wlanSymbolTimingEstimate

Fine symbol timing estimate using L-LTF

Syntax

startOffset = wlanSymbolTimingEstimate(rxSig,cbw)

startOffset = wlanSymbolTimingEstimate(rxSig,cbw,threshold)

startOffset = wlanSymbolTimingEstimate(___,OversamplingFactor=osf)

[startOffset,M] = wlanSymbolTimingEstimate(___)

Description

startOffset = wlanSymbolTimingEstimate(rxSig,cbw) estimates the timing offset between the start of received waveform rxSig and the start of the L-STF ¹ for channel bandwidth cbw.

Note

This function supports OFDM-modulated signals only.

startOffset = wlanSymbolTimingEstimate(rxSig,cbw,threshold) specifies the threshold that the decision metric must meet or exceed to obtain a symbol timing estimate.

startOffset = wlanSymbolTimingEstimate(___,OversamplingFactor=osf) specifies an oversampling factor in addition to any input argument combination from the previous syntaxes. Use this syntax to estimate the timing offset for an oversampled signal.

[startOffset,M] = wlanSymbolTimingEstimate(___) also returns the decision metric of the symbol timing algorithm using any combination of input arguments in previous syntaxes.

Examples

Detect HT Packet and Estimate Symbol Timing

Detect a received 802.11n™ packet and estimate its symbol timing at 20 dB SNR.

Create an HT format configuration object and TGn channel configuration object.

cfgHT = wlanHTConfig;
tgn = wlanTGnChannel;

Generate a transmit waveform and add a delay at the start of the waveform.

txWaveform = wlanWaveformGenerator([1;0;0;1],cfgHT);
txWaveform = [zeros(100,1);txWaveform];

Pass the waveform through the TGn channel model and add noise.

SNR = 20; % In decibels
fadedSig = tgn(txWaveform);
rxWaveform = awgn(fadedSig,SNR,0);

Detect the packet. Extract the non-HT fields. Estimate the fine packet offset using the coarse detection for the first symbol of the waveform and the non-HT preamble field indices.

startOffset = wlanPacketDetect(rxWaveform,cfgHT.ChannelBandwidth);
ind = wlanFieldIndices(cfgHT);
nonHTFields = rxWaveform(startOffset+(ind.LSTF(1):ind.LSIG(2)),:);

startOffset = wlanSymbolTimingEstimate(nonHTFields, ...
    cfgHT.ChannelBandwidth)

startOffset = 
6

Detect HT Packet and Set Threshold When Estimating Symbol Timing

Impair an HT waveform by passing it through a TGn channel configured to model a large delay spread. Detect the waveform and estimate the symbol timing. Adjust the decision metric threshold and estimate the symbol timing again.

Create an HT format configuration object and TGn channel configuration object. Specify the Model-E delay profile, which introduces a large delay spread.

cfgHT = wlanHTConfig;

tgn = wlanTGnChannel;
tgn.DelayProfile = 'Model-E';

Generate a transmit waveform and add a delay at the start of the waveform.

txWaveform = wlanWaveformGenerator([1;0;0;1],cfgHT);
txWaveform = [zeros(100,1);txWaveform];

Pass the waveform through the TGn channel model and add noise.

SNR = 50; % In decibels
fadedSig = tgn(txWaveform);
rxWaveform = awgn(fadedSig,SNR,0);

Detect the packet. Extract the non-HT fields. Estimate the fine packet offset using the coarse detection for the first symbol of the waveform and the non-HT preamble field indices. Adjust the decision metric threshold and estimate the fine packet offset again.

startOffset = wlanPacketDetect(rxWaveform,cfgHT.ChannelBandwidth);
ind = wlanFieldIndices(cfgHT);
nonHTFields = rxWaveform(startOffset+(ind.LSTF(1):ind.LSIG(2)),:);

startOffset = wlanSymbolTimingEstimate(nonHTFields, ...
    cfgHT.ChannelBandwidth)

startOffset = 
5

threshold = 0.1

threshold = 
0.1000

startOffset = wlanSymbolTimingEstimate(nonHTFields, ...
    cfgHT.ChannelBandwidth,threshold)

startOffset = 
9

Detecting the correct timing offset is more challenging for a channel model with large delay spread. For large delay spread channels, you can try lowering the threshold setting to see if performance improves in an end-to-end simulation.

Estimate Symbol Timing of TGn-Impaired HT Waveform

Detect a received 802.11n™ packet and estimate its symbol timing at 15 dB SNR.

Create an HT format configuration object. Specify two transmit antennas and two space-time streams.

cfgHT = wlanHTConfig;
nAnt = 2;
cfgHT.NumTransmitAntennas = nAnt;
cfgHT.NumSpaceTimeStreams = nAnt;

Show the logic behind the MCS selection for BPSK modulation.

if cfgHT.NumSpaceTimeStreams == 1
    cfgHT.MCS = 0;
elseif cfgHT.NumSpaceTimeStreams == 2
    cfgHT.MCS = 8;
elseif cfgHT.NumSpaceTimeStreams == 3
    cfgHT.MCS = 16;
elseif cfgHT.NumSpaceTimeStreams == 4
    cfgHT.MCS = 24;
end

Generate a transmit waveform and add a delay at the start of the waveform.

txWaveform = wlanWaveformGenerator([1;0;0;1],cfgHT);
txWaveform = [zeros(100,cfgHT.NumTransmitAntennas);txWaveform];

Create a TGn channel configuration object for two transmit antennas and two receive antennas. Specify the Model-B delay profile. Pass the waveform through the TGn channel model and add noise.

tgn = wlanTGnChannel;
tgn.NumTransmitAntennas = nAnt;
tgn.NumReceiveAntennas = nAnt;
tgn.DelayProfile = 'Model-B';

SNR = 15; % In decibels
fadedSig = tgn(txWaveform);
rxWaveform = awgn(fadedSig,SNR,0);

Detect the packet. Extract the non-HT fields. Estimate the fine packet offset using the coarse detection for the first symbol of the waveform and the non-HT preamble field indices.

startOffset = wlanPacketDetect(rxWaveform,cfgHT.ChannelBandwidth);
ind = wlanFieldIndices(cfgHT);
nonHTFields = rxWaveform(startOffset+(ind.LSTF(1):ind.LSIG(2)),:);

startOffset = wlanSymbolTimingEstimate(nonHTFields, ...
    cfgHT.ChannelBandwidth)

startOffset = 
8

Estimate VHT Packet Symbol Timing

Return the symbol timing and decision metric of an 802.11ac™ packet without channel impairments.

Create a VHT format configuration object. Specify two transmit antennas and two space-time streams.

cfgVHT = wlanVHTConfig;
cfgVHT.NumTransmitAntennas = 2;
cfgVHT.NumSpaceTimeStreams = 2;

Generate a VHT format transmit waveform. Add a 50-sample delay at the start of the waveform.

txWaveform = wlanWaveformGenerator([1;0;0;1],cfgVHT);
txWaveform = [zeros(50,cfgVHT.NumTransmitAntennas); txWaveform];

Extract the non-HT preamble fields. Obtain the timing offset estimate and decision metric.

ind = wlanFieldIndices(cfgVHT);
nonhtfields = txWaveform(ind.LSTF(1):ind.LSIG(2),:);
[startOffset,M] = wlanSymbolTimingEstimate(nonhtfields, ...
    cfgVHT.ChannelBandwidth);

Plot the returned decision metric for the non-HT preamble of the VHT format transmission waveform.

figure
plot(M)
xlabel('Symbol Timing Index')
ylabel('Decision Metric (M)')

Input Arguments

rxSig — Received signal

complex-valued matrix

Received signal containing an L-LTF, specified as a complex-valued matrix of size N_S-by-N_R. N_S is the number of time-domain samples in the L-LTF and N_R is the number of receive antennas.

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

threshold — Decision threshold

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

Decision threshold, specified as a scalar in the interval [0, 1].

To maximize the packet reception performance, you can try different valued of this input. For channels with small delay spread with respect to the cyclic prefix length, MathWorks^® recommends the default value. For a wireless channel with large delay spread with respect to the cyclic prefix length, such as TGn channel with 'Model E' delay profile, MathWorks suggests a value of 0.5.

By lowering the threshold setting, you add a nonnegative corrector to the symbol timing estimate as compared to the estimate using the default threshold setting. The range of the timing corrector is [0, CSD ns/sampling duration]. For more information, see Cyclic Shift Delay (CSD).

Data Types: 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

startOffset — Timing offset

integer | []

Timing offset, in samples, between the start of rxSig and the start of the L-STF, returned as an integer in the interval [–L, N_S– 2L]. L is the length of the L-LTF and N_S is the number of samples. Using the cbw input to determine the range of symbol timing, the function estimates the offset to the start of L-STF by cross-correlating the received signal with a locally generated L-LTF of the first antenna.

• The function returns this output as [] when N_S is less than L.

• The function returns this output as a negative integer when the input waveform does not contain a complete L-STF.

Data Types: double

M — Cross-correlation

real-valued row vector

Cross-correlation between the received signal and the locally generated L-LTF of the first transmit antenna, returned as a real-valued row vector of length N_S – L + 1.

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.

L-LTF

The L-LTF is the second field in the 802.11 OFDM PLCP legacy preamble. The L-LTF is a component of EHT, HE, VHT, HT, and non-HT PPDUs.

Channel estimation, fine frequency offset estimation, and fine symbol timing offset estimation rely on the L-LTF.

The L-LTF is composed of a cyclic prefix (CP) followed by two identical long training symbols (C1 and C2). The CP consists of the second half of the long training symbol.

The L-LTF duration varies with channel bandwidth.

Channel Bandwidth (MHz)	Subcarrier Frequency Spacing ΔF (kHz)	Fast Fourier Transform (FFT) Period (TFFT = 1 / ΔF)	Cyclic Prefix or Training Symbol Guard Interval (GI2) Duration (TGI2 = TFFT / 2)	L-LTF Duration (TLONG = TGI2 + 2 × TFFT)
20, 40, 80, 160, and 320	312.5	3.2 μs	1.6 μs	8 μs
10	156.25	6.4 μs	3.2 μs	16 μs
5	78.125	12.8 μs	6.4 μs	32 μs

Cyclic Shift Delay (CSD)

A CSD is added to the L-LTF for each transmit antenna, which causes multiple strong peaks in the correlation function M. The multiple peaks affect the accuracy of fine symbol timing estimation. For more information, see Section 21.3.8.2.1 and Table 21-10 of [1].

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 802.11-2020 (Revision of IEEE Std 802.11-2016). “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.

Extended Capabilities

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

Version History

Introduced in R2017a

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.