CONSTANT ENVELOPE MULTICARRIER MODULATION

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CONSTANT ENVELOPE MULTICARRIER MODULATION Powered By Docstoc
					    CONSTANT ENVELOPE MULTICARRIER
              MODULATION
Markku Kiviranta (VTT), Prof. A. Mämmelä (VTT), Prof. R. Brodersen (BWRC)

       Technologies for 60 GHz Adaptive Antenna Array Front End (TAFE) project
                       Technical Research Centre of Finland (VTT)
                                  in co-operation with
                       Berkeley Wireless Research Center (BWRC)
VTT ELEKTRONIIKKA


       Pros and Cons of Multicarrier Modulation
• Multicarrier modulation such as orthogonal frequency division
  multiplexing (OFDM) is attractive for a number of reasons.
    • They have high spectral efficiency since the subcarriers overlap in
      frequency.
    • The intersymbol interference (ISI) is easy to mitigate by employing
      a cyclic guard interval.

• OFDM is not without its disadvantages.
    • The cyclic guard interval imposes a power and bandwidth penalty,
      and the closely spaced subcarriers make the performance sensitive
      to frequency offsets and phase noise.
    • They are sensitive to nonlinear distortion in power amplifiers (PA),
      since the envelope is not constant.




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      Constant Envelope Multicarrier Modulation
• Constant envelope multicarrier modulation scheme is considered
  that combines OFDM and continuous phase modulation (CPM).



                     Data    OFDM               CPM              HPA


                                    High PAPR         0dB PAPR




• The key features of the OFDM-CPM study are
    • Constant envelope signal allows PA to operate at or near saturation
      levels thus maximizing the achievable power efficiency.
    • Spectral spreading and the detection performance can be controlled
      using modulation index.
    • OFDM feature of the increased robustness to channel dispersion,
      multipath fading and impulsive noise has to be sustained.


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                       Signal Definitions for OFDM
• During an OFDM symbol period 0  t  NTb , the discrete complex
  baseband signal is written as
                                N 1
                            1
                   x ( n) 
                            N
                                 X (k )e
                                k 0
                                                       j 2 kn / N
                                                                     , n  1, ..., N  1

 where N is the number of subcarriers and X(k) are M-ary frequency
 domain data symbols with rate 1/Tb.
• Peak-to-average power ratio (PAPR) is given as


             PAPR  10 log10
                                max x(n)          2
                                                       
                                                  
                                                                 [dB]
                                               2
                                  E x ( n)


    The variance and PAPR for OFDM signal with binary antipodal data
    symbols X (k )   N are equal to 1 and 10 log2(N) dB, respectively.

                                                                                           Large dynamic range of OFDM signal (N = 16).


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                      Signal Definitions for CPM
• The general CPM signal is written as
                                            s (t )  e jf ( t ,α )
  where the phase f(t,a) has the form

                                        n
                                                            n L 
                         f(t , α)  2h  ai q(t  iTb )  h  ai  mod 2
                                       i  n  L 1         i  

• In the above, ai are M-ary data symbols, and h is the modulation index.
  The phase pulse q(t) is normalized in such a way that

                                            0     t0
                                    q(t )  
                                            1 / 2 t  LTb
• Full response CPM signals have L = 1. Otherwise, CPM signals are partial
  response type ones. By choosing different phase pulses q(t) and varying
  parameters h and M, a great variety of CPM signals is obtained.

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                Signal Definitions for OFDM-CPM
• A particular full response (L = 1) type CPM signal is obtained by replacing
 data symbols ai with discrete OFDM symbols xn, and thus

                                                    n1 
                                 f(t , x)  hxn  h  xi  mod 2
                                                    i  
• Since phase f(t, x) is a real signal, we have to
  maintain the conjugate symmetry at the OFDM
  signal frequency domain by defining

                    X 0  Re( X 0 )
                    X , k  1, , N / 2  1
                   
              Xk   k
                    X N  Im(X 0 )
                       ~

                    X N k  X k , k  1, , N / 2  1
                   
                                




      The maximum absolute phase shift value for neighbor phase
      samples with binary data modulated OFDM signal is

                           f  h  max xn   h N
                                                                       Dynamic phase range [0, 2[ (N = 16)



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            Optimal Receiver in an AWGN Channel
• In general, the maximum likelihood (ML) bit error probability for CPM
  system can be upper bounded as
                                          d2 E     
                                   Pb  Q m in b   
                                           N0      
                                                   

 where d 2min is the minimum Euclidean distance between all the possible pairs
 of signals in the Viterbi-algorithm.
• In OFDM-CPM system, the error probability
  is more difficult to control.
     • The phase transition values are not evenly
       spaced or equally likely. The large phase
       shifts correspond OFDM signal peak values.
• The ML receiver is complex
    • OFDM-CPM receiver with binary data
      modulation requires 2N/2 matched filters.
                                                        Phase transition values mapped into a unit circle (N = 16)



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                             Heuristic Receiver
• The normalised phase difference with neighbor OFDM-CPM signal samples is

                                        ~
                                        fn 
                                              1 ~
                                              h
                                                        ~
                                                 fn 1  fn   
       ~                                                        ~
 where f n are phase estimates. With the definition of ~(n)  fn the estimate
                                                         x
                                 ~
 of the transmitted data symbol X ( k ) is obtained by N-point FFT.

• Assumption of high SNR, the bit error
  probability is approximated by

                           2 Eb   
                 Pb  Q h        
                           N0     
                                  

• When we increase the modulation index h,
  the performance gains are obtained at the
  cost of spectrum spreading.
                                                              Performance with different modulation index values (N = 16)


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          Measured Results in an AWGN channel
  • OFDM-CPM receiver (h = 0.2) operates on binary data symbol 1/Tb rate.
                                   ~
    • Oversampling is required if fn  
    • For binary data modulated OFDM-CPM oversampling factor is F  h N

  • OFDM-CPM receiver has performance loss, but it has 0 dB PAPR.
  • If the maximum power is limited by saturation level of PA, OFDM
    scheme has to back off of roughly PAPR dB, compared to OFDM-CPM
    system with 0 dB PAPR.

    • OFDM-CPM scheme has capability to transmit
      roughly PAPR dB more energy into the
      channel for a given PA.
          – The PAPR for binary data modulated OFDM signal
            with N = 16 is 12 dB.
          – The actual amount of PAPR gain depends on the
            amount of clipping allowed to OFDM signal with
            infinite error probability, i.e.

                           PAPR clip  PAPR
                                                             Performance in AWGN channel (N = 16, h = 0.2)


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                   Measured Results in an ISI channel
• The simulation results show that OFDM-CPM receiver with adequate
  channel equalization can operate in an ISI channel.
            • PAPR gain and increasing modulation index could shift the curves to the left.


  Binary        N-point                                                         Add          ISI
                                        CPM
   Data          IFFT                                                          Guard       channel


           Tb             High PAPR               0dB PAPR




  Binary        N-point                Phase                                  Remove
                                                             Equalizer                     AWGN
   Data          FFT                  detection                                Guard




System parameters                                                        ISI channel Model
• M=2                                                                    • Tap number 1
• N = 16                                                                        • Delay (Tb): 0
• h = 0.2                                                                       • Amplitude: 0.995
• Guard Interval (GI) = 1                                                • Tap number 2
• Frequency domain Zero Force (ZF)                                              • Delay (Tb): 1
  equalizer with N = 16 taps                                                    • Amplitude: 0.0995e-j 0.75   Performance in ISI channel

• Future work includes more critical study for pros and cons of OFDM-CPM
       • Spectrum and equalization analyses in conjunction with orthogonality principle.
           ― OFDM-PM (phase modulation).

       • The effect of frequency offset and phase noise.
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