DIGITAL COMMUNICATIONS
Course Content
DIGITAL COMMUNICATIONS
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- Introduction
- Digital Communications
- Information Capacity
- Digital Radio
- Bandwidth Efficiency
- PSK and QAM Summary
- Carrier Recovery
- Differential Phase Shift Keying
- Differential BPSK
- Clock Recovery
- Probability or Error and Bit Error Rate
- Applications for Digital Modulation
Digital communications refers to the field of study concerned with the transmission of digital data. This is in contrast with analog communications. While analog communications use a continuously varying signal, a digital transmission can be broken down into discrete messages. Transmitting data in discrete messages allows for greater signal processing capability. The ability to process a communications signal means that errors caused by random processes can be detected and corrected. Digital signals can also be sampled instead of continuously monitored and multiple signals can be multiplexed together to form one signal.
Because of all these advantages, and because recent advances in wideband communication channels and solid-state electronics have allowed scientists to fully realize these advantages, digital communications has grown quickly. Digital communications is quickly edging out analog communication because of the vast demand to transmit computer data and the ability of digital communications to do so.
Source: http://en.wikipedia.org/wiki/Digital_communication
Two major categories of information signals
- ANALOG SIGNALS
- Analog signals represents a varying physical quantity such as voltage, voice, temperature, pressure or video intensity
- Analog signals does not impose a set of "allowed" values within the range
- Analog signal is the continuous wave varying in amplitude, frequency or phase
- DIGITAL SIGNALS
- Digital signals is allowed, at any instant of time, to have only one value from a set of previously defined specific values
- Digital signals use distinct, discrete signal values to represent the information it is trying to convey
- Digital signals is a discrete representation of a binary pulse characterized by the change between two states (high/low level voltage, on/off signal, mark/space pulse, logic 1/0)
- The discrete values can be represented by amplitude, phase or frequency variations
- Examples of digital signals (discrete) are financial numbers and typed text.
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Performance Comparison of Analog and Digital Systems
Advantages of Digital over analog
- Easier to multiplex
- Easier to integrate into switching system
- Easier to interface with other digital equipment
- Noise immunity
- Better performance monitorability
- Easy to encode, decode, encrypt and scramble
Disadvantages of Digital over Analog
- Large bandwidth
- Need for synchronization
- Need for additional equipment
- Not compatible with existing systems
- Need for AD/DA conversion
- Restrictions in wired topology
Regeneration - the process of restoring a noise corrupted signal to its original value
DIGITAL COMMUNICATIONS
Covers a broad area of communications techniques including digital transmission and digital radio.
Digital Radio - is the transmittal of digitally modulated analog carriers between two or more points in a communications system; the transmission medium is free space or Earth's atmosphere.
INFORMATION CAPACITY
The information capacity of a communications system represents the number of independent symbols that can be carried through the system in a given unit of time; it is express in bits per second (bps).
Information theory is a discipline in applied mathematics involving the quantification of data with the goal of enabling as much data as possible to be reliably stored on a medium or communicated over a channel. The measure of information, known as information entropy, is usually expressed by the average number of bits needed for storage or communication. For example, if a daily weather description has an entropy of 3 bits, then, over enough days, we can describe daily weather with an average of approximately 3 bits per day.
Hartley's Law
where I = information capacity in bps
B = bandwidth in Hz
T = transmission time in seconds
Shannon-Hartley Law
where N = number of bits encoded
Shannon Law
where NR = Nyquist rate
DIGITAL RADIO
- The property that distinguishes a digital radio system from a conventional AM, FM, or PM radio system is that the modulating and demodulated signals are digital pulses rather than analog waveforms
- Digital radio uses analog carriers
- There are three digital modulation techniques used in digital radio; the Frequency Shift Keying (FSK), Phase Shift Keying (PSK), and Quadrature Amplitude Modulation (QAM).
AMPLITUDE SHIFT KEYING
Amplitude-shift keying (ASK) is a form of modulation that represents digital data as variations in the amplitude of a carrier wave.
The simplest and most common form of ASK operates as a switch, using the presence of a carrier wave to indicate a binary one and its absence to indicate a binary zero. This type of modulation is called on-off keying, and is used at radio frequencies to transmit Morse code (referred to as continuous wave operation).
ON-OFF KEYING
The amplitude of an analog carrier signal varies in accordance with the bit stream (modulating signal), keeping frequency and phase constant. The level of amplitude can be used to represent binary logic 0s and 1s. We can think of a carrier signal as an ON or OFF switch. In the modulated signal, logic 0 is represented by the absence of a carrier, thus giving OFF/ON keying operation and hence the name given.
On-off keying (OOK) is a type of modulation that represents digital data as the presence or absence of a carrier wave. In its simplest form, the presence of a carrier for a specific duration represents a binary one, while its absence for the same duration represents a binary zero. Some more sophisticated schemes vary these durations to convey additional information.
FREQUENCY SHIFT KEYING
- Two sine wave frequencies are used to represent binary digits
The general expression for a binary FSK is
where v(t) = binary FSK waveform
Vc = peak unmodulated carrier amplitude
c = radian carrier frequency
vm(t) = binary digital modulating signal
= change in radian output frequency
FSK Transmitter
- The carrier frequency is shifted by the binary input data.
- The output rate of change is equal to the input rate of change
- In digital modulation, the rate of change at the input modulator, is called bit rate
- The rate of change at the output of the modulator is called baud or baud rate
Bandwidth Considerations of FSK
- FSK modulators are very often voltage-controlled oscillators (VCOs)
- The rest frequency of the VCO is halfway between the mark and space frequencies
- Modulation index is given as
where MI = modulation index
f = frequency deviation (Hz)
fa = modulating frequency (Hz)
fb = input bit rate
Deviation Ratio - worst-case modulation index which yields the widest output bandwidth; it occurs when both the frequency deviation and the modulating frequency are at their maximum values
FSK Receiver
- The most common circuit used for demodulating binary FSK signals is the phased-locked loop (PLL)
Minimum Shift Keying FSK (MSK)
- A form of continuous-phase FSK
- the mark and space frequency are synchronized with the input binary bit rate
- the mark and space frequency are selected such that they are separated from the center frequency by an exact odd multiple of one-half of the bit rate, to ensure that there is a smooth phase transition in the analog output signal when it changes from a mark to a space frequency, or vice versa
PHASE SHIFT KEYING
- Binary PSK
- Two output phases are possible for a single carrier frequency
- As the digital signal changes state, the phase of the output carrier shifts between two angles that are 180 out of phase
- Other names for BPSK are phase reversal keying and biphase modulation.
- A form of suppressed carrier, square-wave modulation of a continuous wave signal
- Quaternary PSK
- Four output phases are possible for a single carrier frequency
- The baud rate is one-half of the bit rate
- Each of the four possible phasors has exactly the same amplitude
- The angular separation between any two adjacent phasors is 90
- Minimum bandwidth equals
Quadrature PSK
Binary input |
Phase (degrees) |
0 |
0 |
-135 |
0 |
1 |
-45 |
1 |
0 |
+135 |
1 |
1 |
+45 |
Lambda/4–QPSK
This final variant of QPSK uses two identical constellations which are rotated by 45° (x/4 radians, hence the name) with respect to one another. Usually, either the even or odd data bits are used to select points from one of the constellations and the other bits select points from the other constellation. This also reduces the phase-shifts from a maximum of 180°, but only to a maximum of 135° and so the amplitude fluctuations of x/4–QPSK are between OQPSK and non-offset QPSK.
- Eight-Phase PSK
- There are eight possible output phases
- The baud rate is equal to fb/3, the same as the minimum bandwidth
Binary Input |
Phase (degrees) |
0 |
0 |
0 |
-112.5 |
0 |
0 |
1 |
-157.5 |
0 |
1 |
0 |
-67.5 |
0 |
1 |
1 |
-22.5 |
1 |
0 |
0 |
+112.5 |
1 |
0 |
1 |
+157.5 |
1 |
1 |
0 |
+67.5 |
1 |
1 |
1 |
+22.5 |
- Sixteen-Phase PSK
- There are sixteen different output phases possible
- The baud rate is equal to one-fourth of the incoming bit rate
- The angular separation between adjacent output phases is only 22.5 degrees.
Binary Input |
Phase (degrees) |
0 |
0 |
0 |
0 |
11.25 |
0 |
0 |
0 |
1 |
33.75 |
0 |
0 |
1 |
0 |
56.25 |
0 |
0 |
1 |
1 |
78.75 |
0 |
1 |
0 |
0 |
101.25 |
0 |
1 |
0 |
1 |
123.75 |
0 |
1 |
1 |
0 |
176.25 |
0 |
1 |
1 |
1 |
168.75 |
Binary Input |
Phase (degrees) |
1 |
0 |
0 |
0 |
191.25 |
1 |
0 |
0 |
1 |
213.75 |
1 |
0 |
1 |
0 |
236.25 |
1 |
0 |
1 |
1 |
258.75 |
1 |
1 |
0 |
0 |
281.25 |
1 |
1 |
0 |
1 |
303.75 |
1 |
1 |
1 |
0 |
326.25 |
1 |
1 |
1 |
1 |
348.75 |
Bit-error rate curves for BPSK, QPSK, 8-PSK and 16-PSK.
A form of digital modulation where the digital information is contained in both the amplitude and the phase of the transmitted carrier
- Eight QAM
The minimum bandwidth is fb/3
Binary Input |
Amplitude |
Phase (degrees) |
0 |
0 |
0 |
0.765 V |
-135 |
0 |
0 |
1 |
1.848 V |
-135 |
0 |
1 |
0 |
0.765 V |
-45 |
0 |
1 |
1 |
1.848 V |
-45 |
1 |
0 |
0 |
0.765 V |
+135 |
1 |
0 |
1 |
1.848 V |
+135 |
1 |
1 |
0 |
0.765 V |
+45 |
1 |
1 |
1 |
1.848 V |
+45 |
- Sixteen QAM
Same as 16-PSK
Binary Input |
Amplitude |
Phase (degrees) |
0 |
0 |
0 |
0 |
0.311 V |
-135 |
0 |
0 |
0 |
1 |
0.850 V |
-175 |
0 |
0 |
1 |
0 |
0.311 V |
-45 |
0 |
0 |
1 |
1 |
0.850 V |
-15 |
0 |
1 |
0 |
0 |
0.311 V |
-105 |
0 |
1 |
0 |
1 |
0.850 V |
-135 |
0 |
1 |
1 |
0 |
0.311 V |
-75 |
0 |
1 |
1 |
1 |
0.311 V |
-45 |
Binary Input |
Amplitude |
Phase (degrees) |
1 |
0 |
0 |
0 |
0.311 V |
135 |
1 |
0 |
0 |
1 |
0.850 V |
165 |
1 |
0 |
1 |
0 |
0.311 V |
45 |
1 |
0 |
1 |
1 |
0.850 V |
15 |
1 |
1 |
0 |
0 |
0.311 V |
105 |
1 |
1 |
0 |
1 |
0.850 V |
135 |
1 |
1 |
1 |
0 |
0.311 V |
75 |
1 |
1 |
1 |
1 |
0.850 V |
45 |
- used to compare the performances of one digital modulation technique to another
- the ratio of the transmission bit rate to the minimum bandwidth required
Modulation |
Encoding |
Bandwidth |
Baud |
Bandwidth Efficiency |
FSK |
Single bit |
>=fb |
fb |
<=1 |
BPSK |
Single bit |
fb |
fb |
1 |
QPSK |
Dibit |
fb/2 |
fb/2 |
2 |
8-PSK |
Tribit |
fb/3 |
fb/3 |
3 |
8-QAM |
Tribit |
fb/3 |
fb/3 |
3 |
16-PSK |
Quadbit |
fb/4 |
fb/4 |
4 |
16-QAM |
Quadbit |
fb/4 |
fb/4 |
4 |
is the process of extracting a phase-coherent reference carrier from a received signal
sometimes called phase referencing
Methods of Carrier Recovery
- Squaring Loop
Carrier recovery for BPSK
- Costas Loop
- Remodulator
- An alternative form of digital modulation where the binary input information is contained in the difference between two successive signaling elements rather than the absolute phase
- A received signaling element is delayed by one signaling element time slot and then compared to the next received signaling element
- The difference in the phase of the signaling elements determines the logic condition of the data
Probability of error is a function of the carrier-to-noise power ratio and the number of possible encoding conditions used
- Carrier Power, C (can be stated in watts or dBm)
- Thermal Noise Power, N
or
- Energy-per-bit, Eb
or
- Noise Power Density, No
? Thermal noise power normalized to a 1-Hz bandwidth
- Energy per bit-to-noise power density ratio
? Used to compare two or more digital modulation systems that use different transmission rates, modulation schemes, or encoding techniques
Threshold points
where M = number of signal states
Error distance
where D = peak signal amplitude
Probability of Error
where erf = error function
QAM ERROR PERFORMANCE
Error distance
where L = number of levels on each axis
Bit error probability
where erfc = complementary error function
Two Types of FSK systems:
- Noncoherent (asynchronous) - the transmitter and receiver are not frequency synchronized
- Coherent (synchronous) - local receiver reference signals are in frequency and phase lock with the transmitted signals
Performance Comparison of Various Digital Modulation Schemes (BER = 10-6)
Modulation Technique C/N ratio
(dB) Eb/No ratio
(dB)
BPSK 10.6 10.6
QPSK 13.6 10.6
4-QAM 13.6 10.6
8-QAM 17.6 10.6
8-PSK 18.5 14.0
16-PSK 24.3 18.3
16-QAM 20.5 14.5
32-QAM 24.4 17.4
64-QAM 26.6 18.8
- used in digitally modulated microwave radio
- used in satellite systems
- used for voice band data modems
Last updated: Monday, September 19, 2007, 11:33 AM
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