diff --git a/README.html b/README.html index 56f5237..b740fed 100644 --- a/README.html +++ b/README.html @@ -142,9 +142,18 @@

Idiot's guide to ELEC4402 communication systems

@@ -647,6 +656,8 @@ B &= \begin{cases} \end{align*}

+ +

Noise performance

Coherent detection system.

y(t)=m(t)cos⁡(2πfct+θ)=m(t)cos⁡2(2πfct+θ) After IF mixing.=m(t)12(1+cos⁡(4fct+2θ))=12m(t)+12cos⁡(4fct+2θ)  ⟹  Su(f)=(12)2Su(f)After LPF.\begin{align*} @@ -1078,6 +1089,8 @@ tBitstream[{1, 1, -1, -1, -1, -1, 1, 1, -1, -1}, 1, "Q(t)"] + +

Matched filter

1. Filter function

Find transfer function h(t)h(t) of matched filter and apply to an input:
@@ -2143,6 +2156,8 @@ M1001 80h400000v40h-400000z"/>

  • Minimum distance between any two point
  • Different from bit error since a symbol can contain multiple bits
    • + +

    Information theory

    Entropy for discrete random variables

    H(x)≥0H(x)=−∑xi∈AxpX(xi)log⁡2(pX(xi))H(x,y)=−∑xi∈Ax∑yi∈AypXY(xi,yi)log⁡2(pXY(xi,yi))Joint entropyH(x,y)=H(x)+H(y)Joint entropy if x and y independentH(x∣y=yj)=−∑xi∈AxpX(xi∣y=yj)log⁡2(pX(xi∣y=yj))Conditional entropyH(x∣y)=−∑yj∈AypY(yj)H(x∣y=yj)Average conditional entropy, equivocationH(x∣y)=−∑xi∈Ax∑yi∈AypX(xi,yj)log⁡2(pX(xi∣y=yj))H(x∣y)=H(x,y)−H(y)H(x,y)=H(x)+H(y∣x)=H(y)+H(x∣y)\begin{align*} @@ -2198,7 +2213,7 @@ M347 1759 V0 H263 V1759 v1800 v1759 h84z"/>

    Input has probability distribution pX(ai)=P(X=ai)p_X(a_i)=P(X=a_i)

    Channel maps alphabet ‘{a1,…,aM}→{b1,…,bN}‘`\{a_1,\dots,a_M\} \to \{b_1,\dots,b_N\}`

    -

    Output has probabiltiy distribution pY(bj)=P(y=bj)p_Y(b_j)=P(y=b_j)

    +

    Output has probability distribution pY(bj)=P(y=bj)p_Y(b_j)=P(y=b_j)

    pY(bj)=∑i=1MP[x=ai,y=bj]1≤j≤N=∑i=1MP[X=ai]P[Y=bj∣X=ai][pY(b0)pY(b1)…pY(bj)]=[pX(a0)pX(a1)…pX(ai)]×P\begin{align*} p_Y(b_j) &= \sum_{i=1}^{M}P[x=a_i,y=b_j]\quad 1\leq j\leq N \\ &= \sum_{i=1}^{M}P[X=a_i]P[Y=b_j|X=a_i]\\ @@ -2274,6 +2289,8 @@ M347 1759 V0 H263 V1759 v1800 v1759 h84z"/>

    + +

    Channel code

    Note: Define XOR (⊕\oplus) as exclusive OR, or modulo-2 addition.

    diff --git a/README.md b/README.md index 953e988..3af8182 100644 --- a/README.md +++ b/README.md @@ -2,9 +2,18 @@ @@ -440,6 +449,9 @@ B &= \begin{cases} + +
    + ## Noise performance Coherent detection system. @@ -764,6 +776,9 @@ Remember that $T=2T_b$ | $I(t)$ (Odd, 1st bits) | ![QPSK bits](/images/qpsk-it.svg) | | $Q(t)$ (Even, 2nd bits) | ![QPSK bits](/images/qpsk-qt.svg) | + +
    + ## Matched filter ### 1. Filter function @@ -1005,6 +1020,9 @@ Adapted from table 11.4 M F Mesiya - Contemporary Communication Systems - Minimum distance between any two point - Different from bit error since a symbol can contain multiple bits + +
    + ## Information theory ### Entropy for discrete random variables @@ -1176,6 +1194,9 @@ C=\frac{1}{2}\log_2\left(1+\frac{P_\text{av}}{N_0/2}\right) + +
    + ## Channel code Note: Define XOR ($\oplus$) as exclusive OR, or modulo-2 addition. diff --git a/README.pdf b/README.pdf index 8e02372..9f1f501 100644 Binary files a/README.pdf and b/README.pdf differ