Programmes in which available: Masters of Engineering - Electrical and Electronic Engineering. Masters of Engineering - Electronic Engineering and Computer Science. Master of Science - Communication Systems and Wireless Networking. Master of Science - Smart Telecom and Sensing Networks. Master of Science - Photonic Integrated Circuits, Sensors and Networks To enable an extension of knowledge in fundamental data communications to radio communications and networks widely adopted in modern telecommunications systems. To provide understanding of radio wave utilisation, channel loss properties, mobile communication technologies and network protocol architecture applied to practical wireless systems

1. ©Haris Hassan | Aston University | hharis11@hotmail.com
EE402B Radio Systems and Personal Communication Networks
1. Antenna Gain
G =
Power density radiated in a direction from directional antenna
Power density radiated in any direction from isotropic antenna
=
received signal power in a particular direction
received power of an isotropic antenna
G =
𝑃𝑟
𝑃 𝑟𝑖
=
ρ 𝑟A 𝑒
ρ 𝑖A 𝑒𝑖
=
A 𝑒
A 𝑒𝑖
=
4𝜋A 𝑒
λ2 =
4𝜋𝑓2 𝐴 𝑒
c2 Since
A 𝑒𝑖(effective area of the isotropic antenna) =
λ2
4𝜋
, λ =
f
𝑐
2. Distance between antennas (km)
𝑑 = 3.58(√𝐾ℎ1 + √𝐾ℎ2) Where h = height of antenna
(m), R=radius of earth (km), K = adjustment factor due to
refraction
3. Received Signal Power (In dB format)
𝑃𝑟 = 𝑃𝑡
𝐺𝑡 𝐺 𝑟
𝐿 𝑓
, 𝑃𝑟(𝑑𝐵) = 10 log (𝑃𝑡
𝐺𝑡 𝐺 𝑟
𝐿 𝑓
) = 𝑃𝑡(𝑑𝐵) + 𝐺𝑡(𝑑𝐵) +
𝐺 𝑟(𝑑𝐵) − 𝐿 𝑓(𝑑𝐵) − 𝐿0(𝑑𝐵),
4. Path Loss
𝐿 𝑃 =
𝑃𝑡
𝑃𝑟
=
𝐿 𝑓
𝐺𝑡 𝐺 𝑟
, 𝐿 𝑃(𝑑𝐵) = (−𝐺𝑡(𝑑𝐵)−𝐺 𝑟(𝑑𝐵) + 𝐿 𝑓(𝑑𝐵)) Where
𝐿 𝑓 is free-space loss
For isotropic antennas: 𝐿 𝑃 = 𝐿 𝑓, As 𝐺𝑡 = 𝐺𝑟 = 1
𝐿 𝑓(𝑑𝐵) = 20 log( 𝑑) − 20 log(λ) −𝐺𝑡(𝑑𝐵)−𝐺 𝑟(𝑑𝐵) + 21.98𝑑𝐵
5. Free-space loss
Since 𝑃𝑟 = 𝐴 𝑒 𝑝 𝑟, 𝑝 𝑟 = 𝑃𝑡/(4𝜋𝑑2
), A 𝑒 = λ2
/4𝜋A 𝑒
𝐿 𝑓 =
𝑃𝑡
𝑃𝑟
= (
4𝜋𝑑
λ
)
2
= (
4𝜋𝑓𝑑
c
)
2
, 𝐿 𝑓(𝑑𝐵) = 20 log( 𝑑) −
20 log(λ) + 21.98𝑑𝐵 = 20 log( 𝑓) + 20 log( 𝑑) − 147.56𝑑𝐵
6. Dopplershift
𝑓𝑑 = 𝑓𝑟 − 𝑓𝑡 = 𝑓𝑡
𝑣
𝑐
𝑐𝑜𝑠𝜃 where v=velocity of moving
receiver
7. Average thermal noise power
N = kTB (W) where k --- Boltzmann’s constant = 1.38x 10-23
J /
KT --- absolute temperature in kelvins (K= C+273) B ---
bandwidth (Hz)
N(dB) = −228.6 dBW +10 log T +10 log B
N0 = N/B = kT
8. Link Budget
𝑃𝑟
𝑁0
=
𝑃𝑡 𝐺𝑡 𝐺 𝑟
𝐿 𝑓 𝑘𝑇
(
𝑃𝑟
𝑁0
)
𝑑𝐵
= 𝑃𝑡(𝑑𝐵) + 𝐺𝑡(𝑑𝐵) + 𝐺 𝑟(𝑑𝐵) − 𝐿 𝑓(𝑑𝐵) −
10𝑙𝑜𝑔𝑘 − 10𝑙𝑜𝑔𝑇
9. Signal-to-Noise Ratio (SNR) and Eb / N0
𝑆𝑁𝑅 =
𝑆𝑖𝑔𝑛𝑎𝑙 𝑃𝑜𝑤𝑒𝑟 (𝑆)
𝑁𝑜𝑖𝑠𝑒 𝑃𝑜𝑤𝑒𝑟 (𝑁)
𝐸 𝑏
𝑁0
=
𝑆𝑖𝑔𝑛𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 𝑝𝑒𝑟 𝐵𝑖𝑡
noise power spectral density (W/Hz)
=
𝑆/𝑅
𝑁0
=
𝑆
𝑘𝑇𝑅
where
R=data rate, ; R =1/Tb
(
𝐸 𝑏
𝑁0
)
𝑑𝐵
= 𝑆 𝑑𝐵𝑊 + 228.6𝑑𝐵𝑊 − 10𝑙𝑜𝑔𝑇 − 10𝑙𝑜𝑔𝑅
10. Channel capacity (bits/s)
𝐶 = 𝐵 𝑙𝑜𝑔2 (1 +
𝑆
𝑁
)
Throughput (η) = Data rate (R) – Loss rate (p)
11. Far-Field of Transmitting Antenna
𝑑 𝑓 =
2𝐷2
λ
where D --- The largest linear dimension of
the antenna. λ --- Signal wavelength.
12. Shadow Fading
𝑓(𝐿 𝑠𝑓) =
1
√2𝜋𝐿 𝑠𝑓
𝑒𝑥𝑝 (
−(𝑙𝑛𝐿 𝑠𝑓−)
2
22 ) where μ and σ are the
mean and standard deviation in dB of LSF
13. Multilevel Modulation
L(The number of bits carried by one signal waveform) = log2
M (Total number of signal waveforms or modulation levels)
𝑅 = 𝐷𝑙𝑜𝑔2 𝑀 = 𝐷𝐿 (bps) or 𝐷 =
𝑅
log2 𝑀
=
𝑅
𝐿
(baud)
For QAM and multilevel PSK (MPSK): 𝐵𝑟 = (1 + 𝑟) 𝐷 =
(1 + 𝑟)
𝑅
log2 𝑀
For multilevel FSK (MFSK): 𝐵𝑟 = (1 + 𝑟) 𝑀𝐷 = (1 +
𝑟)
𝑀𝑅
log2 𝑀
For QAM and MPSK: 𝜂 =
𝑅
𝐵 𝑟
=
log2 𝑀
(1+𝑟)
For Multilevel FSK (MFSK): 𝜂 =
𝑅
𝐵 𝑟
=
log2 𝑀
(1+𝑟)𝑀
14. Diversity Improvement
For Rayleigh fading channels, the probability that a single
path has an 𝑥𝑖 less than some threshold x is
𝑃( 𝑥𝑖 < 𝑥) = 1 − exp (−𝑥/𝑋)
The probability that M independent paths are simultaneously
less than some threshold x is
𝑃( 𝑥1, … , 𝑥 𝑀 < 𝑥) = [1 − exp (−𝑥/𝑋)] 𝑀
15. Error correction

2. ©Haris Hassan | Aston University | hharis11@hotmail.com
𝑡 𝑑 ≤ 𝑑 𝑚𝑖𝑛 − 1 𝑡 𝑐 ≤
𝑑 𝑚𝑖𝑛−1
2
for simultaneous correction &
detection 𝑡 𝑐 + 𝑡 𝑑 + 1 = 𝑑 𝑚𝑖𝑛
16. BCH (Bose-Chaudhuri-Hocquenghem) Codes:
𝑛( 𝑏𝑙𝑜𝑐𝑘 𝑙𝑒𝑛𝑔𝑡ℎ) = 2 𝑛
− 1, 𝑛 − 𝑘
≤ 𝑚𝑡 𝑐, 𝑑min≥2𝑡 𝑐 + 1 𝑤ℎ𝑒𝑟𝑒 𝑚 ≥ 3; 𝑡 𝑐
< 2 𝑚−1
17. RS (Reed-Solomon) Codes
m bits per symbol; block length is 𝑛 = (2 𝑚
− 1) 𝑠𝑦𝑚𝑏𝑜𝑙𝑠 =
𝑚(2 𝑚
− 1) 𝑏𝑖𝑡𝑠; 𝑑𝑎𝑡𝑎 𝑙𝑒𝑛𝑔𝑡ℎ 𝑘 𝑠𝑚𝑏𝑜𝑙𝑠 , 𝑛 − 𝑘 = 2𝑡 𝑐 =
2𝑚𝑡 𝑐 𝑏𝑖𝑡𝑠; 𝑑 𝑚𝑖𝑛 = 2𝑡 𝑐 + 1𝑠𝑦𝑚𝑏𝑜𝑙𝑠
18. convolutional codes
The probability of error-free transmission of a block data
is 𝑃𝑒𝑓 = (1 − 𝑝) 𝑛
The probability of block error (a block contains one or
more errors) is 𝑃𝑒 = 1 − (1 − 𝑝) 𝑛
The probability of having t errors in a block is 𝑃𝑡 =
( 𝑛
𝑡
)𝑝 𝑡(1 − 𝑝) 𝑛−𝑡
𝑤ℎ𝑒𝑟𝑒 ( 𝑛
𝑡
) =
𝑛!
(𝑛−𝑡)!𝑡!
For an (n, k) block code with error-correction capability 𝑡 𝑐,
the probability of block error after decoding is 𝑃𝑒
′
≤ 1 −
∑ ( 𝑛
𝑡
) 𝑝𝑖(1 − 𝑝) 𝑛−𝑖𝑡 𝑐
𝑖=0
19. Frequency hopping
Processing gain: 𝐺 𝑝 = 𝑊𝑠𝑠 /𝑊𝑑 = 2 𝑘
𝑊𝑠𝑠 = 2 𝑘
𝑊𝑑 𝑤ℎ𝑒𝑟𝑒 𝑊𝑑 --- bandwidth of the modulated
signal, 𝑊𝑠𝑠 is of the spread-spectrum signal
20. CDMA
𝑅 𝑐ℎ𝑖𝑝 = 𝑘𝑅 𝑑
21. Satellites
𝑑 =
𝑅+ℎ
𝑐𝑜𝑠𝜃
𝑠𝑖𝑛𝛽; D (coverage)=2𝑅𝛽
𝐶𝑁𝑅 =
𝑝𝑜𝑤𝑒𝑟 𝑜𝑓 𝑟𝑒𝑐𝑖𝑒𝑣𝑒𝑑 𝑤𝑎𝑛𝑡𝑒𝑑 𝑠𝑖𝑔𝑛𝑎𝑙 𝑎𝑡 𝑖𝑛𝑝𝑢𝑡 𝑜𝑓 1𝑠𝑡 𝑎𝑚𝑝𝑙𝑖𝑓𝑖𝑒𝑟
𝑝𝑜𝑤𝑒𝑟 𝑜𝑓 𝑟𝑒𝑐𝑖𝑒𝑣𝑒𝑑 𝑛𝑜𝑖𝑠𝑒 𝑎𝑡 𝑖𝑛𝑝𝑢𝑡 𝑜𝑓 1𝑠𝑡 𝑎𝑚𝑝𝑙𝑖𝑓𝑖𝑒𝑟
=
𝑃𝑐𝑎𝑟𝑟
𝑁
𝑃𝑐𝑎𝑟𝑟 = 𝑃𝑡 𝐺𝑡 𝐺𝑟/𝐿 𝑓 𝑁 = 𝑁𝑜 𝐵 = 𝑘𝑇𝐵
𝐶𝑁𝑅 𝑑𝐵 = 𝑃𝑐𝑎𝑟𝑟( 𝑑𝐵) − 𝑁 𝑑𝐵 = 𝑃 𝑡(𝑑𝐵) + 𝐺 𝑡(𝑑𝐵) + 𝐺 𝑟(𝑑𝐵) −
𝐿 𝑓(𝑑𝐵) + 228.6𝑑𝐵𝑊 − 𝑇𝑑𝐵 − 𝐵 𝑑𝐵
𝐶𝑁𝑅 =
1
1
𝐶𝑁𝑅 𝑢
+
1
𝐶𝑁𝑅 𝑑
𝑤ℎ𝑒𝑟𝑒 𝐶𝑁𝑅 𝑢 − 𝑢𝑝 −
𝑙𝑖𝑛𝑘 𝐶𝑁𝑅 𝑎𝑛𝑑 𝐶𝑅 𝑑 𝑖𝑠 𝑑𝑜𝑤𝑛𝑙𝑖𝑛𝑘 𝐶𝑁𝑅