Digital Communication Formulas

electronrev electr onreview. iew.word word ress. ress.com com

DIGITAL COMMUNICATION FORMULAS r  1 H R 

Pulse Code Modulation (PCM) Number of Levels and Scale Factor ; SF  

  2n M  

Rate of Information H  R   T  T  t1P1  t 2P2  t3P3    ...

1 M 

Bandwidth and Data rate

BWPCM  fb  nf nfS  

Information Capacity

Dynamic Range V  DR   max V min DR   2n  1 DRdB  20logDR  

Shannon-Hartley Theorem

I  2B log2  M 

Hartley’s Theorem

Line Code Parameters Code Type Bandwidth NRZ f 

Resolution or Quantization Step V  resolution  max 2n

b

2

Maximum Quantization Error resolution Qe max  2

RZ

f b

Manchester

f b

 AMI

f b 2

Coding Efficiency     

  S  I  B log2  1    N    H  

Frequency Shift Keying B  2  fb  f  

Bmin Bmax

fm  fs  f   Aliasing falias N   f  Nfs   f folding  

nf b 2

MSK 

Phase Shift Keying and Quadrature Amplitude Modulation System Bitrate/Baudrate ratio Binary 1 Quadrature 2 83 16 4 32 5

f s 2

Signal to Quantzation Noise Ratio   6. 6.02n  1.76 1.76 SQNRideal   sin  SQNR peak   6.02n  4.76 SQNRaveragetri   6.02n

Probability of Error

uLaw Companding

Pe  erfc  

   V in    ln 1   V max     Vout   V max  ln 1        

v out 

N o

Pe  0.5e Pe  erfc  

A-law Companding

  v in    A   V   v max  max  1  ln A     v in   1  ln  A    v max  V max 1  ln A 

2E b

Pe  erfc   if

if

0

1 A

v in Vmax



v in V max



 E     b   N o 

S 2N 

S N 

Coherent Systems / Matched Filter

Noncoherent Systems

On-Off Binary Polar Binary

1 A

1

Information Measure 1 Ii  logb   logb P i   P i 

Hamming Distance ( m + n , m ) Hamming distance for correction HdD  e  1

HdC   2e  1

Hamming distance for detection

2  m n1

Relationship between data and correction

n

Bit Error Rate error  BER   total E      E b  1 1 N  t dt   1  erfc     N   2     e 2  o  E      N    b o

Average Information / Entropy H  P1I1  P2I2  P3I3    ...

BERQPSK 

2

b

o

Hmax  logb N  Relative Entropy H  H R   H max Redundancy electronreview.wordpress.com – Leslie Caminade

Leslie