Basics of outage probability and its variation with several parameters.

1. Fundamental of Outage Probability
Domain: Wireless Communication Research
Dr. Varun Kumar
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2. Outlines
1 Introduction to Communication
2 Challenges of Wireless Communication
3 Introduction to Outage
4 Outage Variation with Different Parameters
5 References
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3. Introduction to Communication
⇒ Communication is a process for sending information/signal/data from
source to sink.
⇒ As per the nature of signal (analog and digital), it is categorized into
two parts.
Analog communication ⇒ When analog signal is transmitted from
source to sink.
Digital communication ⇒ When digital signal is transmitted from
source to sink.
⇒ By default all signals are analog in nature, whereas for convenience in
signal processing operation, this signal is converted into digital.
⇒ Digital signal is a man-made signal.
⇒ Digital signal has lots advantageous features compare to analog, like
noise immunity, storage, encryption and many more.
⇒ In modern wired and wireless communication; digital signal is the raw
ingredient for effective communication.
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4. Challenges of effective communication
Power ⇒ Communication at low power without losing the quality of
service (QoS)
Energy-efficient communication ⇒ Green communication
Signal strength at receiver end is below the certain threshold ⇒
Outage in existing communication network. This impairment is
measured in terms of outage probability.
Bandwidth ⇒ It is a scarce resource of wired as well as wireless
communication. Available bandwidth for commercial usage is very
less as per the data demand.
Spectrum-efficient communication
If effective data rate is below certain threshold then there arise a
problem of outage ⇒ Outage capacity
Time/Latency ⇒ Network latency is a critical challenge for coherent
transmission and detection.
Coherent time : The time over which the wireless channel are supposed
to be highly correlated or considered as constant.
Lower the latency greater be the system throughput.
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5. Continued–
Space ⇒ Due to multi-antenna integration across eNB as well as user
equipment (UE), spatial multiplexing/diversity could be possible in
modern communication.
Multiple antenna enhances diversity and multiplexing and reduces
outage at the cost of computational complexity, large bandwidth
requirement and many more.
Low complex precoder/decoder is an important design constraints.
Due to leakage of power between adjacent antenna elements in
multiple antenna system. Hence, high power can’t be transmitted
through Tx − Rx unit.
Code ⇒ Orthogonal code (pilot) is used for channel estimation. This
code is a very scarce resource in wireless communication.
In multi-user scenario, if number of users increases then the length of
code sequence is also very large that also increases the requirement of
other wireless resource significantly (especially time and frequency).
Note: There are end-less challenges comes in wireless communication.
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6. Introduction to outage and outage probability
Outage due to large scale effect→ Shadowing
From above figure A, B, C, D are the points on trajectory, where UE is
going to move.
Radial separation between base station and UE is d.
Let path loss exponent between A → B and C→ D is ν = 2.4
Between B → C, signal strength drops significantly due to shadowing.
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7. Continued–
Path loss expression,
Pr =
Pt
Z(d/d0)ν
(1)
where, Pr → Received power at UE, Pt → Transmitted power from BS,
d0 → Reference distance, Z → Log-normal random variable or
log(Z) ∼ N(0, σ2
) is a Gaussian distributed RV. Taking log on both side.
log10{Pr (d)} = log10 Pt − ν log10(d/d0)
Mean Pathloss ¯PL
− log10(Z) (2)
Pr (d)|dB = Pt|dB − PL(d) ⇒ PL(d) = ¯PL(d) + Xσ = ¯Pr (d) − Xσ (3)
Let Ω = 10 log10(Ω ) ⇒ Ω → log-normal RV, iff Ω is Gaussian distributed RV.
If Pr (d) < Pmin → Outage and P(Pr (d) < Pmin) → Outage probability
Pr (d)|dB − Pmin = β → Margin (4)
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8. Continued–
From (3), Xσ is a Gaussian distributed RV, whereas from (4)
P(Xσ > β) =
∞
β
1
√
2πσ
e− x2
2σ2
dx =
∞
β/σ
1
√
2π
e− y2
2 dy = Q
β
σ
(5)
Note :
Margin β depends on receiver sensitivity.
Apart from that multiple factors, like distance (d), path-loss exponent (ν),
operating carrier frequency (f ), power dispersive environment, and
many-more also affects the outage probability.
Q β
σ = Q Pr (d)−Pmin
σ = Q Pt −ν log(d/d0)−Pmin
σ
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9. Graphical representation
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10. Continued–
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11. Continued–
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12. References
W. Lin, S. Qian, and T. Matsumoto, “Lossy-forward relaying for lossy
communications: Rate-distortion and outage probability analyses,” IEEE
Transactions on Wireless Communications, vol. 18, no. 8, pp. 3974–3986, 2019.
J. Lee, H. Wang, J. G. Andrews, and D. Hong, “Outage probability of cognitive
relay networks with interference constraints,” IEEE Transactions on Wireless
Communications, vol. 10, no. 2, pp. 390–395, 2010.
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