1. TRANSMISSION OF INFORMATION
David Falconer and Halim Yanikomeroglu
Systems and Computer Engineering
Carleton University

2. Topics to be Covered Analog and digital signals
Power spectral density and bandwidth
Analog to digital conversion (ADC):
PCM (pulse code modulation)
Digital transmission

3. Analog Signal
An analog signal is any continuous signal for which the time varying feature (variable) of the signal is a representation of some other time varying quantity. For example, in an analog audio signal, the instantaneous voltage of the signal varies continuously with the pressure of the sound waves.
Analog signal differs from a digital signal, in which the continuous quantity is a representation of a sequence of discrete values which can only take on one of a finite number of values.
[Source: Wikipedia & Google images]

4. Digital Signal
A digital signal is a signal that represents a sequence of discrete values at clock times (discrete in amplitude & discrete in time)
[Source: Wikipedia & Google images]

5. Detection of Analog and Digital Signals
Digital signal + noise analog signal + noise
[Source: Google images]
Fundamental question: Is detection easier in digital signaling or in analog signaling?

6. 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, , data, video, etc. (a bit is a bit).
Better encryption.

7. 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

8. 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
spectral
density
(watts/Hz)
“High-fidelity speech
Telephone speech
(limited by filtering)
Bandwidth

9. Power Spectrum of Analog Signals
Source: Wikipedia

10. Power Spectrum of Digital Signals
Source: Wikipedia

11. 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 …

12. Bandwidth
3-dB Bandwidth
Source: Google images

13. Bandwidth
Digital Communications, B. Sklar

14. Bandwidth
Digital Communications, B. Sklar

15. Bandwidth
Digital Communications, B. Sklar

16. Bandwidth
Digital Communications, B. Sklar

17. 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

18. 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)
Filter
Sample at t=n Quantize Encode

19. Pulse-Code Modulation (PCM)
Sampling and quantization of a signal (red) for 4-bit PCM
The PCM process is commonly implemented on a single integrated circuit and is generally referred to as an analog-to-digital converter (ADC)

20. 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.

21. Quantization LPMC: Uncompressed
Uniform (Linear PCM: LPCM) Nonuniform
Output signal
Output signal
Input signal
Input 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

22. -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.

23. 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.

24. 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.
Coder: Decoder: +
Quant. +
Predictor
Predictor

25. 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 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 is an extension to G.711, published as ITU-T Recommendation G in March 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 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.

26. 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)

27. 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.

28. 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: 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. 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.

29. PCM Standards
MPEG-1 Audio Layer III: 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 (CD) and 48 kHz (DVD). 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. The bitrate limit for LPCM audio on DVD-Video is also Mbit/s, allowing 8 channels (7.1 surround) × 48 kHz × 16-bit per sample = 6,144 kbit/s

30. T1 (DS1) Format (North America) 24
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
DS0
PCM T-Carrier Multiplexing Hierarchy
Digital Signal Designation
Line rate
Channels (DS0s)
Line
DS0
64 kbit/s 1
DS1
1.544 Mbit/s 24 T1
DS1C
3.152 Mbit/s 48
T1C
DS2
6.312 Mbit/s 96 T2
DS3
Mbit/s
672 T3
DS4
Mbit/s
4032 T4
DS5
Mbit/s
5760 T5

31. Regenerative Repeater
Amplifier/
equalizer
Regenerator
Structure of a regenerative
repeater:
Timing circuit
By appropriate repeater design and inter-repeater spacing, the effect of
occasional bit errors due to noise can be controlled. Received signal quality is
essentially independent of distance.

32. PCM Transmission Formats and Spectra
Time
Frequency
Power spectra
Unipolar NRZ
T T 3T 4T /T -2/T -1/T /T 2/T 3/T
Bipolar NRZ
T 2T 3T 4T /T /T -1/T /T 2/T /T 
Unipolar RZ
T 2T 3T /T -1/ -2/T -1/T /T 2/T 1/ /T
Min. bandwidth
Bandlimited
T T 3T 4T /2T 1/2T

33. Multilevel Transmission
Binary:
L=2
4-level:
L=4
T T T T
Bit rate =
Bandwidth proportional to 1/T for NRZ signals

34. Additive White Gaussian Noise (AWGN)
AWGN is a channel model in which the only impairment to communication is noise.
AWGN: A linear addition of white noise with a constant spectral density and a Gaussian distribution of amplitude. [Wiki]
The model does not account for channel impairments. However, it produces simple and tractable mathematical models which are useful for gaining insight into the underlying behavior of a system before these other phenomena are considered. [Wiki]
Gaussian noise: Noise amplitude is a Gaussian distributed random variable (central limit theorem).
White noise: An idealized noise process with a power spectral density independent of frequency.

35. Additive White Gaussian Noise (AWGN)
Pnoise= k T B F = N0 B F
k: Boltzmann’s constant = 1.38 x J/K
T: Temperature in degrees Kelvin (generally taken as 290oK)
N0: Noise power spectral density (constant)
B: Bandwidth (signal bandwidth)
F: Noise figure
N0 = k T = -174 dBm/Hz
Ex: 200 KHz channel (LTE resource block)
F = 7 dB  Pnoise = -114 dBm
Broadband signal  Pnoise increases
White noise power spectral density f
SN(f)
N0/2
Infinite total power (?)

36. 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.

37. 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 = 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.
Note: For any x, log2(x)=(1/log10(2)) log10(x)=3.32 log10(x)
e.g. for SNR=10 dB, R/W=3.45 bit/s per Hz
For high SNR, R/W 0.332 X (SNR expressed in dB)
e. g. for SNR=30 dB, R/W 10 bits/s per Hz.

38. Fundamental Limits in Digital Data Rates Mobile device for everything?
Mobile device for everything 3G
Gbps 2G
Mbps 1G
Kbps
2010 – will be the decade of LTE
2020 -> - will be 5th G what will it hold?
Not entirely sure but – what is sure is that Between Now and then-
Cell size will definitely shrink – and consequently
Cell count will increase
All in an order of magnitude
Devices will undoubtedly expand exponentially
Data M2M will explode – And this will inevitably lead to a concatenation of growth trends
The growing need for information and interaction will spur a number of Mega-trends ……
bps
AMPS
1980
1990
2000
2010
2020
Time 38

39. Information Theory and Digital Communications
Ralph V.L. Hartley
1888 – 1970
Harry Nyquist
1889 – 1976
Norbert Wiener
1894 – 1964
Claude Shannon
1916 – 2001
Emre Telatar
1964 –
Gerard J. Foschini
1940 –

40. Fundamental Limits in Digital Data Rates
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) =  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) 40

41. Fundamental Limits in Digital Data Rates
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) 41

42. 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:
power spectrum density
bandwidth
multiplexing
channel capacity
We have discussed the fundamental enablers of transmission rate.