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## QPSK Modulation-Quadrature Phase Shift Keying modulation

This page describes QPSK modulation basics or Quadrature Phase Shift Keying modulation. Difference between QPSK modulation,BPSK modulation types,QPSK modulation matlab code links are also provided.

As mentioned QPSK stands for Quadrature Phase Shift Keying. It is digital modulation technique. QPSK is bandwidth efficient as each signal point represents two bits.

For example, instead of a phase shift of 180 degree, as allowed in BPSK, a common encoding technique, known as QPSK uses phase shifts of multiples of 90 degrees i.e. pi by 2.
QPSK modulation can be represented mathematically as mentioned below.

S(t)= A* cos(2*pi*fc*t + pi/4) for '11' input bits
S(t)= A *cos(2*pi*fc*t + (3*pi4)/4) for '01' input bits
S(t)= A *cos(2*pi*fc*t -(3*pi4)/4) for '00' input bits
S(t)= A *cos(2*pi*fc*t -pi/4) for '10' input bits Figure mention the constellation points and encoding rule,which is taken from IEEE standard 802.16-2004 to demonstrate QPSK modulation concept.

It converts two binary bits represented simultaneously at the input to the complex signal S(t) or d as mentioned. This complex signal selects one of the four phases based on two binary digits. Each state of the complex signal or waveform is called as symbol.

For QPSK, input bit stream need to break up to two-two bits and later these two bits are entered simultaneously to the input of the QPSK modulator. Hence, as shown in the constellation diagram for the input of 11 the output is (1+ j*1)*KMOD, where KMOD is normalization factor. For most of the systems KMOD is 0.707
As mentioned this output of 0.707+j*0.707 is called as symbol which represent two binary information digits.

### QPSK Modulation Applications

• Similar to BPSK, QPSK is used in various cellular wireless standards such as GSM, CDMA, LTE, 802.11 WLAN, 802.16 fixed and mobile WiMAX, Satellite and CABLE TV applications.

• As difference between any two constellation point is 90 degree maximum, QPSK modulation type has many benefits. It is robust compare to other modulation techniques except BPSK.

• It has double data rate carrying capacity compare to BPSK as two bits are mapped on each constellation points. In BPSK only 1 bit is mapped to each constellation point.

### What is Difference between QPSK and BPSK

• Refer QPSK vs BPSK which mentions difference between QPSK and BPSK modulation types.

• Refer QPSK vs OQPSK vs pi/4QPSK which mentions difference between various QPSK modulation types. It covers QPSK, OQPSK and pi/4QPSK modulation techniques.

### QPSK Modulation MATLAB CODE

Following link covers QPSK MATLAB code and provide matlab codes for other modulation types.
BPSK QPSK 16QAM 64QAM modulation matlab code