通信原理(英文版)总复习

Principles of Communications1

Chapter 1 Introduction1. Information content I =loga [1/P(x)] = -logaP(x) [1/P Usually, set a = 2, the unit of the information content will be called a bit. For an equal probability binary symbol: I = log2 [1/P(x)] = log2 [1/(1/2)] = 1 bit [1/P For an equal probability M-ary symbol: MI = log2 [1/P(x)] = log2 [1/(1/M)] = log2 M bit2

2. Two kinds of communication systems Analog communication system Requirement - High fidelity Criterion - Signal to noise ratio Digital communication system Requirement - correct decision Criterion - Error probability

u

Specifications of Digital Communication Systems Relationship between efficiency & reliability (rate ~ accuracy)Transmission rate: rate: Symbol rate: RB -Baud rate: Information rate: Rb - bit/second rate: For M-ary system:Rb = RB log2 M system: Error probability: probability: Symbol error probability Pe = number of received symbols in error/total number of transmitted symbols4

3. ChannelWireless channel: channel:Ground wave SkySky-wave LineLine-of –sight propagation

Wired channel: channel:Open wires Symmetrical cables Coaxial cablesequat or

Channel models:Modulation channel model Coding channel model

4. Noise in Channel

【Example 1】 Assume a signal source produces 4-ary signals with equal probability, 4and the width of its symbol is 125 µ s . Find its symbol rate and information rate.

【Example 2】 An information source consists of A, B, C, D. These symbols are represented by binary codeword 00, 01, 10, 11. If each binary symbol is transmitted by the pulse with width 5ms, and the 4 symbols have equal probability of occurrence . Find its symbol rate and information rate.

uu

Chapter 2 SignalsStatistical mean:E [ξ (t )] =

Random process Numerical characteristics of random process:∫∞ ∞

xf ( x , t ) dx = a (t )

Variance:

Dξ(t)]= E{[ (t) a(t)]2} [ ξ

Autocorrelation function:R(t1, t2 ) = E[ξ(t1)ξ(t2 )]9

Stationary random processCharacteristics of generalized stationary random process:E[ξ (t )] = cons tan t = a

R(t1, t 2 ) = R(t1 - t 2 ) = R(τ )

τ = t1 t2

Ergodicity1 T /2 a = lim ∫ x(t )dt T →∞ T T / 21 T /2 R(τ ) = lim ∫ x(t ) x(t + τ )dt T →∞ T T / 2

Autocorrelation function and power spectral density of stationary random processCharacteristics of autocorrelation functionR ( 0 ) = E [ξ 2 ( t )]R (τ ) = R ( τ )R (τ ) ≤ R ( 0 )

R(∞) = E 2 [ξ (t )]R ( 0) R ( ∞ ) = σ 2

Relationship between autocorrelation function & power spectral densitya pair of Fourier transformPξ ( f ) = ∫ R (τ )e jωτ dτ ∞ ∞

R (τ ) = ∫ Pξ ( f )e jωτ df ∞

∞

Gaussian processDefinitionOne dimensional probability density of Gauss process: ( x a) 1 f ( x) = exp 2σ 2 2πσ 2

where, a = E[X(t)] --- mean σ2 = E[X(t) - a]2 --- variance σ --- standard dev

iation Curve of f (x):

Random signal transfer through linear systemsmathematical expectation of output Y(t):E [Y (t ) ] = kH ( 0 )

Autocorrelation function of output Y(t):RY (t1 , t1 + τ ) = RY (τ )

Power spectral density PY( f ) of output Y(t):

PY ( f ) = H ( f ) PX ( f )2

σ

2

【Example 1】 Assume Y (t ) = X cos ω t X sin ω t is a random process, where X1 and X2 are statistically independent Gaussian random variables, and their mathematical expectations are 0, variances are σ . Find: (1) E[Y(t)]、E[Y2(t)] E[Y(t)]、 (2) The probability distribution density of Y(t) (3) R(t1,t2)1 0 2 02

【Example 2】 Assume X1(t) and X2(t) are two statistical independent stationary random process and their autocorrelation functions are R (τ ) and R (τ ) respectively. Find the autocorrelation function of their product X(t)= X1(t)X2(t).X1

X2

Chapter 3 Analog modulation systemAnalog modulation: modulation of a carrier by a source baseband analog signalModulating signal m(t) Modulator Figure 3.1 Modulator Modulated signal s(t)

AMm′(t) ′ 1+m′(t) ′

+1=1+m′(t) ′1 0

1 0

×

=

Frequency densitym(t) M(f) t

-fm

fm C(f)

f

c(t)A

t-A

-f0

f0

f

s(t) S (f)

t

-f0 2fm

f0 2fm

f

Figure 3.2.3 Waveform and spectrum of modulated signal19

Reception of AM signal: envelope detector Principle:

Rectifier

Low-pass filter

Figure 3.2.4 Envelope detector

DSB modulationM(f)Upper-sideband

S(f)Lower-sideband

Upper-sideband

0

f

-f0

0

f0

f

(a) Frequency spectral density of modulating signal

(b) Frequency spectral density of modulated signal

Figure 3.2.5 Spectrum of double-sideband modulation signal