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TRANSMISSION OF INFORMATION

David Falconer and Halim Yanikomeroglu

Dept. of Systems and Computer Engineering

Carleton University

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Topics to be Covered

Analog (continuous time, continuous amplitude) signals

Power spectral density and bandwidth

Analog to digital: PCM (pulse code modulation)

Digital transmission

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Digital and Analog Signals

Some signals (like speech and video) are inherently analog; some (like computer data) are inherently digital.

However, both analog and digital signals can be represented and transmitted digitally.

Advantages of digital:» Reduced sensitivity to line noise, temp. drift, etc.» Low cost digital VLSI for switching and transmission.» Lower maintenance costs than analog.» Uniformity in carrying voice, SMS, email, data, video, etc. (a bit is a bit)» Better encryption.

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Power Spectral Density

Power spectrum (power spectral density) describes how the average power is distributed with respect to frequency.

Deterministic signals Fourier transform

Random signals Power spectral density

A statistical representation for all random signals in a particular application

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Power Spectrum of Analog Signals

Analog (continuous-time, continuous-amplitude) signals (like speech) have a certain bandwidth. Their power spectrum (power spectral density) describes how their average power is distributed with respect to frequency.

Power spectraldensity(watts/Hz)

0 1 2 3 4 5 6 7....

“High-fidelity speech

Telephone speech (limited by filtering)

Bandwidth

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Power Spectrum of Analog Signals

Source: Wikipedia

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Bandwidth

For random signals, bandwidth is determined from the power spectral density.

Bandwidth is determined only from the +ve frequencies.

There are different bandwidth definitions

Absolute bandwidth

Y% bandwidth (for instance, 99%)

X-dB bandwidth (for instance, 3-dB)

Null-to-null bandwidth

…

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Bandwidth

3-dB Bandwidth

Source: Wikipedia

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Bandwidth

Digital Communications, B. Sklar

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Bandwidth

Digital Communications, B. Sklar

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Bandwidth

Digital Communications, B. Sklar

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Bandwidth

Digital Communications, B. Sklar

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Sampling an Analog Signal

Sampling theorem: The original analog signal can be reconstructed if it is sampled at a rate at least twice its bandwidth.

Reconstruction is by filtering samples with a low pass filter.

Sampling Samples Reconstruction

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Pulse Code Modulation (PCM)

PCM is a method used to digitally represent sampled analog signals. It is the standard form of digital audio in computers, Compact Discs, digital telephony and other digital audio applications.

PCM signal is developed by three steps: sampling, quantizing and encoding.

Quantizing noise is reduced by using variable sized steps. It is independent of line length.

s(t) s(n)

Sample at t=n Quantize Encode

011010001...Filter

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Pulse Code Modulation (PCM)

The PCM process is commonly implemented on a single integrated circuit and is generally referred to as an analog-to-digital converter (ADC)

Sampling and quantization of a signal (red) for 4-bit PCM

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Standard PCM in Wired Telephony

• Voice circuit bandwidth is 3400 Hz.

• Sampling rate is 8 KHz (samples are 125 s apart).

• Each sample is quantized to one of 256 levels.

• Each quantized sample is coded into a 8-bit word.

• The 8-bit words are transmitted serially (one bit at a time) over a digital transmission channel. The bit rate is 8x8,000 = 64 Kb/s.

• The bits are regenerated at digital repeaters.

• The received words are decoded back to quantized samples, and filtered to reconstruct the analog signal.

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Quantization

Uniform (Linear PCM: LPCM) Nonuniform

Input signal Input signal

Output signal Output signal

The more steps (levels) the less quantization noise. Nonuniform quantization(e.g. -law) allows a larger dynamic range (important for speech).

LPMC: Uncompressed

Nonuniform quantization: Introduces compression

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-Law Quantization and Coding

• Standardized in North America.

• Based on a logarithmic non-uniform quantizer.

• Range of amplitudes divided into 8 segments, each segment with 16 uniformly spaced levels. Segment i is double the width of segment i-1.

• 8 bit word: 1 bit for sign, 3 bits identify segment, 4 bits identify level within segment.

• Can show for n-bit word, signal to quantization noise ratio is approximately 6n-10 [dB]; e.g., 38 dB for n=8 bits.

• Most of the rest of the world uses a related logarithmic non-uniformity, called A-law.

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Variants of PCM (Form of Compression)

Differential PCM (DPCM) encodes the PCM values as differences between the current and the predicted value. An algorithm predicts the next sample based on the previous samples, and the encoder stores only the difference between this prediction and the actual value. If the prediction is reasonable, fewer bits can be used to represent the same information. For audio, this type of encoding reduces the number of bits required per sample by about 25% compared to PCM.

 

Adaptive DPCM (ADPCM) is a variant of DPCM that varies the size of the quantization step, to allow further reduction of the required bandwidth for a given signal-to-noise ratio.

 

Delta Modulation is a form of DPCM which uses one bit per sample.

 

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Adaptive Differential PCM (ADPCM)

Allows coding with a lower bit rate (with same fidelity) for speech, based on predicting the next sample; e.g., 8 or 16 or 32 Kb/s.

More circuits accommodated in the same transmission bandwidth.

Quant.

PredictorPredictor

+ +

Coder: Decoder:

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PCM Standards

 G.711 is an ITU-T standard for audio companding. It is primarily used in telephony. The standard was released for usage in 1972. Its formal name is Pulse Code Modulation (PCM) of voice frequencies.

G.711 uses a sampling rate of 8,000 samples per second. Non-uniform (logarithmic) quantization with 8 bits is used to represent each sample, resulting in a 64 kbit/s bit rate.

G.711.1 is an extension to G.711, published as ITU-T Recommendation G.711.1 in March 2008. Its formal name is Wideband embedded extension for G.711 pulse code modulation.

G.711.1, allows the addition of narrowband and/or wideband (16000 samples/s) enhancements, each at 25 % of the bitrate of the (included) base G.711 bitstream, leading to data rates of 64, 80 or 96 kbit/s.

G.711.1 is compatible with G.711 at 64 kbit/s, hence an efficient deployment in existing G.711-based voice over IP (VoIP) infrastructures is foreseen.

 

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PCM Standards

 G.726 is an ITU-T ADPCM speech codec standard covering the transmission of voice at rates of 16, 24, 32, and 40 kbit/s (1990).

The most commonly used mode is 32 kbit/s, which doubles the usable network capacity by using half the rate of G.711. It is primarily used on international trunks in the phone network. The principal application of 24 and 16 kbit/s channels is for overload channels carrying voice in digital circuit multiplication equipment (DCME).

It also is the standard codec used in DECT wireless phone systems and is used on some Canon cameras.

Sampling frequency 8 kHz. 16 kbit/s, 24 kbit/s, 32 kbit/s, 40 kbit/s bit rates available.

Testing under ideal conditions yields Mean Opinion Scores of 4.30 for G.726 (32 kbit/s), compared to 4.45 for G.711 (µ-law)

 

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PCM Standards

 Audio Interchange File Format (AIFF) is an audio file format standard used for storing sound data for personal computers and other electronic audio devices.

The audio data in a standard AIFF file is uncompressed pulse-code modulation (PCM). There is also a compressed variant of AIFF known as AIFF-C or AIFC, with various defined compression codecs.

Like any non-compressed, lossless format, it uses much more disk space than MP3—about 10MB for one minute of stereo audio at a sample rate of 44.1 kHz and a sample size of 16 bits.

Developed by Apple Inc. Initial release 21 January 1988.

 

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PCM Standards

 MPEG-1 or MPEG-2 Audio Layer III, more commonly referred to as MP3, is a patented digital audio encoding format using a form of lossy data compression. It is a common audio format for consumer audio storage, as well as a de facto standard of digital audio compression for the transfer and playback of music on digital audio players. Initial release: 1993.

MP3 is an audio-specific format that was designed by the Moving Picture Experts Group (MPEG) as part of its MPEG-1 standard and later extended in MPEG-2 standard.

The use in MP3 of a lossy compression algorithm is designed to greatly reduce the amount of data required to represent the audio recording and still sound like a faithful reproduction of the original uncompressed audio for most listeners. An MP3 file that is created using the setting of 128 kbit/s will result in a file that is about 1/11 the size of the CD file created from the original audio source. An MP3 file can also be constructed at higher or lower bit rates, with higher or lower resulting quality.

The compression works by reducing accuracy of certain parts of sound that are considered to be beyond the auditory resolution ability of most people. This method is commonly referred to as perceptual coding. It uses psychoacoustic models to discard or reduce precision of components less audible to human hearing, and then records the remaining information in an efficient manner.

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PCM Standards

Several bit rates are specified in the MPEG-1 Audio Layer III standard: 32, 40, 48, 56, 64, 80, 96, 112, 128, 160, 192, 224, 256 and 320 kbit/s, and the available sampling frequencies are 32, 44.1 and 48 kHz. Additional extensions were defined in MPEG-2 Audio Layer III: bit rates 8, 16, 24, 32, 40, 48, 56, 64, 80, 96, 112, 128, 144, 160 kbit/s and sampling frequencies 16, 22.05 and 24 kHz.

A sample rate of 44.1 kHz is almost always used, because this is also used for CD audio, the main source used for creating MP3 files. A greater variety of bit rates are used on the Internet. The rate of 128 kbit/s is commonly used, at a compression ratio of 11:1, offering adequate audio quality in a relatively small space. As Internet bandwidth availability and hard drive sizes have increased, higher bit rates up to 320 kbit/s are widespread.

Uncompressed audio as stored on an audio-CD has a bit rate of 1,411.2 kbit/s, so the bitrates 128, 160 and 192 kbit/s represent compression ratios of approximately 11:1, 9:1 and 7:1 respectively.

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1 2 3 4 24

1 2 3 4 5 6 7 8

S bit

24 PCM code words, each representing 1 sample

8 bits per code word

193 bits in 125 s (1.544 Mb/s)

DS1 Format (-Law Countries)

DS0

DS1

Hierarchical Multiplexing:

DS1: 24 DS0

DS3: 28 DS1

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Regenerative Repeater

Regenerativerepeater

Regenerativerepeater

Amplifier/equalizer

Regenerator

Timing circuit

Structure of a regenerativerepeater:

By appropriate repeater design and inter-repeater spacing, the effect of occasional bit errors due to noise can be controlled. Received signal quality isessentially independent of distance.

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PCM Transmission Formats and Spectra

..... 1 0 1 1 .......

Time Frequency

0 T 2T 3T 4T -3/T -2/T -1/T 0 1/T 2/T 3/T

0 T 2T 3T 4T -4/T -2/T -1/T 0 1/T 2/T 4/T

0 T 2T 3T 4T -1/2T 1/2T

Min. bandwidth

Unipolar NRZ

Bipolar NRZ

Bandlimited

Power spectra

0 T 2T 3T -4/T -1/ -2/T -1/T 0 1/T 2/T 1/ 4/T

Unipolar RZ

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Multilevel Transmission

1 0 1 1 0 0 0 1

0 T 2T 3T 4T

Binary:L=2

4-level:L=4

Bit rate = 1T

log2 L

Bandwidth proportional to 1/T for NRZ signals

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Bandwidth Required for Digital Transmission

required bandwidth is approximately

(bit rate)/(log2L) for L-level transmission.

more levels less bandwidth, but greater sensitivity to noise.

Examples:» 64 Kb/s PCM requires about 64 KHz for binary transmission, 32 KHz for 4-

level transmission.» 14.4 Kb/s modem uses a symbol rate 1/T=2400 Hz, and the equivalent of

L=32.

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Channel Capacity

Shannon channel capacity formula:» Highest possible transmission bit rate R, for reliable communication in a

given bandwidth W Hz, with given signal to noise ratio, SNR, is

R=Wlog2(1+SNR) bits/s

R/W = 0.332 SNR [dB] bits/s/Hz (for high SNR)

» Assumptions and qualifications:– Gaussian distributed noise added to the signal by the channel, highly complex

modulation, coding and decoding methods.

– In typical practical situations, the above formula may be roughly modified by dividing SNR by a factor of about 5 to 10.

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1G1G

2G2G

3G3G

44GG

5G5G

Mbps

Kbps

bps

Gbps

20202010200019901980

AMPS

? Mobile device for everything

Time

Fundamental Limits in Digital Data Rates

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Ralph V.L. Hartley

1888 – 1970Claude Shannon

1916 – 2001

Harry Nyquist

1889 – 1976

Norbert Wiener

1894 – 1964

Emre Telatar

1964 –

Gerard J. Foschini

1940 –

Information Theory and Digital Communications

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RBS: Data rate (speed) of a wireless base station (access point)

•W: Bandwidth

•SNR: Signal-to-noise ratio at the receiver

•SE: Spectral efficiency = log2(1+SNR)

•n: Min (# of transmit antennas, # of receive antennas)

None of the three variables (W, SE, n) scales well!

Ex 1: n = 2, W = 10 MHz, log(1+SNR) = 4 RBS = 80 Mbps

Ex 2: n = 8, W = 100 MHz, log(1+SNR) = 4.5 RBS = 3.6 Gbps

(Cellular 4th generation LTE-Advanced)

RBS = n x W x SE = n x W x log2(1+SNR)

Fundamental Limits in Digital Data Rates

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Rnetwork: Network rate

•K: # of BSs in the network

Fundamental dynamics:

4 basic factors that impact network rate: K, n, W, SE

Increasing base station rate: Not easy! (neither of n, W, SE scales well)

Increasing network rate: Possible! (by adding more base stations)

Rnetwork = K x n x W x log2(1+SNR)

Fundamental Limits in Digital Data Rates

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Summary

All information signals can be represented, switched, stored and transmitted digitally.

We have discussed PCM systems and their key elements:» sampling» quantizing» coding» digital transmission

We have discussed the related concepts of:» the telephone set» bandwidth» the sampling theorem» signal to quantization noise ratio» channel capacity.

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More Information

SYSC 5608 Wireless Communications Systems Engineering, lecture notes

E.B. Carne, “Telecommunications Primer”, 2nd edition, Prentice-Hall, 1999

J. Sklar, “Digital Communications”, Chapters 2 and 7