1. Introduction to Digital Communications
Halim Yanıkömeroğlu
Department of Systems & Computer Engineering
Carleton University
Ottawa, Canada

2. Outline dB Notation The Big Picture: OSI Model
Major impairments in communication systems
Noise (AWGN)
SNR
Main goals of digital communications
MAC, RRM, RAN

3. What is wrong with the below figure?

4. What is wrong with the below figure?
The detail is lost for the small values of the vertical axis!

5. What is wrong with the below figure?
The detail is lost for the small values of the vertical axis!
Want to show large and small values on the same scale?

6. Logarithmic versus Linear Scale
What is wrong with the below figure?
The detail is lost for the small values of the vertical axis!
Want to show large and small values on the same scale?
Use logarithmic scale (not linear scale) in the vertical axis.

7. dB Notation Linear dB 5000 37 400 26 10 8 9 5 7 2 3 1 0.5 -3 0.125 -9
logc(a x b) = logc(a) + logc(b) logc(a / b) = logc(a) – logc(b)
Decibel notation: Field quantities: 20 log10 (./.)
Power quantities: 10 log10 (./.)
In this course: 10 log10 (.)
x  + (increased by 1,000,000 times  increased by 60 dB)
÷  - (decreased by 50 times  decreased by 17 dB)
A [unitless] = (10 log10 A [unitless]) [dB]
A [u] = (10 log10 A[u]) [dBu]
Linear dB
5000 37
400 26 10 8 9 5 7 2 3 1
0.5 -3
0.125 -9
0.01
-20
0.0005
-33

8. dB Notation Linear dB 5000 37 400 26 10 8 9 5 7 2 3 1 0.5 -3 0.125 -9
logc(a x b) = logc(a) + logc(b) logc(a / b) = logc(a) – logc(b)
Decibel notation: Field quantities: 20 log10 (./.)
Power quantities: 10 log10 (./.)
In this course: 10 log10 (.)
x  + (increased by 1,000,000 times  increased by 60 dB)
÷  - (decreased by 50 times  decreased by 17 dB)
A [unitless] = (10 log10 A [unitless]) [dB]
A [u] = (10 log10 A[u]) [dBu]
P [W] = (10 log10P[W]) [dBW] Ex: 2 [W] = 3 [dBW]
P [mW] = (10 log10P[mW]) [dBm] Ex: 2 [mW] = 3 [dBm]
P [dBW] = (P+30) [dBm] Ex: 5 [dBW] = 35 [dBm]
10 log10SNR = (10 log10(Psignal [mW] / Pnoise [mW])) [dB]
10 log10SNR = (10 log10Psignal) [dBm] – (10 log10Pnoise) [dBm]
X [dBm] – Y [dBm] = Z [dB]; X [dBm] + Y [dB] = Z [dBm]
Linear dB
5000 37
400 26 10 8 9 5 7 2 3 1
0.5 -3
0.125 -9
0.01
-20
0.0005
-33

9. The Big Picture: OSI Model
The Open Systems Interconnection (OSI) model is a prescription of characterizing and standardizing the functions of a communications system in terms of abstraction layers. [Wiki]
For example, a layer that provides error-free communications across a network provides the path needed by applications above it, while it calls the next lower layer to send and receive packets that make up the contents of that path. Two instances at one layer are connected by a horizontal connection on that layer. [Wiki]

10. The Big Picture: OSI Model
The physical layer defines the means of transmitting raw bits rather than logical data packets over a physical link connecting network nodes. The bit stream may be grouped into code words or symbols and converted to a physical signal that is transmitted over a hardware transmission medium.
The physical layer provides an electrical, mechanical, and procedural interface to the transmission medium. The shapes and properties of the electrical connectors, the frequencies to broadcast on, the modulation scheme to use and similar low-level parameters, are specified here. [Wiki]

11. Imprecise Terminology
Often used synonymously in industry:
Digital Communications (SYSC 5504)
Transmission Technologies
Physical Layer
But they have slightly different meanings

12. Digital Communications Block Diagram
Digital Communications, Sklar

13. Major Impairments in Communication Systems: A Simple Picture
noise
Transmitter
Channel
Receiver
interference

14. Major Impairments in Communication Systems: A Simple Picture
noise
Transmitter
Channel
Receiver
Noise: always present
interference

15. Major Impairments in Communication Systems: A Simple Picture
noise
Transmitter
Channel
Receiver
Noise: always present
Channel
Ideal channel (AWGN channel)
does not distort (change the shape of) the transmitted signal
introduces attenuation and delay: h(t) = a d(t-t)
remains the same (a: fixed)
interference

16. Major Impairments in Communication Systems: A Simple Picture
noise
Transmitter
Channel
Receiver
interference

17. Major Impairments in Communication Systems: A Simple Picture
noise
Transmitter
Channel
Receiver
interference

18. 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.

19. 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 (?)

20. [noise power: noise power in signal BW]
SNR, SINR
Signal-to-Noise Ratio: Defined at the receiver front end
SNR = (signal power) ∕ (noise power)
SNR = Psignal ∕ Pnoise
SNR = (bit energy) ∕ (noise power spectral density)
SNR = Eb ∕ N0
Signal-to-Interference-plus-Noise Ratio:
SINR = Psignal ∕ (Pinterference+ Pnoise)
Classical view: Threat interference as noise  business as usual (use the theory developed for AWGN channel)
Modern view: Can we exploit the structure in the interference signal?
[noise power: noise power in signal BW]

21. Wireless Channel: Fading Signal
SNR
AWGN channel: Ps: fixed  SNR: fixed
Fading channel: Ps: variable  SNR: variable

22. Main Goal of Digital Communications
SNR
Transmitter
Channel
Receiver
noise
Main Goal: For a given fixed SNR or an SNR distribution what operations should take place at transmitter and receiver to improve the performance?
Performance: Some meaningful metric
User metrics: (ultimately) eye, ear, feeling, smell, …
MOS (mean opinion scores)  frame error rate (FER)  packet error rate (PER)  symbol error rate (SER)  bit error rate (BER) 
maximize SNR
resort to better transmission and/or reception techniques

23. Main Goal of Digital Communications
If SNR=15 dB and the target BER = 10-3,
which modulation level should be used?
SNR=10 dB

24. + Main Goal of Digital Communications
noise + TX
Channel RX
How do you send information (reliably) through a channel?
For a given channel (medium), design TX and RX for best performance
Best? Maximize/minimize SER, BER, SNR, mutual information, …
Network metrics may be different than link metrics:
number of users, outage, sum (aggregate) rate, revenue, …

25. Main Goal of Digital Communications
SNR
Transmitter
Channel
Receiver
noise
For a given fixed SNR (or an SNR distribution) what operations should take place at transmitter and receiver to improve the performance?
Pulse shaping
Modulation, demodulation
Channel coding, decoding
Diversity
Equalization …

26. MAC, RRM, RAN Want SNR ↑ ?  PS ↑ and/or Pn ↓ (limited control on Pn)
Want SINR ↑ ?  PS ↑ and/or PI ↓ and/or Pn ↓(limited control on Pn)
How can we increase PS ?
How can we decrease PI ?
Answer: Medium Access Control (MAC) [layer 2]
Radio Resource Management (RRM) [layer 2]
Radio Access Network (RAN)
How do we compute PS ?  Propagation modeling

27. Part II Analog and digital signals
Power spectral density and bandwidth
Digital transmission

28. [Source: Wikipedia & Google images]
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]

29. [Source: Wikipedia & Google images]
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]

30. Detection & Estimaiton 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?

31. 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.

32. 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

33. 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

34. Power Spectrum of Analog Signals
Source: Wikipedia

35. Power Spectrum of Digital Signals
Source: Wikipedia

36. 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 …

37. Bandwidth
3-dB Bandwidth
Source: Google images

38. Digital Communications, B. Sklar
Bandwidth
Digital Communications, B. Sklar

39. Digital Communications, B. Sklar
Bandwidth
Digital Communications, B. Sklar

40. Digital Communications, B. Sklar
Bandwidth
Digital Communications, B. Sklar

41. Digital Communications, B. Sklar
Bandwidth
Digital Communications, B. Sklar

42. Channel Capacity
Channel capacity, Shannon capacity, information-theoretic capacity
C = log2(1+SNR), bits per second per Hertz
Non-constructive existence theorem
Developments
Shannon’s original formulation: 1948
Block codes, convolutional codes, …
Turbo codes (1993)
Low-density parity check (LDPC) codes (1963, 1996)
Polar codes (2008)

43. Bandwidth vs Rate T: Pulse duration, R: Rate  R = 1/T W: Bandwidth
Inverse relation between T and W
Direct relation between R and W
Narrow pulses (high rates)  Large bandwidth

44. 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 44

45. 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 –

46. 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) 46

47. 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) 47

48. 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.