wlanCoarseCFOEstimate

Perform coarse CFO estimation

Syntax

fOffset = wlanCoarseCFOEstimate(rxSig,cbw)

fOffset = wlanCoarseCFOEstimate(rxSig,cbw,corrOffset)

fOffset = wlanCoarseCFOEstimate(___,OversamplingFactor=osf)

Description

fOffset = wlanCoarseCFOEstimate(rxSig,cbw) performs coarse carrier frequency offset (CFO) estimation on received time-domain L-STF¹ samples rxSig for channel bandwidth cbw. The function can estimate a maximum CFO of 625 kHz, or twice the subcarrier spacing.

fOffset = wlanCoarseCFOEstimate(rxSig,cbw,corrOffset) specifies the correlation offset as a fraction of a short training symbol.

fOffset = wlanCoarseCFOEstimate(___,OversamplingFactor=osf) specifies an oversampling factor in addition to any input argument combination from the previous syntaxes. Use this syntax to perform coarse CFO estimation on an oversampled signal.

Examples

Coarse Estimate of CFO for Non-HT Waveform

Create a non-HT configuration object.

nht = wlanNonHTConfig;

Generate a non-HT waveform.

txSig = wlanWaveformGenerator([1;0;0;1],nht);

Create a phase and frequency offset object and introduce a 2 kHz frequency offset.

pfOffset = comm.PhaseFrequencyOffset('SampleRate',20e6,'FrequencyOffset',2000);
rxSig = pfOffset(txSig);

Extract the L-STF.

ind = wlanFieldIndices(nht,'L-STF');
rxLSTF = rxSig(ind(1):ind(2),:);

Estimate the frequency offset from the L-STF.

freqOffsetEst = wlanCoarseCFOEstimate(rxLSTF,'CBW20')

freqOffsetEst = 
2.0000e+03

Estimate and Correct CFO for VHT Waveform with Correlation Offset

Estimate the frequency offset for a VHT signal passing through a noisy, TGac channel. Correct for the frequency offset.

Create a VHT configuration object and create the L-STF.

vht = wlanVHTConfig;
txstf = wlanLSTF(vht);

Set the channel bandwidth and sample rate.

cbw = 'CBW80';
fs = 80e6;

Create TGac and thermal noise channel objects. Set the delay profile of the TGac channel to 'Model-C'. Set the noise figure of the thermal noise channel to 9 dB.

tgacChan = wlanTGacChannel('SampleRate',fs,'ChannelBandwidth',cbw, ...
    'DelayProfile','Model-C','LargeScaleFadingEffect','Pathloss');

noise = comm.ThermalNoise('SampleRate',fs,'NoiseMethod','Noise figure', ...
    'NoiseFigure',9);

Pass the L-STF through the noisy TGac channel.

rxstfNoNoise = tgacChan(txstf);
rxstf = noise(rxstfNoNoise);

Create a phase and frequency offset object and introduce a 750 Hz frequency offset.

pfOffset = comm.PhaseFrequencyOffset('SampleRate',fs, ...
    'FrequencyOffsetSource','Input port');
rxstf = pfOffset(rxstf,750);

For the model-C delay profile, the RMS delay spread is 30 ns, which is 3/8 of the 80 ns short training symbol duration. As such, set the correlation offset to 0.375.

corrOffset = 0.375;

Estimate the frequency offset. Your results may differ slightly.

fOffsetEst = wlanCoarseCFOEstimate(rxstf,cbw,corrOffset)

fOffsetEst = 
746.2700

The estimate is very close to the introduced CFO of 750 Hz.

Change the delay profile to 'Model-E', which has an RMS delay spread of 100 ns.

release(tgacChan)
tgacChan.DelayProfile = 'Model-E';

Pass the transmitted signal through the modified channel and apply the 750 Hz CFO.

rxstfNoNoise = tgacChan(txstf);
rxstf = noise(rxstfNoNoise);
rxstf = pfOffset(rxstf,750);

Estimate the frequency offset.

fOffsetEst = wlanCoarseCFOEstimate(rxstf,cbw,corrOffset)

fOffsetEst = 
947.7234

The estimate is inaccurate because the RMS delay spread is greater than the duration of the training symbol.

Set the correlation offset to the maximum value of 1 and estimate the CFO.

corrOffset = 1;
fOffsetEst = wlanCoarseCFOEstimate(rxstf,cbw,corrOffset)

fOffsetEst = 
745.3640

The estimate is accurate because the autocorrelation does not use the first training symbol. The channel delay renders this symbol useless.

Correct for the estimated frequency offset.

rxstfCorrected = pfOffset(rxstf,-fOffsetEst);

Estimate the frequency offset of the corrected signal.

fOffsetEstCorr = wlanCoarseCFOEstimate(rxstfCorrected,cbw,corrOffset)

fOffsetEstCorr = 
1.9929e-11

The corrected signal has negligible frequency offset.

Two-Step CFO Estimation and Correction

Estimate and correct for a significant carrier frequency offset in two steps. Estimate the frequency offset after all corrections have been made.

Set the channel bandwidth and the corresponding sample rate.

cbw = 'CBW40';
fs = 40e6;

Coarse Frequency Correction

Generate an HT format configuration object.

cfg = wlanHTConfig('ChannelBandwidth',cbw);

Generate the transmit waveform.

txSig = wlanWaveformGenerator([1;0;0;1],cfg);

Create TGn and thermal noise channel objects. Set the noise figure of the receiver to 9 dB.

tgnChan = wlanTGnChannel('SampleRate',fs,'DelayProfile','Model-D', ...
    'LargeScaleFadingEffect','Pathloss and shadowing');
noise = comm.ThermalNoise('SampleRate',fs, ...
    'NoiseMethod','Noise figure', ...
    'NoiseFigure',9);

Pass the waveform through the TGn channel and add noise.

rxSigNoNoise = tgnChan(txSig);
rxSig = noise(rxSigNoNoise);

Create a phase and frequency offset object to introduce a carrier frequency offset. Introduce a 2 kHz frequency offset.

pfOffset = comm.PhaseFrequencyOffset('SampleRate',fs,'FrequencyOffsetSource','Input port');
rxSig = pfOffset(rxSig,2e3);

Extract the L-STF signal for coarse frequency offset estimation.

istf = wlanFieldIndices(cfg,'L-STF');
rxstf = rxSig(istf(1):istf(2),:);

Perform a coarse estimate of the frequency offset. Your results may differ.

foffset1 = wlanCoarseCFOEstimate(rxstf,cbw)

foffset1 = 
2.0221e+03

Correct for the estimated offset.

rxSigCorr1 = pfOffset(rxSig,-foffset1);

Fine Frequency Correction

Extract the L-LTF signal for fine offset estimation.

iltf = wlanFieldIndices(cfg,'L-LTF');
rxltf1 = rxSigCorr1(iltf(1):iltf(2),:);

Perform a fine estimate of the corrected signal.

foffset2 = wlanFineCFOEstimate(rxltf1,cbw)

foffset2 = 
-11.0795

The corrected signal offset is reduced from 2000 Hz to approximately 7 Hz.

Correct for the remaining offset.

rxSigCorr2 = pfOffset(rxSigCorr1,-foffset2);

Determine the frequency offset of the twice corrected signal.

rxltf2 = rxSigCorr2(iltf(1):iltf(2),:);
deltaFreq = wlanFineCFOEstimate(rxltf2,cbw)

deltaFreq = 
-1.9722e-11

The CFO is zero.

Input Arguments

rxSig — Received L-STF samples

complex-valued matrix

Received L-STF samples, specified as a complex-valued matrix of size N_S-by-N_R. N_S is the number of samples in the L-STF and N_R is the number of receive antennas.

Note

If the number of samples in this input is greater than the number of samples in the L-STF, the function estimates the CFO by using only the first N_S samples.

Data Types: single | double
Complex Number Support: Yes

cbw — Channel bandwidth

'CBW5' | 'CBW10' | 'CBW20' | 'CBW40' | 'CBW80' | 'CBW160' | 'CBW320'

Channel bandwidth, specified as one of these values.

• 'CBW5' — Channel bandwidth of 5 MHz

• 'CBW10' — Channel bandwidth of 10 MHz

• 'CBW20' — Channel bandwidth of 20 MHz

• 'CBW40' — Channel bandwidth of 40 MHz

• 'CBW80' — Channel bandwidth of 80 MHz

• 'CBW160' — Channel bandwidth of 160 MHz

• 'CBW320' — Channel bandwidth of 320 MHz

Data Types: char | string

corrOffset — Correlation offset

0.75 (default) | scalar in the interval [0, 1]

Correlation offset as a fraction of a short training symbol, specified as a scalar in the interval [0, 1]. The duration of the short training symbol varies with bandwidth. For more information, see L-STF.

Data Types: single | double

osf — Oversampling factor

1 (default) | scalar greater than or equal to 1

Oversampling factor, specified as a scalar greater than or equal to 1. The oversampled cyclic prefix length must be an integer number of samples.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

fOffset — Frequency offset

real-valued scalar

Frequency offset, in Hz, returned as a real-valued scalar. The function can estimate a maximum CFO of 625 kHz, or twice the subcarrier spacing.

Data Types: double

More About

L-STF

The legacy short training field (L-STF) is the first field of the 802.11™ OFDM PLCP legacy preamble. The L-STF is a component of EHT, HE, VHT, HT, and non-HT PPDUs.

The L-STF duration varies with channel bandwidth.

Channel Bandwidth (MHz)	Subcarrier Frequency Spacing, ΔF (kHz)	Fast Fourier Transform (FFT) Period (TFFT = 1 / ΔF)	L-STF Duration (TSHORT = 10 × TFFT / 4)
20, 40, 80, 160, and 320	312.5	3.2 μs	8 μs
10	156.25	6.4 μs	16 μs
5	78.125	12.8 μs	32 μs

Because the sequence has good correlation properties, receivers use it for start-of-packet detection, coarse frequency correction, and setting the AGC. The sequence uses 12 of the 52 subcarriers that are available per 20 MHz channel bandwidth segment. For 5 MHz, 10 MHz, and 20 MHz bandwidths, the number of channel bandwidth segments is one.

FFT-Based Oversampling

An oversampled signal is a signal sampled at a frequency that is higher than the Nyquist rate. WLAN signals maximize occupied bandwidth by using small guardbands, which can pose problems for anti-imaging and anti-aliasing filters. Oversampling increases the guardband width relative to the total signal bandwidth, which increases the number of samples in the signal.

This diagram shows the oversampling process for an OFDM waveform with N_FFT subcarriers made up of N_g guardband subcarriers on either side of N_st occupied bandwidth subcarriers.

References

[1] IEEE Std 802.11™-2016 (Revision of IEEE Std 802.11-2012). “Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications.” IEEE Standard for Information technology — Telecommunications and information exchange between systems — Local and metropolitan area networks — Specific requirements.

[2] Li, Jian. “Carrier Frequency Offset Estimation for OFDM-Based WLANs.” IEEE Signal Processing Letters. Vol. 8, Issue 3, Mar 2001, pp. 80–82.

[3] Moose, P. H. “A technique for orthogonal frequency division multiplexing frequency offset correction.” IEEE Transactions on Communications. Vol. 42, Issue 10, Oct 1994, pp. 2908–2914.

[4] Perahia, E. and R. Stacey. Next Generation Wireless LANs: 802.11n and 802.11ac. 2nd Edition. United Kingdom: Cambridge University Press, 2013.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2015b

R2024b: Process oversampled waveforms

This function now supports processing oversampled waveforms. To use this feature, specify the osf argument as a scalar greater than 1.