Coarse Frequency Compensator

Compensate for carrier frequency offset in PAM, PSK, or QAM

Libraries:
Communications Toolbox / RF Impairments Correction
Communications Toolbox / Synchronization

Description

The Coarse Frequency Compensator block compensates for carrier frequency offset in QAM, 8-PSK, BPSK, OQPSK, PAM, and QPSK modulation schemes.

Examples

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Compensate Signal Frequency and Phase Offset in Simulink

This example uses:

Open Model

Compensate for a frequency offset imposed on a noisy 8-PSK channel by using the Coarse Frequency Compensator block.

The doc_coarsefreqcomp model compares a frequency offset impaired signal to one that has coarse frequency compensation applied.

A spectrum analyzer plot shows the transmitted signal before and after applying coarse frequency compensation.

Estimated frequency offset is 1999.9694824.2 Hz.

Ports

Input

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In — Input signal
column vector

Input signal, specified as a column vector.

Data Types: single | double
Complex Number Support: Yes

Output

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Out — Compensated output signal
complex column vector

Compensated output signal, returned as a complex column vector with the same dimensions and data type as the input In.

Data Types: single | double

FreqEst — Estimate of frequency offset
scalar

Estimate of the frequency offset, returned as a scalar.

Dependencies

To add this port, select Estimated frequency offset output port.

Data Types: single | double

Parameters

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To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Modulation type of input signal — Modulation type
`QAM` (default) | `8PSK` | `BPSK` | `OQPSK` | `PAM` | `QPSK`

Modulation type, specified as QAM, 8PSK, BPSK, OQPSK, PAM, or QPSK.

Estimation algorithm — Algorithm used to estimate frequency offset
`FFT-based` (default) | `Correlation-based`

Specify the frequency offset estimation algorithm as FFT-based or Correlation-based.

The table shows the allowable combinations of the modulation type and the estimation algorithm.

Modulation	FFT-Based Algorithm	Correlation-Based Algorithm
`8PSK`, `BPSK`, `PAM`, `QPSK`	✓	✓
`OQPSK`, `QAM`	✓	—

For more information, see Algorithms.

Dependencies

This parameter appears when you set Modulation type of input signal to 8PSK, BPSK, PAM, or QPSK.

Frequency resolution (Hz) — Frequency resolution
`100` (default) | positive scalar

Frequency resolution in Hz, specified as a positive real scalar.

Dependencies

This parameter applies when you set Estimation algorithm to FFT-based.

Samples per symbol — Number of samples per symbol
`4` (default) | even integer greater than or equal to `4`

Number of samples per symbol, specified as an even integer scalar greater than or equal to 4.

Dependencies

This parameter appears when you set Modulation type of input signal to OQPSK.

Maximum frequency offset (Hz) — Maximum measurable frequency offset
`5e3` (default) | positive scalar

Maximum measurable frequency offset in Hz, specified as a positive scalar.

Dependencies

This parameter appears when you set Estimation algorithm to Correlation-based.

Estimated frequency offset output port — Option to add estimated frequency offset output port
`on` (default) | `off`

Select this check box to add the FreqEst output port. The FreqEst port outputs the estimated frequency offset in Hz.

Simulate using — Type of simulation to run
`Code generation` (default) | `Interpreted execution`

Type of simulation to run, specified as Code generation or Interpreted execution.

Code generation — Simulate the model by using generated C code. The first time you run a simulation, Simulink generates C code for the block. The model reuses the C code for subsequent simulations unless the model changes. This option requires additional startup time, but the speed of the subsequent simulations is faster than with the Interpreted execution option.
Interpreted execution — Simulate the model by using the MATLAB^® interpreter. This option shortens startup time, but the speed of subsequent simulations is slower than with the Code generation option. In this mode, you can debug the source code of the block.

For more information, see Interpreted Execution vs. Code Generation (Simulink).

Block Characteristics

Data Types	`double` \| `single`
Multidimensional Signals	`no`
Variable-Size Signals	`no`

Algorithms

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Correlation-Based Estimation

Reference [ 1 ] describes the correlation-based estimation algorithm used to estimate the frequency offset for PSK and PAM signals. To determine the frequency offset, Δf, the algorithm performs a maximum likelihood (ML) estimation of the complex-valued oscillation exp(j2πΔft). The observed signal, r_k, is represented as

$r_{k} = e^{j (2 π Δ f k T_{s} + θ)}, 1 \leq k \leq N$

T_s is the sampling interval, θ is an unknown random phase, and N is the number of samples. The ML estimation of the frequency offset is equivalent to seeking the maximum of the likelihood function,

$Λ (Δ f) \approx {| \sum_{i = 1}^{N} r_{i} e^{- j 2 π Δ f i T_{s}} |}^{2} = \sum_{k = 1}^{N} \sum_{m = 1}^{N} r_{k} r_{m}^{*} e^{- j 2 π Δ f T_{s} (k - m)}$

After simplifying, the problem is expressed as a discrete Fourier transform, weighted by a parabolic windowing function. It is expressed as

$Im {\sum_{k = 1}^{N - 1} k (N - k) R (k) e^{j 2 π Δ \hat{f} T_{s}}} = 0$

R(k) denotes the estimated autocorrelation of the sequence r_k and is represented as

$R (k) ≜ \frac{1}{N - k} \sum_{i = k + 1}^{N} r_{i} r_{i - k}^{*}, 0 \leq k \leq N - 1$

The term k(N–k) is the parabolic windowing function. In [ 1 ], it is shown that R(k) is a poor estimate of the autocorrelation of r_k when k = 0 or when k is close to N. Consequently, the windowing function can be expressed as a rectangular sequence of 1s for k = 1, 2, ..., L, where L ≤ N – 1. The result is a modified ML estimation strategy in which

$Im {\sum_{k = 1}^{L} R (k) e^{- j 2 π Δ \hat{f} k T_{s}}} = 0$

This equation results in an estimate of $Δ \hat{f}$ in which

$Δ \hat{f} ≅ \frac{f_{s a m p}}{π (L + 1)} \arg {\sum_{k = 1}^{L} R (k)}$

The sampling frequency, f_samp, is the reciprocal of T_s. The number of elements used to compute the autocorrelation sequence, L, are determined as

$L = round (\frac{f_{s a m p}}{f_{m a x}}) - 1$

f_max is the maximum expected frequency offset and round is the nearest integer function. The frequency offset estimate improves when L ≥ 7 and leads to the recommendation that f_max ≤ f_samp / (4M).

FFT-Based Estimation

FFT-based estimation algorithms can be used to estimate the frequency offset for various modulation types. The coarse frequency compensator implementation supports these modulation methods by using the algorithm noted.

For BPSK, QPSK, 8PSK, PAM, or QAM modulation, the coarse frequency compensator uses the FFT-based algorithm described in [ 2 ]. The algorithm estimates $Δ \hat{f}$ by using a periodogram of the m^th power of the received signal and is given as

$Δ \hat{f} = \frac{f_{s a m p}}{N \cdot m} \arg \max_{f} | \sum_{k = 0}^{N - 1} r^{m} (k) e^{- j 2 π k t / N} |, (- \frac{R_{s y m}}{2} \leq f \leq \frac{R_{s y m}}{2})$
where m is the modulation order, r(k) is the received sequence, R_sym is the symbol rate, and N is the number of samples. The algorithm searches for a frequency that maximizes the time average of the mth power of the received signal multiplied by various frequencies in the range of [–R_sym / 2, R_sym / 2]. Because the form of the algorithm is the definition of the discrete Fourier transform of r^m(t), searching for a frequency that maximizes the time average is equivalent to searching for a peak line in the spectrum of r^m(t). The number of points required by the FFT is

$N = 2^{⌈ \log_{2} (\frac{f_{s a m p}}{f_{r}}) ⌉}$
where f_r is the desired frequency resolution.
For OQPSK modulation, the coarse frequency compensator uses the FFT-based algorithm described in [ 4 ]. The algorithm searches for spectral peaks at ±200 kHz around the symbol rate. This technique locates desired peaks in the presence of interference from spectral content around baseband frequencies due to filtering.

References

[1] Luise, M., and R. Reggiannini. “Carrier Frequency Recovery in All-Digital Modems for Burst-Mode Transmissions.” IEEE^® Transactions on Communications 43, no. 2/3/4 (Feb. 1995): 1169–78.

[2] Wang, Y., et al. “Non-Data-Aided Feedforward Carrier Frequency Offset Estimators for QAM Constellations: A Nonlinear Least-Squares Approach.” EURASIP Journal on Advances in Signal Processing 2004, no. 13 (Dec. 2004): 856139. https://doi.org/10.1155/S1110865704403175.

[3] Nakagawa, Tadao, et al. “Non-Data-Aided Wide-Range Frequency Offset Estimator for QAM Optical Coherent Receivers.” Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OMJ1. OSA, 2011. https://doi.org/10.1364/OFC.2011.OMJ1.

[4] Olds, Jonathan. Designing an OQPSK demodulator.

Extended Capabilities

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

Version History

Introduced in R2015b

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R2023b: Default settings change

The Coarse Frequency Compensator block parameters have new default values.

Parameter	New Default	Previous Default
Frequency resolution (Hz)	`100`	`0.001`
Maximum frequency offset (Hz)	`5e3`	`0.05`

When executing code created in a previous release, confirm the coarse frequency compensator settings. The new default settings change your results. To produce results using the previous default settings, you can manually update the settings of your block.

Coarse Frequency Compensator

Description

Examples

Compensate Signal Frequency and Phase Offset in Simulink

Ports

Input

In — Input signal
column vector

Output

Out — Compensated output signal
complex column vector

FreqEst — Estimate of frequency offset
scalar

Dependencies

Parameters

Modulation type of input signal — Modulation type
`QAM` (default) | `8PSK` | `BPSK` | `OQPSK` | `PAM` | `QPSK`

Estimation algorithm — Algorithm used to estimate frequency offset
`FFT-based` (default) | `Correlation-based`

Dependencies

Frequency resolution (Hz) — Frequency resolution
`100` (default) | positive scalar

Dependencies

Samples per symbol — Number of samples per symbol
`4` (default) | even integer greater than or equal to `4`

Dependencies

Maximum frequency offset (Hz) — Maximum measurable frequency offset
`5e3` (default) | positive scalar

Dependencies

Estimated frequency offset output port — Option to add estimated frequency offset output port
`on` (default) | `off`

Simulate using — Type of simulation to run
`Code generation` (default) | `Interpreted execution`

Block Characteristics

Algorithms

Correlation-Based Estimation

FFT-Based Estimation

References

Extended Capabilities

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

Version History

R2023b: Default settings change

See Also

Blocks

Objects

Coarse Frequency Compensator

Description

Examples

Compensate Signal Frequency and Phase Offset in Simulink

Ports

Input

In — Input signal column vector

Output

Out — Compensated output signal complex column vector

FreqEst — Estimate of frequency offset scalar

Dependencies

Parameters

Modulation type of input signal — Modulation type QAM (default) | 8PSK | BPSK | OQPSK | PAM | QPSK

Estimation algorithm — Algorithm used to estimate frequency offset FFT-based (default) | Correlation-based

Dependencies

Frequency resolution (Hz) — Frequency resolution 100 (default) | positive scalar

Dependencies

Samples per symbol — Number of samples per symbol 4 (default) | even integer greater than or equal to 4

Dependencies

Maximum frequency offset (Hz) — Maximum measurable frequency offset 5e3 (default) | positive scalar

Dependencies

Estimated frequency offset output port — Option to add estimated frequency offset output port on (default) | off

Simulate using — Type of simulation to run Code generation (default) | Interpreted execution

Block Characteristics

Algorithms

Correlation-Based Estimation

FFT-Based Estimation

References

Extended Capabilities

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

Version History

R2023b: Default settings change

See Also

Blocks

Objects

In — Input signal
column vector

Out — Compensated output signal
complex column vector

FreqEst — Estimate of frequency offset
scalar

Modulation type of input signal — Modulation type
`QAM` (default) | `8PSK` | `BPSK` | `OQPSK` | `PAM` | `QPSK`

Estimation algorithm — Algorithm used to estimate frequency offset
`FFT-based` (default) | `Correlation-based`

Frequency resolution (Hz) — Frequency resolution
`100` (default) | positive scalar

Samples per symbol — Number of samples per symbol
`4` (default) | even integer greater than or equal to `4`

Maximum frequency offset (Hz) — Maximum measurable frequency offset
`5e3` (default) | positive scalar

Estimated frequency offset output port — Option to add estimated frequency offset output port
`on` (default) | `off`

Simulate using — Type of simulation to run
`Code generation` (default) | `Interpreted execution`

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