### Quadrature Phase Shift keying:-

The designing of digital communication system requires two important goals to achieve

1. To achieve low probability of error P_{e}.

2. To utilize Channel Band width efficiently.

QPSK is A Band width conserving modulation scheme, which is an example of Quadrature Carrier Multiplexing.

The modulation schemes such as ASK, PSK & FSK does not meet the Band width requirements of data Communication systems since the Bit rate and Baud rate are same in these schemes. Since the channel band width depends up on the bit rate (or) signalling rate of the modulation scheme. If two (or) more bits are combined into a symbol, then the signalling rate is reduced. Therefore the frequency of the carrier is also reduced, this reduces the transmission channel band width. Thus grouping of bits into symbols reduces Channel Band width.

### Meaning of QPSK:-

In Quadri Phase Shift Keying as with Binary PSK information carried by the transmitted signal is contained in the phase of the carrier. The phase of the carrier Φ_{c} takes on one of four equally spaced values such as π/4, 3π/4, 5π/4 and 7π/4 that is in QPSK two successive bits are combined into a di-bit or symbol and each possible value of the phase corresponds to a unique di-bit.

for example the foregoing set of phase values are chosen to represent the gray encoded set of di-bits 10, 00, 01 and 11 , where only a single bit is changed from one di-bit to the next.

### Generation of QPSK/ QPSK transmitter:-

Consider the generation and detection of QPSK signals. The figure shows a Block diagram of a typical QPSK Transmitter.The incoming binary sequence is first transmitted into polar form by a Non-Return to zero level encoder. Thus symbols 1 and 0 are represented by

√ E_{s} and –√ E_{s}

This binary wave is next divided by means of a de-multiplexer into two separate binary waves. Consisting of the odd and even numbered input bits {b_{e}(t)} and {b_{o}(t)} represents those two binary waves.

The two bit streams b_{e}(t) and b_{o}(t) are modulated by two ortho-normal basis functions Φ_{1}(t) and Φ_{2}(t).finally, the two binary PSK signals are added to produce the desired QPSK signal.

i.e, S_{QPSK}(t) = S_{e}(t) + S_{o}(t).

S_{oPSK}(t)= b_{o}(t)* √(2/T_{s})* cos 2πf_{c} t

S_{ePSK}(t)= b_{e}(t)* √(2/T_{s})* sin 2πf_{c} t

S_{QPSK}(t)= b_{o}(t)* √(2/T_{s})* cos 2πf_{c} t + b_{e}(t)* √(2/T_{s})* sin 2πf_{c} t.

### QPSK Receiver:-

The QPSK Receiver consists of a pair of correlators called as In-phase channel and Quadrature phase channel with a common input. The input x(t) is supplied with a pair of coherent reference signals Φ_{1}(t) and Φ_{2}(t). The two correlators produces two signals x_{1}(t) and x_{2}(t) in response to the received signal x(t).these signals x_{1}(t) and x_{2}(t) are compared with threshold voltage 0V by the decision devices in the two channels.

If x_{1} >0, a decision has been made in favor of symbol ‘1’ for the in-phase channel output. but if x_{1}<0 a decision has been made in favor of ‘0’. simillarly for the Q-phase channel,

x_{2}>0—-> a symbol ‘1’ is decided.

x_{2}<0—-> a symbol ‘0’ is decided.

finally these two binary sequences at the I-phase and Q-phase channel outputs are combined in a multiplexer to reproduce the original binary sequence at the Receiver output with the minimum probability of symbol error in AWGN channel.