INTRODUCTION
To combat ISI caused by multipath reception and avoid complex adaptive
equalization, mobile engineers and researchers explored the use of Orthogonal
Frequency Division Multiplexing (OFDM). OFDM divides the entire data stream
into small number of low datarate subcarriers, thus reducing the effect
of frequency selective fading and Doppler spread. OFDM became popular
because of its easy implementation as it makes an efficient use of Discrete
Fourier Transforms (Weinstein and Ebert, 1971).
OFDM, due to the presence of Cyclic Prefix (CP), maintains the receiver
carrier synchronization, therefore, does not need complex equalizers,
making the receiver simple and efficient (Prasad, 2004). Although, highly
spectrally efficient and robust against ISI, OFDM technique faces certain
problems such as (Prasad, 2004).
• 
It is very sensitive to Carrier Frequency Offsets (CFO)
caused by frequency differences between oscillators in the transmitter
and receiver. Several methods are proposed to overcome this problem. 
• 
It has a high PeaktoAverage Power Ratio (PAPR) that calls for
High Power Amplifier (HPA) of very large linear region. This high
PAPR forces the signal peaks to get into 
• 
nonlinear region of HPA which distorts the signal by introducing
intermodulation among the subcarriers and outofband radiation.

In this study, an OFDM transceiver is proposed (Latif and Gohar, 2006)
which make use of hybrid modulation scheme instead of conventional Modulator
like QAM or PSK. In spite of improved BER performance, it exhibits low
PAPR. The modified OFDM Transceiver makes use of multilevel QAM constellations,
where the level of QAM is decided by specific number of bits chosen from
a group of bits to be encoded in the QAM symbol. The simulated results
show that PAPR is considerably reduced at the cost of sight increase in
detection complexity. Like PTS or SLM (Müller Weinfurtner et al.,
1997; Muller and Huber, 1997; Latif and Gohar, 2002, 2003), it works with
arbitrary number of subcarriers but needs no side information to be transmitted.
It is also shown that PAPR reduction capability of the proposed system
is comparable to PTS. To further reduce the PAPR, one has to alter the
Hybrid MQAM/LFSK (HQFM) signal sets like in PTS. At the receiver, these
deformation can be recovered (needs not to be transmitted) in one or two
iteration. Thus, increasing the detection complexity.
PROPOSED HYBRID MQAM/LFSK (HQFM) OFDM TRANSCEIVER
In a typical OFDM system, the bit rate per carrier (not the total bit
rate) is reduced by converting binary serial bit stream into N_{used}
parallel streams, with n bits in each stream. Then a suitable modulation
technique, MQAM/MPSK (M = 2^{n}), is applied to map these bits
to N_{used} active carriers.
Here a novel modulator is proposed, which replace QAM signals with hybrid
LFSK modulated MQAM (HQFM) signals. In HQFM, instead of modulating n =
log_{2}ML information bits using a single frequency f_{c},
nk = log_{2}L bits, the choice being arbitrary, are used to select
the modulating frequency f_{c} + f_{c}`, f_{c}`«
f_{c} from a LFSK according to f_{c}` = lf_{Δ},
l = 0, 1, 2,..., L (Proakis, 1989; Rappaport, 2002). The minimum frequency
separation for LFSK to meet the condition for orthogonality is f_{Δ}
= 1/T_{s}. The remaining k = log_{2}M bits are modulated
using ordinary MQAM.
The complex form of HQFM signal can be expressed as:
where, u_{l}(t) = exp(2πlf_{Δ}t), m {0, 1,
2, ..., M1} (from QAM), lε {0, 1, 2, ..., L1} (from FSK), 0≤t≤T_{s},
T_{s} = T_{b}log_{2}ML, T_{b} being bit
duration in seconds. C_{mc}`s and C_{ms}`s can takes up
to values from (2m1√M), defining the I and Qaxis of the signal
space diagram.
From (1) it can be observed that L/M HQFM constitute of L sets, each
with MQAM modulated symbols, where in each set, the cross correlation
coefficient ρ = 0 implies that the frequency difference, f_{Δ},
is an integral multiple of 1/T_{s} (noncoherent detection), or
in other words, the modulation index h = f_{Δ}T_{s}
is a positive integer.
It is worth mentioning that, QAM uses 2D, while, HQFM uses 2^{L+1}
dimensional signaling. Also, for ordinary MQAM, L = 1. For L = 2, M =
4, HQFM reduces to special modulation format known as Q2KSK (Saha and
Birdshall, 1989) which is a member of general class of modulation format
known as JPFM (Ghareeb, 1995). However, JPFM generally phase shifts the
carriers, while HQFM utilizes amplitude/phase shift (QAM). One advantage
of QAM over PSK is that QAM is more power efficient and supports high
data rates for the same required SNR (Proakis, 1989; Rappaport, 2002).
As all the FSK frequencies are orthogonal to each other, the points lying
in the HQFM signal space can be viewed as points lying in a smaller QAM
with different orthogonal planes, where each plane is distinguished by
its corresponding FSK frequency (Fig. 1). In this way
MLQAM signal can be split into smaller ML/2, ML/4, ML/8... MQAMs with
carrier frequencies taken from 2, 4, 8, ... LFSK, respectively.
For transformation of these HQFM signals to an OFDM symbol, usually Nedused
inactive carriers (set to zero) are added appropriately and then Npoint
IFFT is applied. The zero padded signals are used to shape the power spectral
density of the transmitted signal. In order to avoid ISI and ICI, the
transmitted signal is made periodic by cyclically appending CP (N_{CP}≤25%)
of the OFDM symbol. This CP also plays a decisive role in synchronizing
the OFDM frames properly. The signal is then D/A converted to produce
the analog baseband signal, upconverted to RF and then transmitted. This
whole process is shown in Fig. 2.

Fig. 1: 
Decomposition of 16QAM into 4QAM using 4FSK for HQFM 

Fig. 2: 
Hybrid MQAM/LFSK (HQFMOFDM) transmitter 
A continuous time OFDM symbols are expressed as:
where, Δf = 1/NT_{s} is the frequency separation between
each subcarrier, N number of OFDM subcarriers, T_{s} is
the data symbol period and c_{p,q} = (c_{p,0}, c_{p,1},...,
c_{p,Nq}) is a set of alphabet taken from HQFM.
At the receiver side, HQFM signals are recovered after removal of CP
and application of FFT. As mentioned earlier, L/M HQFM signals consist
of L set of M QAM modulated signal where members of each set are orthogonal
to the members of other sets. So a two stage demodulation process is carried
out to extract the information bits: Multiple representations of received
signal are passed through Lsubreceivers, where unique frequencies, f_{i},
i = 0, 1, ..., L1, orthogonal to each other are known to each
subreceiver. Meanwhile, each subreceiver estimate QAM symbols by computing
the minimum distance between the received signal and M possible transmitted
signal. Among these subreceivers, that receiver is chosen which give
the maximum value for the assigned frequency matched to that particular
signal and zero for all other frequencies.

Fig. 3: 
Hybrid MQAM/LFSK Demodulator 
Thus, a correct estimate of frequency is made (noncoherent part). Consequently,
the estimated QAM symbol for the chosen subreceiver is selected (coherent
part). Figure 3 shows a complete picture of the proposed
demodulator (After/IFFT).
CCDF of PeakToAverage Power Ratio (PAPR): PeaktoAverage Power
Ratio (PAPR) of the p^{th} OFDM symbol s_{i,k} is defined
as:
where, s_{p,q} = (s_{p,0}, s_{p,1},..., s_{p,N1})
is the time domain representation of vectors associated with the p^{th}
OFDM symbol and E{s_{i,k}^{2}} denotes the expectation.
The distribution of PAPR of the OFDM signal can be well understood by
famous “Waterfall Curves” for Pr{PAPR_{0}}.
These curves describe the Complementary Cumulative Distribution Function
(CCDF) of PAPR which is the most frequently used analysis tool described
in literature.
Assuming symbol size N large (N≥64) and the transmitted signal nearly
Complex Gaussian Distributed, the OFDM signal follows a Rayleigh distribution
with zero mean and a variance σ^{2}_{OFDM} If the
OFDM symbols are assumed to be i.i.d., the probability that magnitude
of the entire OFDM symbol that exceeds a certain threshold can be approximated
as (Müller Weinfurtner et al., 1997; Muller and Huber, 1997):
Equation 4 shows that large PAPR occurs against a certain threshold infrequently.
Also, PAPR is highly dependent on the IFFT length N of the OFDM transmitter,
i.e., PAPR increases with the increase in subcarriers for a single OFDM
symbol.
Relationship between OFDM subcarrier separation, Δf and FSK tone
separation, f _{Δ}, is f_{Δ} = NΔf⇔N
= f_{Δ}/Δf. Also, PAPR is direct function of N or f_{Δ}/Δf.
As mentioned earlier, for fixed N, PAPR can be reduced by decreasing f_{Δ}.
Bringing FSK tones closer to each other while maintaining their orthogonality,
means that more frequencies can be adjusted in a given frequency band.
Therefore PAPR decreases by decreasing f_{Δ} or increasing
L. This is justified for HQFMOFDM, for which PAPR decreases by increasing
the number of FSK tones as compared to 2^{n}QAMOFDM (L = 1).
MODIFIED HQFMOFDM
The PAPR reduction capabilities of HQFMOFDM are not as good as reduction algorithms
applied to conventional 256QAMOFDM e.g., PTSOFDM. Therefore, a modification
is proposed, termed as HQFMI. It will be shown in the next section that HQFMOFDM
shows a strong dependence of decrease in PAPR on number of keying frequencies
(L). In HQFMI, a multistage modulator is designed which uses variable FSK
modulator to generate frequencies. In first stage, nk = log_{2}L bits
are used to generate L frequencies and remaining k = log_{2}M bits are
used for QAM Modulation. Other stages generate 2L, 4L, ..., frequencies which
are used for M/2, M/4,..., QAM Modulation, respectively. The overall number
of bits, n, for HQFM signal remains constant. After applying IFFT, HQFM signal
with least PAPR is chosen. The receiver first demodulates the OFDM symbols using
FFT, then determine the number of bits used by QAM by observing the maximum
amplitude C_{max}. The demodulation process is carried out to detect
the correct HQFM symbol as per Fig. 3. Only twostage HQFM
modulator is sufficient to achieve the desirable results. Monte Carlo simulations
show that PAPR reduction capability is comparable to PTSOFDM.
To further reduce the PAPR, PTS algorithm is used. The whole HQFM signal
set is divided into V subblocks, V = p; P = 0, 1, 2, ... with number of
carriers N_{v}≥32 in each subblock. Phase vector of {0} is
sufficient to obtain the results, which can be detected, in one or two
iterations, without transmitting it, hence increasing the detection complexity.
RESULTS AND DISCUSSION
All the simulations in this section are done in Matlab® and a Simulink^{TM}
model is designed to implement the 16QAM with 16FSK (16/16 FDM transciere
HQFM) modulator and demodulator according to block diagrams shown in Fig.
2, 3, respectively. Number of subcarriers assumed
to be N = 512 i.e., IFFT length. Results are compared with 256QAM OFDM
transceiver.
Figure 4 shows a portion of an arbitrary 512carrier
OFDM symbol, when 256QAM is employed and is compared with 16/16 HQFM OFDM
symbol. The figure clearly shows that the peak of the OFDM symbol is drastically
reduced when the hybrid signals are injected into the IFFT resulting in
low PAPR.
Figure 5 plots the probabilities Pr(PAPR_{0})
against a specified threshold PAPR_{0}. The outermost line shows
the Pr(PAPR_{0}) against a specified threshold PAPR_{0}
for conventional OFDM and is the theoretical expansion of Eq. 4. From
Fig. 5, it is obvious that:
• 
HQFM make the probabilities to decay faster, yielding
a more desirable statistical behavior. PAPR for HQFM does not exceed
~13dB while it can take up a value of ~15.5dB for a conventional one
at Pr(PAPR_{0}) = 106. 
• 
For a fixed number of bits/subcarrier, PAPR decays more fast if
the number of FSK frequencies increases. 
• 
16FSK is enough to reduce the PAPR for the OFDM symbol. Although,
by increasing the number of FSK frequencies, one can achieve more
PAPR reduction, but, at the cost of reduced bandwidth efficiency.
There is no improvement in PAPR statistics if L≥32. 
Figure 6 shows the performance of 16/16 HQFM OFDM with
different number of subcarriers and is compared with 256QAM OFDM. The
conclusion drawn by viewing this graph is that using HQFM with 4N
subcarriers allows transmission with PAPR significantly below the original
OFDM system with N subcarriers.
Although, non orthogonal FSK (h<1) can be employed to achieve the
bandwidth efficiency (Ghareeb, 1995), but noncoherent detection of these
HQFM formats becomes difficult, hence, exhibit performance degradation
(Ghareeb, 1995). Figure 7 show that the modulation index,
h = 1 is the optimum choice for orthogonal HQFM. Therefore, having h =
1, we get best PAPR reduction capability and BER performance.
One method to reduce PAPR of the HQFMOFDM modulator is to use variable
FSK frequencies and choose that symbol for transmission that exhibits
low PAPR. Figure 8 compares the resulting OFDM transceiver
(HQFMI) with simple OFDM and OFDM employing PTS. The results are comparable
with PTS but, PTS utilizes sideinformation to be transmitted while, HQFM
does not. The correct number of bits employed for FSK (variable level)
for each OFDM symbols are detected at the first stage of the demodulator.

Fig. 4: 
Amplitude and Mean of a Single 512OFDM symbol PAPR_{256QAM}
= 11.706dB, PAPR_{16/16 HQFM} = 8.784dB 

Fig. 5: 
CCDFs of PAPR of 256QAM OFDM compared to different HQFM OFDM Transceiver
(each with 8bit/subcarrier) with N= 512 

Fig. 6: 
CCDFs of PAPR of 256QAMOFDM compared with 16/16 HQFM using different
number of subcarriers 

Fig. 7: 
Dependence of PAPR on modulation index h, (h = f_{Δ}T_{s}).
Comparison is made with 256QAMOFDM (outermost) and 16/16 HQFM (N=512) 

Fig. 8: 
CCDFs of PAPR of 256QAMOFDM compared with variable 8/16 FSK (HQFMOFDM)
and PTS with N= 512 

Fig. 9: 
Comparison of PTSOFDM and HQFMOFDM with side Information Vector
(1,1) 
From
Fig. 9 it is obvious that at Probability <10
^{7}, PAPR
of conventional OFDM Symbol with N =
512 is 15.8 dB, which is 3
dB higher than PAPR of PTSOFDM symbol and 4.4 dB higher than 16/16 HQFMII.
In this case, both PTS and HQFMII utilizes sideinformation vector which
is (1, 1, j, j) and (1, 1), respectively. For the case of HQFMII, the
side information can be detected iteratively.
CONCLUSION
In this study, a novel OFDM transceiver is proposed showing low PAPR
as compared to conventional system. The results are discussed and compared
based upon different simulation results. It is shown that this scheme
can work with arbitrary number of subcarriers. In contrast to PTS or SLM,
this system requires no or little sideinformation to be transmitted with
the signal. The receiver complexity is slightly increased as it detects
coherently the FSK carriers and QAM symbols to decode the information
bits properly. This scheme is capable of improving the statistical behavior
of OFDM`s PAPR.
ACKNOWLEDGMENTS
This research is funded by Higher Education Commission (HEC), Pakistan.
The authors are thankful to Faculty of Electronic Engineering, GIKI. Special
acknowledgment to Sobia Baig, also for helpful comments in preparing this
study.