DIGITAL COMMUNICATIONS

Course Content

DIGITAL COMMUNICATIONS

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  1. Introduction
  2. Digital Communications
  3. Information Capacity
  4. Digital Radio
  5. Bandwidth Efficiency
  6. PSK and QAM Summary
  7. Carrier Recovery
  8. Differential Phase Shift Keying
  9. Differential BPSK
  10. Clock Recovery
  11. Probability or Error and Bit Error Rate
  12. Applications for Digital Modulation

Introduction

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

  1. ANALOG SIGNALS

  2. DIGITAL SIGNALS
  3. >

Performance Comparison of Analog and Digital Systems

Advantages of Digital over analog

Disadvantages of Digital over Analog

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

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

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

Bandwidth Considerations of FSK

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

Minimum Shift Keying FSK (MSK)

PHASE SHIFT KEYING

  1. Binary PSK
  2. Quaternary PSK
  3. 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.
    Quarterwave QPSK
  4. Eight-Phase PSK
  5. 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
    8-PSK Constellation Diagram with Gray coding
  6. Sixteen-Phase PSK
  7. 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.

QUADRATURE AMPLITUDE MODULATION

A form of digital modulation where the digital information is contained in both the amplitude and the phase of the transmitted carrier

  1. Eight QAM
  2. 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
  3. Sixteen QAM
  4. 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

BANDWIDTH EFFICIENCY (INFORMATION DENSITY)

DIGITAL MODULATION SUMMARY

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

CARRIER RECOVERY

is the process of extracting a phase-coherent reference carrier from a received signal sometimes called phase referencing

Methods of Carrier Recovery

  1. Squaring Loop
  2. Carrier recovery for BPSK
  3. Costas Loop
  4. Remodulator

DIFFERENTIAL PHASE SHIFT KEYING

DIFFERENTIAL BPSK

CLOCK RECOVERY

PROBABILITY OR ERROR AND BIT ERROR RATE

Probability of error is a function of the carrier-to-noise power ratio and the number of possible encoding conditions used

PSK ERROR PERFORMANCE

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

FSK ERROR PERFORMANCE

Two Types of FSK systems:
  1. Noncoherent (asynchronous) - the transmitter and receiver are not frequency synchronized
  2. 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

APPLICATIONS FOR DIGITAL MODULATION



Last updated: Monday, September 19, 2007, 11:33 AM

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