CONSTANT ENVELOPE MULTICARRIER
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)
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
• 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.
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.
Signal Definitions for OFDM
• During an OFDM symbol period 0 t NTb , the discrete complex
baseband signal is written as
x ( n)
X (k )e
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
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).
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
f(t , α) 2h 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
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.
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
f(t , x) hxn h xi mod 2
• 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
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)
Optimal Receiver in an AWGN Channel
• In general, the maximum likelihood (ML) bit error probability for CPM
system can be upper bounded as
Pb Q m in b
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)
• The normalised phase difference with neighbor OFDM-CPM signal samples is
fn 1 fn
where f n are phase estimates. With the definition of ~(n) fn the estimate
of the transmitted data symbol X ( k ) is obtained by N-point FFT.
• Assumption of high SNR, the bit error
probability is approximated by
Pb Q h
• 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)
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)
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
Data IFFT Guard channel
Tb High PAPR 0dB PAPR
Binary N-point Phase Remove
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.