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Telecom & Networking

Signals and data links: Shannon capacity, path loss, throughput, latency, subnets and Erlang traffic

Shannon Channel Capacity

NEWAdvanced
C=Blog2(1+SNR)C = B \log_2(1 + SNR)

Maximum error-free data rate of a channel given bandwidth and signal-to-noise ratio.

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Nyquist Data Rate

NEWIntermediate
C=2Blog2MC = 2B \log_2 M

Maximum data rate for a noiseless channel with M signal levels.

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Power Decibels

NEWBasic
dB=10log10P1P2dB = 10 \log_{10}\frac{P_1}{P_2}

Ratio of two power levels expressed logarithmically.

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Free-Space Path Loss

NEWAdvanced
FSPL=20log10d+20log10f+32.44FSPL = 20\log_{10}d + 20\log_{10}f + 32.44

Signal attenuation over distance in free space (d in km, f in MHz).

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Throughput

NEWBasic
R=DtR = \frac{D}{t}

Actual data delivered per unit time.

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Propagation Delay

NEWIntermediate
t=dvt = \frac{d}{v}

Time for a signal to travel a distance at propagation speed.

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Bandwidth-Delay Product

NEWAdvanced
BDP=B×RTTBDP = B \times RTT

Amount of data 'in flight' on a link, setting the ideal window size.

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Wavelength

NEWBasic
λ=cf\lambda = \frac{c}{f}

Physical length of one wave cycle for a given frequency.

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Erlang Traffic Intensity

NEWIntermediate
A=λhA = \lambda h

Offered call traffic from call rate and average holding time.

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Bit Rate from Baud

NEWIntermediate
R=Br×log2MR = B_r \times \log_2 M

Bit rate from symbol rate and bits carried per symbol.

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Packet Transmission Time

NEWBasic
t=LRt = \frac{L}{R}

Time to push a packet of L bits onto a link of rate R.

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Usable Subnet Hosts

NEWIntermediate
H=2(32n)2H = 2^{(32-n)} - 2

Number of usable IPv4 addresses in a subnet with an n-bit prefix.

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Queue Utilisation

NEWAdvanced
ρ=λμ\rho = \frac{\lambda}{\mu}

Fraction of a server's capacity being used by arriving traffic.

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Signal-to-Noise Ratio (dB)

NEWBasic
SNRdB=10log10SNSNR_{dB} = 10\log_{10}\frac{S}{N}

Ratio of signal power to noise power in decibels.

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Bit Error Rate

NEWIntermediate
BER=ENBER = \frac{E}{N}

Fraction of transmitted bits received in error.

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Download Time

NEWBasic
t=SRt = \frac{S}{R}

Time to transfer a file of size S at rate R.

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Antenna Gain (dBi)

NEWIntermediate
GdBi=10log10GG_{dBi} = 10\log_{10} G

Directional gain of an antenna relative to an isotropic radiator, in decibels.

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