Quadrature Phase Shift Keying (QPSK) is a form of phase modulation technique, in which two information bits (combined as one symbol) are modulated at once, selecting one of the four possible carrier phase shift states.
The QPSK signal within a symbol duration is defined as
where the signal phase is given by
Therefore, the four possible initial signal phases are and radians. Equation (1) can be re-written as
The above expression indicates the use of two orthonormal basis functions: together with the inphase and quadrature signaling points: . Therefore, on a two dimensional co-ordinate system with the axes set to and , the QPSK signal is represented by four constellation points dictated by the vectors with .
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QPSK transmitter
The QPSK transmitter, shown in Figure 1, is implemented as a matlab function qpsk_mod. In this implementation, a splitter separates the odd and even bits from the generated information bits. Each stream of odd bits (quadrature arm) and even bits (in-phase arm) are converted to NRZ format in a parallel manner.
Refer Digital Modulations using Matlab : Build Simulation Models from Scratch for full Matlab code. Refer Digital Modulations using Python for full Python code
File 1: qpsk_mod.m: QPSK modulator
function [s,t,I,Q] = qpsk_mod(a,fc,OF)%Modulate an incoming binary stream using conventional QPSK%a - input binary data stream (0's and 1's) to modulate%fc - carrier frequency in Hertz%OF - oversampling factor (multiples of fc) - at least 4 is better%s - QPSK modulated signal with carrier%t - time base for the carrier modulated signal%I - baseband I channel waveform (no carrier)%Q - baseband Q channel waveform (no carrier)L = 2*OF;%samples in each symbol (QPSK has 2 bits in each symbol)ak = 2*a-1; %NRZ encoding 0-> -1, 1->+1I = ak(1:2:end);Q = ak(2:2:end);%even and odd bit streamsI=repmat(I,1,L).'; Q=repmat(Q,1,L).';%even/odd streams at 1/2Tb baudI = I(:).'; Q = Q(:).'; %serializefs = OF*fc; %sampling frequencyt=0:1/fs:(length(I)-1)/fs; %time baseiChannel = I.*cos(2*pi*fc*t);qChannel = -Q.*sin(2*pi*fc*t);s = iChannel + qChannel; %QPSK modulated baseband signal
The timing diagram for BPSK and QPSK modulation is shown in Figure 2. For BPSK modulation the symbol duration for each bit is same as bit duration, but for QPSK the symbol duration is twice the bit duration: . Therefore, if the QPSK symbols were transmitted at same rate as BPSK, it is clear that QPSK sends twice as much data as BPSK does. After oversampling and pulse shaping, it is intuitively clear that the signal on the I-arm and Q-arm are BPSK signals with symbol duration . The signal on the in-phase arm is then multiplied by and the signal on the quadrature arm is multiplied by . QPSK modulated signal is obtained by adding the signal from both in-phase and quadrature arms.
Note: The oversampling rate for the simulation is chosen as , where is the given carrier frequency and is the sampling frequency satisfying Nyquist sampling theorem with respect to the carrier frequency (). This configuration gives integral number of carrier cycles for one symbol duration.
QPSK receiver
Due to its special relationship with BPSK, the QPSK receiver takes the simplest form as shown in Figure 3. In this implementation, the I-channel and Q-channel signals are individually demodulated in the same way as that of BPSK demodulation. After demodulation, the I-channel bits and Q-channel sequences are combined into a single sequence. The function qpsk_demod implements a QPSK demodulator as per Figure 3.
Read more about QPSK, implementation of their modulator and demodulator, performance simulation in these books:
Digital Modulations using Matlab : Build Simulation Models from Scratch
Digital Modulations using Python
Performance simulation over AWGN
The complete waveform simulation for the aforementioned QPSK modulation and demodulation is given next. The simulation involves, generating random message bits, modulating them using QPSK modulation, addition of AWGN channel noise corresponding to the given signal-to-noise ratio and demodulating the noisy signal using a coherent QPSK receiver. The waveforms at the various stages of the modulator are shown in the Figure 4.
The performance simulation for the QPSK transmitter-receiver combination was also coded in the code given above and the resulting bit-error rate performance curve will be same as that of conventional BPSK. A QPSK signal essentially combines two orthogonally modulated BPSK signals. Therefore, the resulting performance curves for QPSK – Vs. bits-in-error – will be same as that of conventional BPSK.
QPSK variants
QPSK modulation has several variants, three such flavors among them are: Offset QPSK, π/4-QPSK and π/4-DQPSK.
Offset QPSK
Offset QPSK is essentially same as QPSK, except that the orthogonal carrier signals on the I-channel and the Q-channel are staggered (one of them is delayed in time). In OQPSK, the orthogonal components cannot change states at the same time, this is because the components change state only at the middle of the symbol periods (due to the half symbol offset in the Q-channel). This eliminates 180° phase shifts all together and the phase changes are limited to 0° or 90° every bit period.
Elimination of 180° phase shifts in OQPSK offers many advantages over QPSK. Unlike QPSK, the spectrum of OQPSK remains unchanged when band-limited [1]. Additionally, OQPSK performs better than QPSK when subjected to phase jitters [2]. Further improvements to OQPSK can be obtained if the phase transitions are avoided altogether – as evident from continuous modulation schemes like Minimum Shift Keying (MSK) technique.
π/4-QPSK and π/4-DQPSK
In π/4-QPSK, the signaling points of the modulated signals are chosen from two QPSK constellations that are just shifted π/4 radians (45°) with respect to each other. Switching between the two constellations every successive bit ensures that the phase changes are confined to odd multiples of 45°. Therefore, phase transitions of 90° and 180° are eliminated.
π/4-QPSK preserves the constant envelope property better than QPSK and OQPSK. Unlike QPSK and OQPSK schemes, π/4-QPSK can be differentially encoded, therefore enabling the use of both coherent and non-coherent demodulation techniques. Choice of non-coherent demodulation results in simpler receiver design. Differentially encoded π/4-QPSK is referred as π/4-DQPSK.
Read more about QPSK and its variants, implementation of their modulator and demodulator, performance simulation in these books:
Digital Modulations using Matlab : Build Simulation Models from Scratch
Digital Modulations using Python
Constellation diagram
The phase transition properties of the different variants of QPSK schemes, are easily investigated using constellation diagram. Refer this article that discusses the method to plot signal space constellations, for the various modulations used in the transmitter.
Refer Digital Modulations using Matlab : Build Simulation Models from Scratch for full Matlab code. Refer Digital Modulations using Python for full Python code
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Determine the reference constellation points. Plot the constellation. Reconfigure the object for bit input and plot the constellation to show the binary values of the Gray-encoded mapping. Create a QPSK demodulator having phase offset set to 0 .
qpskmod = comm.QPSKModulator creates a System object™ to modulate input signals using the QPSK method. qpskmod = comm. QPSKModulator( Name , Value ) sets properties using one or more name-value arguments.
This can be achieved by using a PLL (phase lock loop) at the receiver. A PLL essentially locks to the incoming carrier frequency and tracks the variations in frequency and phase. For the following simulation , a PLL is not used but instead we simple use the output of the PLL.
The QPSK Demodulator Baseband block demodulates a signal that was modulated using the quadrature phase shift keying method. The input is a baseband representation of the modulated signal. The input must be a complex signal. This block accepts a scalar or column vector input signal.
Frequency modulate the signal at a carrier frequency of 3 kHz using a modulation constant of 0.1. fc = 3e3; rx = modulate(s,fc,fs,'fm',0.1); Frequency demodulate the signal using the same carrier frequency and modulation constant.
November 7, 2020 October 19, 2010 by Mathuranathan. Quadrature Phase Shift Keying (QPSK) is a form of phase modulation technique, in which two information bits (combined as one symbol) are modulated at once, selecting one of the four possible carrier phase shift states.
y = modulate( x , fc , fs ) modulates the real message signal x with a carrier frequency fc and sample rate fs . If x is a matrix, the modulated signal is computed independently for each column and stored in the corresponding column of y . [ y , t ] = modulate( x , fc , fs ) also returns the internal time vector t .
y = awgn( x , snr ) adds white Gaussian noise to the vector signal x . This syntax assumes that the power of x is 0 dBW. For more information about additive white Gaussian noise, see What is AWGN? y = awgn( x , snr , signalpower ) accepts an input signal power value in dBW.
QPSK is not more power efficient modulation technique compare to other modulation types as more power is required to transmit two bits. QPSK is more complex compared to BPSK receiver due to four states needed to recover binary data information.
QPSK Modulator The mathematical analysis shows that QPSK S n (t)=√(2 s/T)cos(2Πfct+(2n-1)Π/4); for n=1,2,3,4 (1) This yields the four phases π/4 3π/4 5π/4 and 7π/4 as needed. This results in a two-dimensional signal space with unit basis functions.
An AM radio signal can be demodulated by rectifying it to remove one side of the carrier, and then filtering to remove the radio-frequency component, leaving only the modulating audio component. This is equivalent to peak detection with a suitably long time constant.
Based on this nonlinearity, the demodulation methods can be broadly classified as methods using rectification (non-synchronous detection) and methods using mixing with a reference oscillator signal (synchronous detection).
In QPSK modulation schemes, it is necessary to have two carrier signals of equal amplitude at frequency fc that have a phase difference of 90 degrees (π/2 rad). A circuit that can generate two signals of equal amplitude that are 90 degrees out of phase is depicted in Fig. 9.18.
In modulation, the message signal is added on a carrier wave for transmission.In demodulation, the message is separated from the carrier signal. Modulation process is need for mixing of two signal of different parameters together. Demodulation is needed for recovery of original signal from a mix of two signals.
Modem stands for Modulator-demodulator. It is a device which connects the computers to the internet. It converts the analog signals from the transmission wires into digital signals which can be read by the computer devices (modulation).
z = fmdemod( y , Fc , Fs , freqdev ) returns a demodulated signal z , given the input frequency modulated (FM) signal y , where the carrier signal has frequency Fc and sampling rate Fs . freqdev is the frequency deviation of the modulated signal. The value of Fs must satisfy Fs ≥ 2 Fc .
y = fmmod( x , Fc , Fs , freqdev ) returns a frequency modulated (FM) signal y , given the input message signal x , where the carrier signal has frequency Fc and sampling rate Fs . freqdev is the frequency deviation of the modulated signal.
Description. z = amdemod( y , Fc , Fs ) returns a demodulated signal z , given the input amplitude modulated (AM) signal y , where the carrier signal has frequency Fc . The carrier signal and y have sampling frequency Fs .
To add signals using MATLAB® expressions and variables, select the Signal Editor Signal > Author Signal option. Time — Enter the range of time for the data. Data — Enter the MATLAB expression for the signal. Data type — Select or enter the signal data type.
You can achieve this through the numpy.random.normal function, which draws a given number of samples from a Gaussian distribution. You can achieve this with any kind of distribution as long as there are no autocorrelations in the signal.
Gaussian noise means the probability density function of the noise has a Gaussian distribution, which basically defines the probability of the signal having a certain value. Whereas white noise simply means that the signal power is distributed equally over time.
Frequency modulation is more effective in terms of noise tolerance and more suited for data transmission than AM. Phase modulation is more complex and costly but is relatively immune to noise and theoretically makes the best use of bandwidth for a given transmission rate.
Both QAM and QPSK are modulation techniques used in IEEE 802.11 (Wi-Fi*), IEEE 802.16 (WiMAX*) and 3G (WCDMA/HSDPA) wireless technologies. The modulated signals are then demodulated at the receiver where the original digital message can be recovered.
With 6x6 antenna configurations, QPSK has the lowest BER while 2x2 QAM has highest BER during simulation. QAM utilise both amplitude and phase variations. Although QAM is widely used in wireless communication system in terms of data carrying capacity, but QAM is more susceptible to noise compare to QPSK.
The QPSK signal is generated by phase-shifting the carrier. This applies for any carrier frequency. All symbol transitions are possible. I/Q Signals of quadrature modulation.
It provides good noise immunity. Compared to BPSK, bandwidth used by QPSK is reduced to half. The information transmission rate of Quadrature Phase Shift Keying is higher as it transmits two bits per carrier symbol.
QPSK uses four points on the constellation diagram, equispaced around a circle. With four phases, QPSK can encode two bits per symbol, shown in the diagram with Gray coding to minimize the bit error rate (BER) – sometimes misperceived as twice the BER of BPSK.
On the I/Q plane, QPSK represents four equally spaced points separated by π/2 (see Figure 4.5). Each of the four possible phases of carriers represents two bits of data. Thus, there are two bits per symbol.
In comparison to OOK and BPSK, QPSK enables the data rate to be doubled while keeping the same bandwidth, meaning it's also possible to stay at the same data rate at half the bandwidth, with the same bit error ratio (BER). So QPSK is suitable for data rates of 100 Gbps as well.
Decoding the modulated signal back to its original form is called demodulation. Amplitude, frequency, and phase modulation are the three different types of modulation. Analog, digital, pulse, and spread spectrum modulation are the four different types of modulation mechanisms.
Conclusion. The most commonly used circuits (methods) for demodulating amplitude modulated signals are synchronous detection, product detector and diode rectifier envelope detector. These demodulators can be used with any radio equipment used for amplitude modulated broadcast or radio communications.
Complete answer: A demodulator is a device that performs demodulation, which is the opposite process of modulation. The most basic equipment used for AM demodulation is a diode detector. A diode detector is made up of a diode and a few other parts.
In order to demodulate a double-modulated signal such as , at least two demodulators are necessary. Using the tandem technique, the in-phase or X-component of demodulated signal at the carrier frequency is internally routed to the second demodulator at sideband frequency.
A simple and effective FM demodulation technique involves a high-pass filter (for FM-to-AM conversion) followed by an AM demodulator. A high-pass-filter-based FM demodulator is preceded by a limiter to prevent amplitude variations from contributing error to the demodulated signal.
QPSK is used for satellite transmission of MPEG2 video, cable modems, videoconferencing, cellular phone systems, and other forms of digital communication over an RF carrier.
Quadrature Phase Shift Keying (QPSK) employs shifting the phase of the carrier at a 600 baud rate plus an encoding technique. QPSK is used in Bell 212A compatible modems and V. 22 - both are 1200 bps Full Duplex standards.
OQPSK and pi/4 QPSK are variants of the basic QPSK modulation schemes. They are widely used based on their unique individual phase transition functionalities compare to one another. This page explain these modulation types and explain difference between QPSK vs OQPSK vs pi/4QPSK.
Abstract: Carrier synchronization is one of the key technologies of digital wireless communication. As a kind of four phase shift keying modulation method, QPSK has strong anti-interference ability of the suppressed carrier, which is widely used in digital wireless communications.
Modulations which have an order of 4 and above usually are termed as higher-order modulations. Examples of these are quadrature phase shift keying (QPSK) and its generalisation as m-ary quadrature amplitude modulation (m-QAM).
Y = step(H,X) decodes the differentially encoded input data, X , and returns the decoded data, Y . The input X must be a column vector of data type logical, numeric, or fixed-point (embedded.fi objects). Y has the same data type as X . The object treats non-binary inputs as binary signals.
An AM radio signal can be demodulated by rectifying it to remove one side of the carrier, and then filtering to remove the radio-frequency component, leaving only the modulating audio component. This is equivalent to peak detection with a suitably long time constant.
bpskdemodulator = comm.BPSKDemodulator creates a demodulator System object that demodulates the input signal using the BPSK method. bpskdemodulator = comm. BPSKDemodulator( Name , Value ) creates a BPSK demodulator System object with each specified property set to the specified value.
y = modulate( x , fc , fs ) modulates the real message signal x with a carrier frequency fc and sample rate fs . If x is a matrix, the modulated signal is computed independently for each column and stored in the corresponding column of y . [ y , t ] = modulate( x , fc , fs ) also returns the internal time vector t .
MATLAB and Simulink help you analyze signals using built-in apps for visualizing and preprocessing signals in time, frequency, and time-frequency domains to detect patterns and trends without having to manually write code.
The diode detector is the simplest form of detector or demodulator used for AM demodulation – it detects the AM signal envelope. The diode detector is the simplest and most basic form of amplitude modulation, AM signal detector and it detects the envelope of the AM signal.
Quadrature Phase Shift Keying (QPSK) is a form of Phase Shift Keying in which two bits are modulated at once, selecting one of four possible carrier phase shifts (0, 90, 180, or 270 degrees). QPSK allows the signal to carry twice as much information as ordinary PSK using the same bandwidth.
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is defined as
and 
radians. Equation (1) can be re-written as
together with the inphase and quadrature signaling points: 
. Therefore, on a two dimensional co-ordinate system with the axes set to 
and 
, the QPSK signal is represented by four constellation points dictated by the vectors 
.
. Therefore, if the QPSK symbols were transmitted at same rate as BPSK, it is clear that QPSK sends twice as much data as BPSK does. After oversampling and pulse shaping, it is intuitively clear that the signal on the I-arm and Q-arm are BPSK signals with symbol duration 
. The signal on the in-phase arm is then multiplied by 
and the signal on the quadrature arm is multiplied by 
. QPSK modulated signal is obtained by adding the signal from both in-phase and quadrature arms.
, where 
is the given carrier frequency and 
is the sampling frequency satisfying Nyquist sampling theorem with respect to the carrier frequency (
). This configuration gives integral number of carrier cycles for one symbol duration.
Vs. bits-in-error – will be same as that of conventional BPSK.
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