From 3e14893802123fd0cb0e7a7b23096a9fa3269fdc Mon Sep 17 00:00:00 2001 From: Peter Tanner Date: Sat, 2 Nov 2024 16:53:18 +0800 Subject: [PATCH] better print --- README.html | 25 +++++++++++++++++++++---- README.md | 27 ++++++++++++++++++++++++--- README.pdf | Bin 658222 -> 658651 bytes 3 files changed, 45 insertions(+), 7 deletions(-) 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)cos2(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)=xiAxpX(xi)log2(pX(xi))H(x,y)=xiAxyiAypXY(xi,yi)log2(pXY(xi,yi))Joint entropyH(x,y)=H(x)+H(y)Joint entropy if x and y independentH(xy=yj)=xiAxpX(xiy=yj)log2(pX(xiy=yj))Conditional entropyH(xy)=yjAypY(yj)H(xy=yj)Average conditional entropy, equivocationH(xy)=xiAxyiAypX(xi,yj)log2(pX(xiy=yj))H(xy)=H(x,y)H(y)H(x,y)=H(x)+H(yx)=H(y)+H(xy)\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]1jN=i=1MP[X=ai]P[Y=bjX=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 8e02372a4b0d40870b9e7b66343f3d8865ca7b8d..9f1f501679ee06c6d54629a1bb6a9d68b3f7d992 100644 GIT binary patch delta 124231 zcmV(-K-|BsmMGhqD6sf6f3jW2apn8@it`ADjjNgmhpY#=-R@9?+hGYEQZ%gx#uZ3H zz631-wA|4@-?dg|)~qa{?Z>}b3dhIq4u3f~Vn2Ly z{KZ%9_|1pIuiqT{L#`qFB45v6sXm0@T+YYw?}w0L&f)mxyTdQOe}0`_yQ4q8`TFqX ztN;G}k3YP7`@`|$4`03i@b&jUeDONI`tJDs7rwmu`uO<$`;YJ5|M>lnAC4d2efReG zA8&tn_x+#VJsv;cvv=RT|LW6{7aQZ$0?!7oop; z`!#fB)h5{re-^83prJ@WWT%{m0Y0_utqb zEp`4Kv44DX_}AlK4yhbNOh=#n(YuG9{PBmk$KM~{Uz*G3N0R(QE-t2aK9VRgq z<@^xp`1@8%V=3PJ`S3ao3Jk?}6wfhNpN?<-G`jH*Up+nk`1IAsx5qDD`xO1FF==nV z{`%eHySMK@9>2mY4Vrj*`u?xuzdwBc-S{lzoOFS&P<|;7In@;WF}5&z>-?mn9^tGdvf3eV`m$9dZ>iwYG^w36)eym37#a3ew()fFuqvuO~jc;-*{HC|WZ%VBD zZ)EO&`%g#z;CgZ{9RE77-;96$eE9N@NB7{4e>!+~{O99e#*g0nXcQ$p|2_Ca9Ssj^ zZSEnC_P-mo$A?hTM4mPzj!DWLNUjeqga!HC@n1JGf0%u`)}(u=p)YOL^5Akp5_NFKDezp4;{^eNzlDr$t!2V|}{#g1eeVb!zd5pSa-3{@B 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