Chapter 7 Fundamentals of Digital Transmission Baseband Transmission

Chapter 7 Fundamentals of Digital Transmission

Baseband Transmission (Line codes) ON-OFF or Unipolar (NRZ) Non-Return-to-Zero Polar (NRZ)

Performance Criteria of Line Codes o o Zero DC value Inherent Bit-Synchronization n o Average Transmitted Power n o Rich in transitions For a given Bit Error Rate (BER) Spectral Efficiency (Bandwidth) n Inversely proportional to pulse width.

Comparison Between On-Off and Polar o Zero DC value: n o Bandwidth: n o Comparable Power: n n o Polar is better. BER is proportional to the difference between the two levels For the same difference between the two levels, Polar consumes half the power of on-off scheme. Bit Synchronization: n Both are poor (think of long sequence of same bit)

More Line Codes On-Off RZ Better synch. , at extra bandwidth Bi-Polar Better synch. , at same bandwidth

More Line Codes Polar RZ Perfect synch 3 levels Manchester (Bi-Phase) Perfect Synch. 2 levels

Spectra of Some Line Codes

Pulse Shaping o o The line codes presented above have been demonstrated using (rectangular) pulses. There are two problems in transmitting such pulses: n n They require infinite bandwidth. When transmitted over bandlimited channels become time unlimited on the other side, and spread over adjacent symbols, resulting in Inter-Symbol. Interference (ISI).

Nyquist-Criterion for Zero ISI o Use a pulse that has the following characteristics o One such pulse is the sinc function.

The Sinc Pulse 1 -6 Tb -5 Tb -4 Tb -3 Tb -2 Tb p(t) t -Tb Tb 2 Tb 3 Tb 4 Tb Note that such pulse has a bandwidth of Rb/2 Hz. Therefore, the minimum channel bandwidth required for transmitting pulses at a rate of Rb pulses/sec is Rb/2 Hz -1/(2 Tb) 5 Tb 6 Tb P(f) 1/(2 Tb) f

Zero ISI

More on Pulse Shaping o o The sinc pulse has the minimum bandwidth among pulses satisfying Nyquist criterion. However, the sinc pulse is not fast decaying; n n o Misalignment in sampling results in significant ISI. Requires long delays for realization. There is a set of pulses that satisfy the Nyquist criterion and decay at a faster rate. However, they require bandwidth more than Rb/2.

Raised-Cosine Pulses where b is 2 Rb and x is the excess bandwidth. It defines how much bandwidth required above the minimum bandwidth of a sinc pulse, where

Spectrum of Raised-Cosine Pulses

Extremes of Raised-Cosine Spectra

Raised-Cosine Pulses

Carrier Modulation of Digital Signals Information Amplitude Shift Keying Frequency Shift Keying Phase Shift Keying 1 0 1 +1 -1 0 T 2 T 3 T 4 T 5 T 6 T t +1 -1 t t

Bandwidth Requirement of Passband Transmission o o Passband transmission requires double the bandwidth of baseband transmission. Therefore, the minimum bandwidth required to transmit Rb pulses/sec using carrier modulation is Rb Hz.

Transmission rates of Typical Services o o o Speech Audio Fax Coloured Image Video

Speech (PCM) o o o B = 3. 4 k. Hz Rs = 8000 samples/sec Encoding = 8 bits/sample Transmission rate = 64 kbps Required bandwidth (passband) = 64 k. Hz One hour of speech = 64000 x 3600 = 230. 4 Mb

Audio o o B = 16 -24 k. Hz Rs = 44 000 samples/sec Encoding = 16 bits/sample Stereo type = 2 channels Transmission rate = 1. 4 Mbps

Fax o o o Resolution 200 x 100 pixels/square inch 1 bit/pixel (white or black) A 4 Paper size = 8 x 12 inch Total size = 1. 92 Mb = 240 KB Over a basic telephone channel (3. 4 k. Hz, baseband) it takes around 4. 7 minutes to send one page.

Colour Image (still pictures) o o Resolution 400 x 400 pixels/inch square 8 bits/pixel 3 colours/photo A 8 x 10 inch picture is represented by 307. 2 Mb = 38. 4 MB !

Video (moving pictures) o o o Size of still pictures 15 frames/sec 307 Mb/frame x 15 frames/sec = 4605 Mbps =4. 6 Gbps !!

Solutions o Compression n o reduces data size M-ary communication n Expands channel ability to carry information

M-ary Transmission o o o In the binary case one pulse carries one bit. Let each pulse carry (represent) m bits. Bit rate becomes m multiples of pulse rate We need to generate 2 m different pulses. They can be generated based on: n n Multiple Amplitudes (baseband passband) Multiple Phases (passband) Multiple frequencies (passband) Some combination (Amplitude and Phase).

Signal Constellation o o o Signal constellation is a convenient way of representing transmitted pulses. Each pulse is represented by a point in a 2 -dimensional space. The square of the distance to the origin represents the pulse energy. The received signals form clouds around the transmitted pulses. A received points is decoded to the closest pulse point.

Multiple Amplitudes (PAM) 0 1 2 “levels” 1 bits / pulse B bits per second 00 10 11 01 4 “levels” 2 bits / pulse 2×B bits per second 000 110 011 101 001 8 “levels” 3 bits / pulse 3×B bits per second

Same-maximum-power Scenario typical noise 4 signal levels 8 signal levels

signal + noise High SNR t t t noise signal + noise Low SNR t SNR = t Average Signal Power Average Noise Power t

Same-BER Scenario o o Average power for binary case: ½ A 2 + ½ A 2 = A 2 Average power for 4 -ary case: ¼ (9 A 2 + 9 A 2 ) = 5 A 2

Multiple Phases (MPSK) 4 “phase” 2 bits / pulse 2×B bits per second 8 “phases” 3 bits / pulse 3×B bits per second

Quadrature Amplitude Modulation (QAM) QAM 16 QAM Bk Bk Ak Ak 4 “levels”or pulses 2 bits / pulse 2 x. B bits per second 16 “levels” or pulses 4 bits / pulse 4 x. B bits per second

The Modulation Process of QAM Modulate cos(wct) and sin (wct) by multiplying them by Ak and Bk respectively: Ak x Yi(t) = Ak cos(wc t) Bk x sin(wc t) + Yq(t) = Bk sin(wc t) Y(t)

QAM Demodulation Y(t) x LPF 2 cos(wc t) x 2 sin(wc t) Ak 2 cos 2(wct)+2 Bk cos(wct)sin(wct) = Ak {1 + cos(2 wct)}+Bk {0 + sin(2 wct)} LPF Bk 2 Bk sin 2(wct)+2 Ak cos(wct)sin(wct) = Bk {1 - cos(2 wct)}+Ak {0 + sin(2 wct)}