# ECE Fall

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```							        ECE 4331, Fall, 2009

Zhu Han
Department of Electrical and Computer Engineering

Class 20

Nov. 3rd, 2009
Outline
   Digital Carrier Systems
– Carrier band vs. baseband
– Baud rate, bit rate, bandwidth efficiency
– Spectrum
– Gray coding
– BER
– Comparison
– Practical implementation example
Digital Carrier System Baseband analysis

Signal in baseband: xTp (t )  T   d (l )  jd (l )  gTx (t  lT )
l 

ES  T 2 D           
2         2
mean symbol energy:                                             gTx (t )dt

signal in carrier band:


xBp (t )  2 Re xTp (t )e j 2 f0t   
                                                     

 2T cos(2 f 0 )  d (l ) gTx (t  lT )  sin(2 f 0 )  d (l ) gTx (t  lT ) 
            l                                   l                      
 D 2 D 2  
mean symbol energy:                       EX  T 2  2               gTx (t )dt ES

2

 2     2  
            
D2

Conclusion: analysis of carrier band = base band. Fc=0 in project
Baud Rate, Bit Rate, Bandwidth Efficiency

   Remember channel capacity C=Wlog2 (1+ SNR)> fb
   Baseband
   Sy(W)=Sx(W) P(W)
   ASK: Sy(t)=b Acoswct, Square wave convolute with sinusoid.
FSK Spectrum
   FSK: two sinc added together
 A cos2f t 
                  binary 1
s t              1
 A cos2f 2t 

binary 0
BPSK Spectrum
   BPSK: Sx(W): NRZ. P(t): raised cosine function. Sy(W)= P(W)
   Rb
baud rate
QPSK Spectrum
   Same Rb
Narrow BW
Pulse Shaped M-PSK
   Different 
Bandwidth vs. Power Efficiency
   Bandwidth efficiency high, required SNR is high and low power efficiency
QAM efficiencies
   For l =1  PSD for BPSK
   For l =2  PSD for QPSK, OQPSK …
    PSD for complex envelope of the bandpass multilevel signal is
same as the PSD of baseband multilevel signals
   Same baud rate, higher bit rate.
   Same bit rate, less bandwidth. But higher power
Minimum Shift Keying spectra
   Continuous phase and constant envelop. So narrow spectrum
GMSK spectral shaping
Gray coding
   It is very unlikely that switches will change states exactly in synchrony. So
there might be misunderstanding. E.g. 011->100
   In a digital modulation scheme such as QAM where data is typically
transmitted in symbols of 4 bits or more, the signal's constellation diagram
is arranged so that the bit patterns conveyed by adjacent constellation points
differ by only one bit. By combining this with forward error correction
capable of correcting single-bit errors,
it is possible for a receiver to correct
any transmission errors that cause a
constellation point to deviate into the
area of an adjacent point. This makes
the transmission system less susceptible
to noise.
Coherent Reception
   An estimate of the channel phase and attenuation is recovered. It
is then possible to reproduce the transmitted signal, and
demodulate. It is necessary to have an accurate version of the
carrier, otherwise errors are introduced. Carrier recovery
methods include:
Coherent BER
   PSK
– BPSK     QPSK
– MPSK
Coherent BER performance
 1    Eb 
   ASK    Pb  2(1  L )Q
1
 L 1 N 

         

 1    Eb 
Pb  2(1  L )Q
1
 L 1 N 

         

 1.217Eb   
Pb  Q



   FSK             N      
   MSK: less bandwidth but the same BER
   MQAM
Non-coherent detection
   Non-coherent detection
– does not require carrier phase recovery (uses differentially encoded mod.
or energy detectors) and hence, has less complexity at the price of higher
error rate.
   No need in a reference in phase with the received carrier
   Differentially coherent detection
– Differential PSK (DPSK)
   The information bits and previous symbol, determine the phase of the
current symbol.
   Energy detection
– Non-coherent detection for orthogonal signals (e.g. M-FSK)
   Carrier-phase offset causes partial correlation between I and Q
braches for each candidate signal.
    The received energy corresponding to each candidate signal is used
for detection.
Differential Reception
Differential Coherent
   DBPSK
   3dB loss
Non-coherent detection of BFSK

2 / T cos(1t )

z11
 2
T

0
z11  z12
2         2

2 / T sin(1t )
T   z12
r (t )

0
 2           +   z (T )
Decision stage:
ˆ
m
2 / T cos( 2t )                                                if z (T )  0, m  1
ˆ
if z (T )  0, m  0
ˆ
T   z 21
 2

-
0

z 21  z 22
2          2
2 / T sin( 2t )
T   z 22

0
 2
Non-coherent detection BER
   Non-coherent detection of BFSK
1                       1
PB  Pr(z1  z 2 | s 2 )  Pr(z 2  z1 | s1 )
2                       2
 Pr(z1  z 2 | s 2 )  E Pr(z1  z 2 | s 2 , z 2 )

  Pr(z1  z 2 | s 2 , z 2 ) p( z 2 | s 2 )dz2  

  p( z | s )dz  p( z | s )dz
0                                              0       z2
       1   2   1
     2   2    2

1    Eb 
 2N 
PB  exp    
Rayleigh pdf        Rician pdf
2      0 

   Similarly, non-coherent detection of DBPSK

1    Eb 
 N 
PB  exp    
2      0 
BER Example
Example of samples of matched filter output
for some bandpass modulation schemes
Comparison of Digital Modulation
Comparison of Digital Modulation
Figure 6.45 Comparison of the noise performance of different PSK and FSK schemes.
Bandwidth vs. Power Efficiency
   Bandwidth efficiency high, required SNR is high and low power efficiency
   GSM- Digital Cellular
– Data Rate = 270kb/s, bandwidth = 200kHz
– Bandwidth Efficiency = 270/200 =1.35bits/sec/Hz
– Modulation: Gaussian Minimum Shift Keying (FSK with
orthogonal frequencies).
– “Gaussian” refers to filter response.
   IS-54 North American Digital Cellular
– Data Rate = 48kb/s, bandwidth = 30kHz
– Bandwidth Efficiency = 48/30 =1.6bits/sec/Hz
– Modulation: pi/4 DPSK
Modulation Summary
   Phase Shift Keying is often used, as it provides a highly
bandwidth efficient modulation scheme.
   QPSK, modulation is very robust, but requires some form of
linear amplification. OQPSK and p/4-QPSK can be
implemented, and reduce the envelope variations of the signal.
   High level M-ary schemes (such as 64-QAM) are very
bandwidth efficient, but more susceptible to noise and require
linear amplification.
   Constant envelope schemes (such as GMSK) can be employed
since an efficient, non-linear amplifier can be used.
   Coherent reception provides better performance than
differential, but requires a more complex receiver.
Homework 5
   6.2, 6.5, 6.7, 6.8, 6.11, 6.15, 6.21, 6.32,
   Due on 11/17
   Make up class 11/6, 11/13, 11/20 4:00pm-5:30pm

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