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If the data signal is digital and the phase of the carrier wave is varied proportional to the data signal then that processing is called phase shift keying (PSK). Every digital modulation design uses a finite number of different signals to indicate the digital data. Phase shift keying uses a finite number of phases; all assigns a single model of binary digits. Generally, each phase encodes an identical number of bits. Every sample of bits shapes the symbol that is represented by the exacting phase. The simplest form of phase shift keying is binary phase shift keying (BPSK). BPSK uses the two phases that are separated by 180°. BPSK also called as phase reversal keying (PRK) and biphase modulation. It is not important where the constellation points are placed. The figure (1.4) shows the phase shift keying wave form with respective to the data signal and figure (1.5) shows the constellation diagram for BPSK .Here the constellation points are shown on real axis i.e; 0° and 180°.
Electronic communication system is basically divided into two communication systems. They are analog communication system and digital communication system. In analog communication system for modulation purpose we use amplitude modulation, frequency modulation, and phase modulation but these modulation techniques are hastily replaced with digital communication system, because it has the advantages such as no difficulty of multiplexing, no complexity of processing, and noise resistance. Digital modulation is preferably suitable for large number of communication applications together with both cable and wireless systems. The applications of digital modulation are low speed voice band data communication modems (these are found in personal computers), high speed data transmission systems (broadband digital subscriber lines (DSL)), and digital microwave and satellite communication systems, cellular telephone personal communication systems (PCS). In digital communication system three types of modulation techniques are there. They are amplitude shift keying, frequency shift keying, and phase shift keying.
[WAYNE TOMASI, (2004) ADVANCED ELECTRONIC COMMUNICATION SYSTEMS, SIXTH EDITION].
In spite of this phase shift keying (PSK) have some advantages comparing to frequency shift keying (FSK) and amplitude shift keying (ASK) . Those are PSK utilise less band width, consumes less power, less effected to noise, detection is easy, and it has low error rate comparing to fsk and ask. These are some advantages of phase shift keying.
[MICHAEL, J.R, MICHAEL, J.F (2002), COMMUNICATION AND INFORMATION SYSTEMS. AUSTRALIA: ARGOS PRESS CANBERRA]
Binary phase shift keying is the simplest form of phase shift keying modulation. For BPSK two phases are possible for the carrier wave. One phase represents the logic 0 and the other phase represents logic 1. If there is a change in the input digital signal state i.e; from 1 to 0 or 0 to 1 then the phase of the output carrier shifts between two angles separated by 180°. Binary phase shift keying is also called as phase reversal keying (PRK) , and biphase modulation. Because of this simplicity it is used in biometric passports, RF standards, credit cards , wireless LANs at IEEE 802.15.4 standard . In wireless communication these wireless LANs are suitable. BPSK is apt because of its low data transfer rate , low power and small circuit. These are the main concerns for BPSK.
[WAYNE TOMASI, (2004) ADVANCED ELECTRONIC COMMUNICATION SYSTEMS, SIXTH EDITION]; [http://www.museumstuff.com/learn/topics/BPSK::sub::Applications]
This chapter explains about the principles of BPSK, mathematical representation of BPSK modulator and demodulator, modulation and demodulation of BPSK, hardware design of BPSK, and error probability for BPSK.
3.1. PRINCIPLES OF BPSK:
The technique of the binary phase shift keying is phase modulation in which two phases are available for carrier wave. That are represented by the +v or -v which are given by logic 0 and logic 1. BPSK signal is generated by multiplying the carrier signal with digital data signal, thus the carrier signal is modulated according to the input data.
The principle used for generation of BPSK is shown is figure (3.1)
FIG 3.1 BPSK MODULATOR
3.2 MATHEMATICAL REPRESENTATION OF BPSK MODULATOR:
BPSK modulation depends upon the binary input information signal that produces an output voltage which is symbolized in the form of non return to zero (NRZ) in which b(t) is given as
b(t) = +1 when logic 1 is transmitted
b(t) = -1 when logic 0 is transmitted
if the carrier wave is given as
and the dissipation power is given as
If the binary bit 1 is transmitted then the resulting modulated signal is given as
If the binary bit 0 is transmitted then resulting modulated signal is given as
Consequently the binary phase shift keying (BPSK) signal can be given as
The BPSK signal moves the information into two symbols which are given by logic 1 and logic 0 , mathematically it is given as
Equation (3.6) can also be written as
Here (t) is the orthogonal carrier signal.
Then s(t) can be written as
Now the energy bit is equal to the product of duration of bit and power. i.e;
[CHITODE .J.S. (2008) DIGITAL COMMUNICATION , INDIA TECHNICAL PUBLICATIONS PUNE]
Therefore BPSK signal s(t) is shown in below figure 3.1.a
FIGURE 3.1 a BINARY PHASE SHIFT SIGNAL KEYING MODULATING SIGNAL
[CHARAN LANGTON (2005) ALL ABOUT MODULATION COMPARISION]
3.3. MODULATION OF BPSK:
In binary phase shift technique for a single carrier frequency there will be two stages of output. One stage signifies the logic 0 and another stage signifies the logic 1. Depending upon the input data signal the phase of the output carrier changes from one point to another point. Consequently the carrier wave will be in phase of 0° or out of phase for 180° with respective to the location of carrier signal.
Figure (3.2) Generation of BPSK modulator
The above figure (3.2) shows the binary phase shift key modulator.
Operation of BPSK modulation: The data of the input which is in digital form is given to the level converter. Level converter will convert the nonstandard positive or negative logic input voltages to the digital or logic levels and it will make the signals as unipolar to bipolar that are assigned to the data signal with logic 0 and logic 1 for input data signal for the both positive and negative voltages. For the multiplier the signal is processed from the level converter. Multiplier has two inputs first one is the data signal and the other is carrier signal. For the multiplier as we are giving the input as data signal the output will be in the form of 0° or 180° in phase or out of phase with reference to the carrier signal. The binary phase shift keying waveform is as shown in the figure (3.3) .from that figure it can be seen that with the change in the input data signal the phase of the carrier signal also changes.
Figure (3.3) Binary Phase Shift Keying waveform
[tomasi. W (2004) advanced electronic communication system 6th ed, new jersey]
3.4. DEMODULATION OF BINARY PHASE SHIFT KEYING:
For binary phase shift keying on demodulation side as we are using multiplier, carrier recovery circuit, integrator and threshold detector circuit. The following diagram (3.4) represents the demodulation of binary phase shift keying.
FIGURE (3.4) DEMODULATION OF BPSK CIRCUIT
[Frank,c. Russell p , j. Russell j.Robert h (2002) telemetry system engineering; great Britain: library of congress cataloging in publication : cannon street]
3.4.1. CARRIER RECOVERY CIRCUIT :
A carrier recovery circuit used for approximation and compensation for the both phase and frequency variations between a received carrier wave and the received local oscillator for the demodulation purpose. In BPSK the carrier recovery circuit is used for recovering the phase coherent carrier from the received local oscillator. In phase modulation method the carrier of the phase modulated depends upon the digital information. So to regenerate the original digital data a phase coherent carrier is recovered and compared with the product detector. It is significant to give a carrier at the receiver i.e; the phase coherent with the transmitter reference oscillator. For the binary phase shift keying demodulator, for carrier recovery circuit a costas loop gain is used.
3.4.2. COSTAS LOOP GAIN :
Costas loop gain circuit is shown in figure (3.5) .
Figure (3.5) Costas loop gain circuit .
Costas loop gain consists of a voltage controlled oscillator that is operated by using two parallel loops. The phase loop (I arm) is the first loop of the costas loop gain it applies direct output from the voltage controlled oscillator. The quadrature loop (Q arm) is the second loop of the Costas loop gain it applies 90° phase shifted signal from voltage controlled oscillator. To control the voltage controlled oscillator the both phase loop and quadrature loop i.e.; both I and Q arm are multiplied and filtered that is applied for the recovery of the carrier from the modulated received signal.
3.4.3. VOLTAGE CONTROLL OSCILLATOR :
A voltage controlled oscillator or VCO is an electronic oscillator, in VCO with the help of voltage input oscillation frequency can be controlled. By applying a DC voltage there will be a change in frequency oscillation. While modulating signals may also be fed into the VCO to cause frequency modulation or phase modulation.