In communications modulation is the processing of a high frequency periodical signal with a low frequency signal that is used to contain encoded information. This high frequency signal is called the carrier signal and has usually a simple form like a sine waveform. Modulation is needed from the low frequency data signal, in order to reach its destination through a communication channel (wire or free space) without exceeding the bandwidth of this channel. Demodulation is taking place at the receiver, in order to retrieve the original signal. A modem is a device that can both modulate and demodulate a signal and is highly used for transmitter and receiver.
Using a modulation for the data signal makes easier transmition in free space. In this case antennas are necessary for transmittals and receptions. However, these antennas must have the same dimensions as the wave length of the signal, which means that for low frequency signals, that have a large wave length, antennas must have a large size. By modulating this signal higher transmitting frequency is achieved, thus smaller wave length. In this case we can use small size antennas to transmit and receive the signal. In addition, modulating a signal in specific frequency band can allow the use of frequency division multiplexing (FDM), thus allowing the use of the same transmittal medium to broadcast in different channel more than one signals, by sharing the bandwidth of the medium to the channels. In addition, modulation can overcome some of the restrictions that transmitters and receivers have. Common examples are filters and amplifiers that are manufactured with a low bandwidth and with the use of modulation the signal is formidable to pass through. Moreover, signal modulation gives radio stations the ability to transmit at the same time in different carrier frequencies. Finally, using the correct modulation for a signal, noise and interference can be prevented for a more reliable transmittal.
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Modulation differs depending of the signal being modulated and this can be analog or digital.
Three are the basic categories for modulating a digital signal and transmit it in an analog form. These three variations come from the tree basic aspects of the carrier signal, which is, amplitude, phase and frequency. The carrier signal modulation is based on the data signal. In digital modulation based on amplitude, the amplitude of the signal changes whenever a change from 1 to 0 or 0 to 1 occurs on the data signal, this modulation is called Amplitude Shifting-Key (ASK). In addition, in phase modulation there is a phase change in the signal, this is called Phase Shifting-Key (PSK). Finally, the frequency changes in Frequency Shifting-Key (FSK) in the same way.
Phase-shift modulation is basically a family of digital modulations, in which data is found on the phase-shifts of a sine carrier. The simplest form is the Binary PSK (BPSK), where the digits 0 and 1 are encoded by two single phase channels. More complex is the four-phase modulation (QPSK), the eight-phase modulation (8-PSK) and the differential PSK modulation.
In this simple form of a PSK modulation, the amplitude and frewuency of a carrier signal are constant. The phase is shifting from 0o to 180o. in [1.1] there is a modulated BPSK signal originated by the input signal. As we can see, the input signal bits refer to a phase shift of the modulated signal, therefore in BPSK modulation baud rate is equal to bit rate.
1.1 Carrier signal, digital input, BPSK signal
A bpsk transmitter is usually consisted from a multiplier. The multiplier is basically a balanced modulator circuit [1.2]. As inputs there is a digital data signal and the sine carrier signal. If there is a bit 0 we get -A Volt and for a bit 1 we get +A Volt at the exit of the multiplier. 0 -> -Asinact = Asin(act + 180o) and 1 -> Asinact. So the signal phase that corresponds to 1 is Phase1 = 0o and to 0 is Phase2 = 180o.
1.2 BPSK modulator
An easy way to display the phases of a PSK modulated signal is the constellation diagram. In a constellation diagram every baud is displayed with a mark. The amplitude of a modulated signal is given from the distance of a mark from zero and the phase is given from the ankle formed between the horizontal axis and the mark to (0,0) point line of the axis[1.3].
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1.3 BPSK constellation diagram
The bandwidth of a BPSK modulated signal is easily calculated Fb = Rb/2 , where Rb is the data rate.
After the multiplier the signal is:
Xmul = sinabt . sinact = ½[cos(ac - ab)t - cos(ac + ab)t = ½[cos(2πfc - 2πfb)t - cos(2πfc + 2πfb)t = ½[cos2π(fc - fb)t - cos2π(fc + fb)t
Since the Xmul(x) signal has these frequences (fc - fb),(fc + fb) the bandwidth is BBPSK = 2fb = Rb and its developed symmetrically around fc.
The BPSK receiver is consisted from a multiplier, a carrier recovery circuit and a low pass filter.
1.4 BPSK demodulator
For input: 1 -> Asinact. After the multiplier X(t)= Asinact sinact = A/2[cos(0o) - cos(2act)] = A/2 - A/2 [cos(2act)]
From a LPF filter only A/2 passes, so Xout= A/2 ->1
For input: 0 -> Asin(act + 180o). After the multiplier X(t)= Asin(act+ 180o)sinact = A/2[cos(180o) - cos(2act + 180o)] = - A/2 - A/2 [cos(2act+ 180o)]
From a LPF filter only -A/2 passes, so Xout= -A/2 ->0
This form of PSK modulation uses four different phases to contain information. Because of the 0 and 1 conditions of the input signal, the binary digits are grouped and form dibits. Every dibit can have four possible variations, which points in a different phase in the modulator and every input dibit shows a phase variation on the output. Resulting, that in QPSK modulation buad rate is equal to the half of bit rate.
The QPSK transmitter is basically two BPSK transmitters, where one is called IN-phase-I and has a carrier phase 0o and the other is called Quadrature-Q and has a carrier phase 180o. the block diagram of a QPSK transmitter is shown in [2.1].
2.1 QPSK modulator
Every dibit of the input digital signal is going through a bit splitter. The first bit of every dibit is going to IN-phase-I and called I-bit and the second one in Quadrature-Q and called Q-bit.
When modulated through BPSK we should have:
For In-phase-I in the condition 0 -> - Asinact = Asin(act+π), in the condition 1 -> Asinact
For Quandrature-Q in the condition 0 -> - Asin(act+π/2) = Asin(act+3π/2), in the condition 1 -> Asin(act+π/2)
Finally the sum of these two QPSK modulated signals has the phase of both. In the constellation diagram [2.2] is is presented the four possible phases of a QPSK modulated signal.
2.2 QPSK constellation diagram
Considering that the QPSK modulator consists of two BPSK modulator which had separated bits as inputs, the bandwidth of each QPSK output for Rb bit rate should be: BW = Rb/2
Considering the linear sum of these two signals is BQPSK = Rb/2
This is the half bandwidth in comparison with a BPSK modulated signal.
The block diagram of a QPSK receiver is shown in [2.3], which consists of two BPSK demodulators. However, in order to demodulate the signal properly one of the two QPSK demodulators must have a carrier signal with a π/2 phase difference with the other.
2.3 QPSK demodulator
In 8-PSK modulation the signal can have eight different phases which represent the converted bits of information. Since every bit has two possible conditions 0 and 1, binary input digits group to form tribits. Every tribit can have 23 = 8 possiple variations from 000 to 111 and each one represents a different phase of the modulated signal. In addition, since every tribit represents a different phase, in 8-PSK modulated signal baud rate equals 1/3 of the bit rate.
An 8-PSK transmitter is similar to that of QPSK modulation [3.1].
3.1 8-PSK modulator
Input signal passes by a serial to parallel converter and is convered in tribit. Every tribit is described by two voltage variations in the mapping circuit. These represent the vertical and horizontal vectors of a tribit in a constellation diagram, in which every mark is defined by the vector sum [3.2]. the X and Y signals are multiplied with the carrier signals Asinact and Asin(act+π/2). Finally the sum of these two modulated signal is transmitted.
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3.2 8-PSK constellation diagram
The method of calculating the Bandwidth of a 8-PSK modulated signal is very similar to QPSK. Since the input bit rate splits in three components, each one has a Bandwidth BWcomp = Rb/3. However, the 8-PSK modulated signal is provided with the linear sum of these three signals BW8psk = Rb/3. Generally, the 8-PSK modulated signal bandwidth is 1/3 in comparison with BPSK, which has the same bit rate input. In 8-PSK modulation Bandwidth is equal to baud rate.
The demodulation of an 8-PSK modulated signal is very similar to QPSK [3.3]. The X and Y signals after the Low Pass Filters are driven to an inverse mapping circuit and compared to the predefined values stored in the system memory to register as tribits. Finally, the produced tribits are described as a digital signal through a parallel to serial circuit.
3.3 8-PSK demodilator
DPSK modulation is commonly used instead of BPSK in telephony circuits. Instead of the information being contained in every phase change (baud), in DPSK information is contained in the phase difference between two continuous baud. Using this Differential modulation one could have DBSK, DQPSK,8-DPSK modulations.
A main advantage in using DPSK modulation is the simplicity of the receiver, since the carrier signal does not have to be in the same phase as the carrier of the transmitter. In addition, a memory circuit is needed to store the previous baud phase and compare it with the present phase, so that a difference can be computed.
In [4.1] there is the block diagram of a DBPSK transmitter, in which, there is a differential coder, a XNOR and a 1 bit delay circuit.
4.1 DBPSK modulator
In [4.2] is described the variation of continuous bits. The bandwidth of a DBPSK modulated signal is equal to that of a BPSK, which has the same Rb bit rate input BWDBPSK = Rb.
4.2 Bits variations
The DBPSK receiver is shown in [4.3], is less complicated than in PSK modulation, since there is no need to duplicate the carrier signal from the modulated one.
4.3 DBPSK demodulator
In a DBPSK modulation the signal is displayed for a time equal to a bit, so there can be a compare between the current bit and the previous. If those two bits have the same phase at the exit of a multiplier there is a +A, the digit 1 or if the phase differs by 180o there is a -A, the digit 0.