EngeePhased.MFSKWaveform

Continuous signal generator with multi-position frequency modulation.

Library	`EngeePhased`
Block	MFSK Waveform

Description

A continuous signal with multi-position frequency modulation (FM) is used in automotive radars to improve simultaneous pulse and Doppler detection of the distance to multiple targets. System object EngeePhased.MFSKWaveform generates a continuous signal with a multi-position FM. A multi-position FM signal consists of two alternating sequences of increasing frequencies, as described in the Algorithms section.

To generate a continuous signal with a multi-position FM, follow these steps:

Create an object EngeePhased.MFSKWaveform and set its properties.
Call the object with arguments as if it were a function.

To learn more about how to work with system objects, see Engee System Objects.

Syntax

Creation

waveform = EngeePhased.MFSKWaveform() — creates a system object waveform a multi-position FM signal generator.
waveform = EngeePhased.MFSKWaveform(Name=Value) — creates a system object waveform a multi-position FM signal generator with the specified property "Name", set to the specified value Value. You can specify additional properties as name-value pairs in any order (Name1=Value1,…,NameN=ValueN).

Using

Y = waveform() — returns the Y signal with a multi-position FM.

Arguments

Output arguments

Y — multi-position FM signal

+ the complex vector

Details

An output signal with a multi-position FM, returned as a complex vector of size . When is the method step! When it reaches the end of the signal, the output samples loop from the beginning of the signal, forming a periodic signal.

Типы данных	`Float64`
Support for complex numbers	yes

Features

# StepTime — frequency step duration
Real number

Details

The duration of each frequency step in seconds, given as a positive scalar.

By default — 1e−4.

# StepsPerSweep — total number of frequency deviation steps
Real number

Details

The total number of frequency deviation steps specified as an even positive integer.

By default — 64.

# SampleRate — sampling rate of the output signal
Real number

Details

The sampling frequency of the signal in the form of a positive scalar. Units of measurement — Hz.

By default — 1e6.

# NumSteps — the number of frequency steps in the signal
Real number

Details

The number of frequency steps in the output signal, specified as a positive integer.

By default — 1.

# NumSamples — the number of samples in the signal
Real number

Details

The number of samples in the output signal, specified as a positive integer.

By default — 1.

# OutputFormat — Output format
String

Details

Output format:

"Steps" (by default) — the output signal consists of all samples contained in the whole number of frequency steps NumSteps.
"Samples" — the output signal consists of an integer number of samples [Property:numSamples].
"Sweeps" — the output signal consists of all samples contained in the whole number of frequency deviation steps NumSweeps.

The values of OutputFormat do not affect the properties of the signal.

# NumSweeps — the number of frequency deviation steps in the signal
Real number

Details

The number of frequency deviation steps in the output signal, specified as a positive integer.

By default — 1.

# FrequencyOffset — frequency offset
Real number

Details

The frequency offset specified as a real scalar. The frequency offset defines the frequency shift between two sequences. Units of measurement — Hz.

By default — 1000.

# SweepBandwidth — frequency deviation
Real number

Details

Frequency deviation in the output signal, specified as a positive scalar. Units of measurement — Hz.

The signal frequency deviation is the difference between the highest and lowest frequencies of any of the sequences.

By default — 1e5.

Methods

Common to all system objects

`step!`	Run the system object operation algorithm
`release!`	Allow changing the value of a system object property
`reset!`	Resetting the internal states of a system object

Special for system objects of signal generators

`bandwidth`	Bandwidth of the signal `getMatchedFilter`: Matched filter coefficients obtained from the signal
`plot`	Plotting the pulse signal

Examples

Generation of signals with multi-position frequency modulation

Details

We will generate a signal with a multi-position frequency modulation with a sampling frequency 10 MHz, the duration of the step 5 iss, number of steps 6, frequency offset 400 kHz and signal band 4 MHz.

Initialize the parameters.

fs = 10e6                # Частота дискретизации (Гц)
tstep = 5e-6             # Длительность одного шага (с)
stepsPerSweep = 6        # Общее число ступеней перестройки частоты
freqOffset = 400e3       # Смещение частоты (Гц)
sweepBW = 4e6            # Полоса перестройки (Гц)

# Дополнительные параметры
PRF = 1 / (stepsPerSweep * tstep);   # Частота повторения
sweeps2plot = 1;

Let’s use EngeePhased.MFSKWaveform to create a probe signal system object mfsk_wav.

mfsk_wav = EngeePhased.MFSKWaveform(
    SampleRate = fs,
    StepTime = tstep,
    StepsPerSweep = stepsPerSweep,
    SweepBandwidth = sweepBW,
    FrequencyOffset = freqOffset,
    OutputFormat = "Sweeps",
    NumSweeps = sweeps2plot
);

Making a call to the system object EngeePhased.MFSKWaveform using the mfsk_wav variable.

mfsk_signal = mfsk_wav();

Using the function plot Let’s construct an oscilloscope in the form of an IQ component, a module, and a phase of the signal.

# построение IQ-компонент
t_grid = range(start = 0,step = 1/fs,length = length(mfsk_signal)) * 1e6 # сетка времени, мкс
fig1 = plot(t_grid,real.(mfsk_signal),title = "синфазная составляющая",lab="",ylab="Амплитуда")
fig2 = plot(t_grid,imag.(mfsk_signal),title = "квадратурная составляющая",lab="",xlab = "Время, мкс",ylab="Амплитуда");

plot(fig1,fig2,layout = (2,1))

object phased mfsk waveform 2 en

# построение модуля и фазы сигнала
fig3 = plot(t_grid,abs.(mfsk_signal),title = "Модуль комплексного сигнала",lab="",ylab="Амплитуда");
fig4 = plot(t_grid,angle.(mfsk_signal)*180/pi,title = "Аргумент комплексного сигнала",lab="",xlab = "Время, мкс",ylab="Фаза, град.");

plot(fig3,fig4,layout = (2,1))

object phased mfsk waveform 3 en

The main characteristic of the signal is the frequency spectrum and the spectrogram. Let’s use the built-in function periodogram.

# расчет спектра сигнала
spec_MFSK,f = EngeePhased.Functions.periodogram(
    mfsk_signal, # исходный сигнал
    ones(size(mfsk_signal)...),
    8192; # длина частоты дискретизации
    out = :data, # тип выхода
    fs = fs, # частота дискретизации
    spectrumtype = "power" # тип спектра
);

Visualize the result using the function plot.

plot(
    f * 1e-6,
    EngeePhased.Functions.mag2db.(spec_MFSK),
    lab="", xlab = "Частота, МГц",
    ylab = "Мощность, дБВт",
    title = "Спектр сигнала",
    ylim = (-70,-20)
)

object phased mfsk waveform 4 en

To calculate the spectrogram, we use the built-in function spectrogram.

# расчет спектрограммы
spectgm_cfm,f1,t1 = EngeeDSP.Functions.spectrogram(
    real.(mfsk_signal);
    nfft = 512, # длина БПФ
    window = round(Int,length(mfsk_signal)/stepsPerSweep),
    noverlap = 0, # перекрытие окна
    spectrumtype = "power", # тип спектра — по мощности
    freqrange = "onesided", # диапазон спектра — односторонний
    out = :data, # тип выхода — массив данных
    fs = fs # частота дискретизации
);

We visualize the result of the spectrogram calculation using the function heatmap.

# построение спектрограммы
heatmap(
    t1[:]*1e6,
    f1[:]*1e-6,
    abs.(spectgm_cfm),color = :jet,
    xlab = "Время, мкс",
    ylab = "Частота Доплера, МГц"
)

object phased mfsk waveform 5 en

Algorithms

A signal with multi-position frequency modulation is formed by switching the carrier frequency in accordance with a given multi-level digital code:

where

— the duration of one character;
— the meaning of an information symbol from a multi-position alphabet;
— frequency spacing between positions.

To generate a stepwise frequency modulated signal, the following parameters must be set:

filter sampling rate ;
pulse duration ;
pulse repetition rate ;
number of pulses ;
number of frequency steps ;
the initial frequency of the signal ;
frequency spacing between positions ;
the final frequency of the signal ;
frequency deviation .

so mfsk waveform 1 en

Each sequence is a set of continuous signals, increasing in frequency. Offset the difference between the two sequences is constant and can be positive or negative. The complete signal consists of an even number of steps the same duration . Then each sequence consists of steps. Signal frequency deviation is the difference between the highest and lowest frequencies of any of the sequences. Meaning it is always positive, which indicates an increase in frequency. The frequency difference between the successive steps of each sequence is determined as follows:

The lowest frequency of the first sequence is always 0 Hz and corresponds to the carrier frequency of the bandpass signal. The lowest frequency of the second sequence can be positive or negative and is equal to . Negative frequencies correspond to the frequencies of the bandpass signal that are lower than the carrier frequency. The duration of the signal is set to . The properties of the system object corresponding to the signal parameters are shown in the table.

Signal Parameter	Property
	SweepBandwidth
	StepTime
	StepsPerSweep
	FrequencyOffset

Signal Parameter

Property

SweepBandwidth

StepTime

StepsPerSweep

FrequencyOffset

Literature

Meinecke, Marc-Michael, and Hermann Rohling, Combination of LFMCW and FSK Modulation Principles for Automotive Radar Systems. German Radar Symposium GRS2000. 2000.
Rohling, Hermann, and Marc-Michael Meinecke. Waveform Design Principles for Automotive Radar Systems. CIE International Conference on Radar. 2001.