CONSTANT ENVELOPE MULTICARRIER MODULATION

1
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)

2
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.

2
3
Constant Envelope Multicarrier Modulation

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

• 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.

4

Signal Definitions for OFDM

• During an OFDM symbol period 0 t NTb , the
  discrete complex baseband signal is written as

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

The variance and PAPR for OFDM signal with binary
antipodal data symbols are
equal to 1 and 10 log2(N) dB, respectively.
Large dynamic range of OFDM signal (N 16).
2
5

Signal Definitions for CPM

• The general CPM signal is written as

where the phase f(t,a) has the form

• 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

• 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.

2
6

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

• Since phase f(t, x) is a real signal, we have to
  maintain the conjugate symmetry at the OFDM
  signal frequency domain by defining

The maximum absolute phase shift value for
neighbor phase samples with binary data modulated
OFDM signal is
Dynamic phase range 0, 2p (N 16)
2
7
Optimal Receiver in an AWGN Channel

• In general, the maximum likelihood (ML) bit error
  probability for CPM system can be upper bounded as

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)
8
Heuristic Receiver

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

where are phase estimates. With the
definition of
the estimate
of the transmitted data symbol is obtained
by N-point FFT.

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

• 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)

9
Measured Results in an AWGN channel

• OFDM-CPM receiver (h 0.2) operates on binary
  data symbol 1/Tb rate.

• Oversampling is required if
• For binary data modulated OFDM-CPM oversampling
  factor is

• 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.

Performance in AWGN channel (N 16, h 0.2)

10
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.

• System parameters
• M 2
• N 16
• h 0.2
• Guard Interval (GI) 1
• Frequency domain Zero Force (ZF) equalizer with N
  16 taps

• ISI channel Model
• Tap number 1
• Delay (Tb) 0
• Amplitude 0.995
• Tap number 2
• Delay (Tb) 1
• Amplitude 0.0995e-j 0.75p

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.