides the frequency offset of each subcarrier to the frequencyshift bank 380. The frequencyshift bank 380 uses the frequency offsets to correspondingly dynamically shift the subcarrier frequencies of the FFT processor 390 to compensate for the Doppler shift.
The system 300 provides frequency synchronization of Dopplershifted OFDM subcarriers based on either an OFDM symbol and a repeated OFDM symbol or based on a cyclic prefix and a corresponding portion of an OFDM symbol. In the former case, the entire symbol is repeated. In the latter case, an effective portion of the symbol is sufficiently repeated by the cyclic prefix.
The process 500 starts at block 505. At block 510, a first OFDM symbol is received. At block 514, subcarriers of the first OFDM symbol are bandpass filtered, for example, via the BFB 420. At block 518, an FFT value of the first symbol R_{1q }is calculated, for example, according to Equation (6). At block 522, a second OFDM symbol is received. At block 526, subcarriers of the second OFDM symbol are bandpass filtered, for example, via the BFB 420. At block 530, an FFT value of the second symbol R_{2q }is calculated according to Equation (7). At block 534, the maximum likelihood estimate {circumflex over (δ)}_{s }of the entiresystem Doppler frequency shift factor δ_{s }is calculated based, for example, on R_{1q }and R_{2q}, white Gaussian noises, and an average of maximum likelihood estimates {circumflex over (δ)} of the Doppler frequency shift factor δ over all channels, according to Equations (11) and (12). In a typical embodiment, the maximum likelihood estimate {circumflex over (δ)}_{s }of the entiresystem Doppler frequency shift factor δ_{s }is calculated, for example, via the SCFS estimator 350. At block 538, the frequency offset is calculated for each subcarrier by multiplying by κ the maximum likelihood estimate {circumflex over (δ)}_{s}, where κ is the subcarrier channel index. At block 542, the subcarriers of the FFT processor 390 are shifted by their respective frequency offsets, for example, via the frequencyshift bank 380. The process 500 ends at block 550.
The process 600 starts at block 605. At block 610, a first OFDM symbol is received. At block 614, the cyclic prefix from the first OFDM symbol is removed and saved, for example, by the cyclic prefix remover 360. At block 618, the subcarriers of the first OFDM symbol are bandpass filtered, for example, via the BFB 420. At block 622, an FFT value of the first symbol R_{1q }is calculated according to Equation (6). At block 626, the cyclic prefix of the symbol is bandpass filtered, for example, via the BFB 420. At block 630, an FFT value of the cyclic prefix R_{2q }is calculated, for example, according to Equation (7). At block 634, a maximum likelihood estimate {circumflex over (δ)}_{s }of the entiresystem Doppler frequency shift factor δ_{s }is calculated based on, for example, R_{1q }and R_{2q}, white Gaussian noises, and an average of maximum likelihood estimates {circumflex over (δ)} of the Doppler frequency shift factor δ over all channels, according to Equations (11) and (12). In a typical embodiment, the maximum likelihood estimate {circumflex over (δ)}_{s }of the entiresystem Doppler frequency shift factor for δ_{s }is calculated, for example, via the SCFS estimator 350. At block 638, the frequency offset for each subcarrier is calculated by multiplying by κ the maximum likelihood estimate {circumflex over (δ)}_{s}, where κ is the subcarrier channel index. At block 642, the subcarriers of the FFT processor are shifted by their respective frequency offsets, for example, via the frequency shift bank 380. The process 600 ends at block 650.
In a typical embodiment, the DSP 740 is operable to frequencysynchronize Dopplershifted OFDM subcarriers. To this end, a typical embodiment of the DSP 740 includes the SCFS estimator 750 operably coupled to the A/D converter 330, a cyclicprefix remover 360 operably coupled to the A/D converter 330, a serialtoparallel converter (“SPC”) 370 operably coupled to the cyclic prefix remover 360, and a frequencyshift bank 380 operably coupled to the SCFS estimator 350. The DSP 740 also includes a 2K+1 subcarrier and N point complex FFT processor 390 operably coupled to the frequencyshift bank 380 and the SPC 370. The DSP 740 also includes a paralleltoserial converter (“PSC”) 394 operably coupled to the FFT processor 390. Although exemplary components of the DSP 740 are described herein as logically distinct, in some embodiments, various components of the DSP 740 may be implemented with shared resources and may be implemented in hardware, software, firmware, or any suitable combination thereof, or in any other suitable manner.
The mutual correlation Γ and autocorrelation Γ_{0 }of the OFDM signal of Equation (2) may be expressed, respectively, as follows:
For Doppler shifts, the Doppler frequency shift factor δ in Equations (13) and (14) is generally <<1.
If X_{κ}^{2 }and H_{κ}^{2 }in Equations (13) and (14) are the same for all subcarrier channels, the mutual and autocorrelation Equations (13) and (14) for double OFDM symbols may be expressed as follows:
It therefore follows that the mutual correlation may be expressed as follows:
Γ=Γ_{0}·sin c[π(2K+1)δ] (17)
where
is a sin c function that has a maximum value of 1 at δ=0. When δ=0, there is no frequency offset and the mutual correlation of the first and second OFDM symbols is equal to the autocorrelation of the first OFDM symbol.
The process 900 starts at block 905. At block 910, a first OFDM symbol is received. At block 918, an autocorrelation value of the first OFDM symbol is calculated, for example, by the correlator 830. At block 922, a second OFDM symbol is received. At block 930, the respective mutual correlations between the first OFDM symbol and the second OFDM symbol are calculated. At block 934, the Doppler frequency shift factor δ is calculated from Equation (17) using the mutual correlation between the first symbol and the second symbol (Γ) and the autocorrelation of the first symbol (Γ_{0}). At block 938, a frequency offset for each subcarrier is calculated by multiplying by κ the Doppler frequency shift factor δ, where κ is the subcarrier channel index. At block 942, the subcarriers of the FFT processor are shifted by their respective frequency offsets, for example, via the frequency shift bank 380. The process 900 ends at block 950.
In a typical embodiment, the DSP 1040 is operable to frequencysynchronize Dopplershifted OFDM subcarriers. To this end, a typical embodiment of the DSP 1040 includes the SCFS estimator 1050 operably coupled to the A/D converter 330, a cyclicprefix remover 360 operably coupled to the A/D converter 330, a serialtoparallel converter (“SPC”) 370 operably coupled to the cyclic prefix remover 360, and a frequencyshift bank 380 operably coupled to the SCFS estimator 350. The DSP 1040 also includes a 2K+1 subcarrier and N point complex FFT processor 390 operably coupled to the frequencyshift bank 380 and the SPC 370. The DSP 1040 also includes a paralleltoserial converter (“PSC”) 394 operably coupled to the FFT processor 390. Although exemplary components of the DSP 1040 are described herein as logically distinct, in some embodiments, various components of the DSP 1040 may be implemented with shared resources and may be implemented in hardware, software, firmware, or any suitable combination thereof, or in any other suitable manner.
OFDM subcarriers are typically not orthogonal to each other within a Cyclic Prefix (“CP”) because a CP is typically shorter than one OFDM symbol. Therefore, the summation over time (n) in Equations (13) and (14) cannot rely on subcarrier orthogonality for CPs. However, one bandpass filter is applied to every subcarrier channel before the correlator 1130 as shown in
where Γ^{q }and Γ_{0}^{q }are the mutual correlation and autocorrelation of qth subcarrier, respectively. And it should be further appreciated, then, that the maximum likelihood estimate {circumflex over (δ)} of the Doppler frequency shift factor δ at subcarrier channel q may be expressed as follows:
An estimate of the maximum likelihood estimate {circumflex over (δ)}_{s }of the entiresystem Doppler frequency shift factor δ_{s }with 2K+1 subcarriers may be expressed as follows:
21)
The process 1200 starts at block 1205. At block 1210, an OFDM symbol is received. At block 1214, the cyclic prefix is removed and saved, for example, by the cyclic prefix remover 360. At block 1216, the subcarriers of the OFDM symbol and the cyclic prefix are bandpass filtered, for example, via the BFB 1120. At block 1218, an autocorrelation is calculated for each subcarrier of the cyclic prefix. At block 1230, respective mutual correlations are calculated between each subcarrier of the cyclic prefix and the respective subcarrier of the symbol. At block 1234, the maximum likelihood estimate {circumflex over (δ)}_{s }of the entiresystem Doppler frequency shift factor δ_{s }is calculated from Equation (21) using the respective mutual correlations (block 1230) as Γ and using the autocorrelation (block 1218) as Γ_{0}. At block 1238, a frequency offset is calculated for each subcarrier by multiplying by κ the maximum likelihood estimate {circumflex over (δ)}_{s}, where κ is the subcarrier channel index. At block 1242, the subcarriers of the FFT processor 390 are shifted by their respective frequency offsets, for example, via the frequencyshift bank 380. The process 1200 ends at block 1250.
Since Equations (20) and (21) are applicable to repeated OFDM symbols as well as to a symbol and its cyclic prefix, another exemplary operational process for the system 1000 (or any other suitable system) includes synchronization of Dopplershifted OFDM subcarriers based on a repeated OFDM symbol, with the first OFDM symbol being treated in a like manner as the cyclic prefix is treated in the process 1200 and the second (i.e., repeated) OFDM symbol being treated in a like manner as the OFDM symbol is treated in the process 1200.
In a typical embodiment, the DSP 1340 is operable to frequencysynchronize Dopplershifted OFDM subcarriers. To this end, a typical embodiment of the DSP 1340 includes the SCFS estimator 1350 operably coupled to the A/D converter 330, a cyclicprefix remover 360 operably coupled to the A/D converter 330, a serialtoparallel converter (“SPC”) 370 operably coupled to the cyclic prefix remover 360, and a frequencyshift bank 380 operably coupled to the SCFS estimator 350. The DSP 1340 also includes a 2K+1 subcarrier and N point complex FFT processor 390 operably coupled to the frequencyshift bank 380 and the SPC 370. The DSP 1340 also includes a paralleltoserial converter (“PSC”) 394 operably coupled to the FFT processor 390. Although exemplary components of the DSP 1340 are described herein as logically distinct, in some embodiments, various components of the DSP 1340 may be implemented with shared resources and may be implemented in hardware, software, firmware, or any suitable combination thereof, or in any other suitable manner.
where N_{m }is the measured length of the OFDM symbol. The mutual correlation is measured within a CP period length. In
where L is a window length of measurement for the mutual correlation, e^{2πjκ′(1+δ)N}^{g}^{/N }is a phase shift due to the CP insertion preceding the second OFDM symbol, and X_{1κ} and X_{2κ}* are from first and second OFDM symbols, respectively, and it should be appreciated that X_{1κ} and X_{2κ}* are independent of each other. Further, it should be appreciated that if 0≤m<N_{g}, r(n) is within the first OFDM symbol while a part of r(n+N) is within the second OFDM symbol, and that the mutual correlation of r(n) and r(n+N) is larger, and may be expressed as:
If m=0, both r(n) and r(n+N) are within the first OFDM symbol, even at L=N_{g}. For m=0 and L=N_{g}, the mutual correlation of r(n) and r(n+N) is largest and, thus, the position of m=0, L=CP length N_{g }and the measured length N_{m }of the OFDM symbol may be found when the mutual correlation Γ achieves maximum value.
The process 1500 starts at step 1505. At block 1510, a sampling window length is set to 2·N+N_{g }in order to accommodate a CP and the copied part of the OFDM symbol. At block 1514, the system 1300 sets the measurement window such that L<N_{g }and the interval of the two signals ΔT=N. At block 1518, the system 1300 changes the starting point m to find a maximum value of mutual correlation Γ. At block 1522, at the maximum Γ, the system 1300 increases ΔT to the maximum, which results in m=0. At block 1526, the system 1300 calculates the measured length of OFDM symbol according to the following expression:
where, in the measurement, the system 1300 selects L to be close to N_{g }to increase the sensitivity of the mutual correlation.
It is apparent from Equation (26) that the resolution and accuracy of the N_{m }measurement rely on the increment of ΔT. Therefore, a typical embodiment uses a large OFDM size and a high sampling rate in the transmitter and the receiver. For example, an LTE OFDM system has an OFDM symbol with the length of 66.67 μs and 2048 points while WiFi (802.11a) has OFDM symbol with the length of 3.2 μs and 64 points.
At block 1530, the system 1300 applies Equation (22) to calculate δ. In block 1534, the system 1300 calculates a frequency offset κδ for each subcarrier by multiplying δ by κ, where κ is the subcarrier channel index.
At block 1538, the system 1300 shifts the subcarriers of the FFT processor 390 by the respective frequency offsets. At block 1542, the system 1300 calculates the FFT of the symbol based on the subcarriers that the system 1300 has shifted to compensate for the Doppler shifts if the symbol conveys data.
The foregoing exemplary embodiments assume that the variation in δ is slow enough that the Doppler frequency shift can be considered substantially constant over at least two OFDM symbol periods. The practicality of such an assumption should be appreciated, as typical OFDM symbol lengths are small (e.g., 45.715 μs and 66.7 μs in WiMAX and LTE, respectively (i.e., half of the useful symbol time T_{b})).
Locations of the SCFS estimator 350 and the SCFS estimator 750 are not limited to the locations shown in
The computer system 1600 may be a physical system, a virtual system, or a combination of both physical and virtual systems. The computer system 1600 may include a bus 1618 or other communication mechanism for communicating information and a processor 1602 coupled to the bus 1618 for processing information. The computer system 1600 includes a main memory 1604, such as randomaccess memory (RAM) or other dynamic storage device, coupled to the bus 1618 for storing computerreadable instructions by the processor 1602.
The main memory 1604 may be used for storing temporary variables or other intermediate information during execution of the instructions to be executed by the processor 1602. The computer system 1600 includes a readonly memory (ROM) 1606 or other static storage device coupled to the bus 1618 for storing static information and instructions for the processor 1602. A computerreadable storage device 1608, such as a magnetic disk or optical disk, is coupled to the bus 1618 for storing information and instructions for the processor 1602. The computer system 1600 may be coupled via the bus 1618 to a display 1610, such as a liquid crystal display (LCD) or a cathode ray tube (CRT), for displaying information to a user. An input device 1612, including, for example, alphanumeric and other keys, is coupled to the bus 1618 for communicating information and command selections to the processor 1602. Another type of user input device is a cursor control 1614, such as a mouse, a trackball, or cursor direction keys for communicating direct information and command selections to the processor 1602 and for controlling cursor movement on the display 1610. The cursor control 1614 typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allow the device to specify positions in a plane.
The term “computer readable instructions” as used above refers to any instructions that may be performed by the processor 1602 and/or other component of the computer system 1600. Similarly, the term “computer readable medium” refers to any nontransitory storage medium that may be used to store the computer readable instructions. Such a medium may take many forms, including, but not limited to, nonvolatile media, volatile media, and transmission media. Nonvolatile media include, for example, optical or magnetic disks, such as the storage device 1608. Volatile media includes dynamic memory, such as the, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, an EPROM, a FLASH EPROM, any other memory chip or cartridge main memory 1604. Transmission media includes coaxial cables, copper wire, and fiber optics, including wires of the bus 1618. Common forms of computer readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD ROM, or any other medium from which a computer can read.
Although various embodiments of the method and apparatus of the present invention have been illustrated in the accompanying Drawings and described in the foregoing Detailed Description, it will be understood that the invention is not limited to the embodiments disclosed, but is capable of numerous rearrangements, modifications and substitutions without departing from the spirit of the invention as set forth herein.