1. Fundamental Dynamics of 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)

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 [U] = (10 log10 A) [dBU]
A [unitless] = (10 log10 A) [dB]
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 [U] = (10 log10 A) [dBU]
A [unitless] = (10 log10 A) [dB]
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 4600)
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
interference

16. 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
Non-idealities in channel
Distortion channel: distorts; may introduce self-interference
Fading channel: ideal channel with a time-varying impulse response
interference

17. 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
Non-idealities in channel
Distortion channel: distorts; may introduce self-interference
Fading channel: ideal channel with a time-varying impulse response
Interference (interference channel)
Major source of interference: other-user interference (co-channel interference)
Occurs mainly in wireless channels
Can be handled via signal processing, beamforming, RRM, …
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. 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?

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
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. 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)

27. 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

28. 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