Introduction
The development of Multi carrier modulation techniques (MCMT) (Chang and Gibby, 1968) has allowed the transmission of high quality audio and digital television pictures to be demonstrated from both terrestrial and satellite based systems (Shelswell, 1995; Sari et al., 1995; Carrasco et al., 1992). The aim of this paper is to investigate the use of (MCMT) for high bit rate wireless applications. In order to improve spectral efficiency the use of differentially encoded (16 DEAPSK) is employed to modulate the parallel carriers (Webb et al., 1991). (MCMT) is a wideband modulation scheme which is specifically designed to cope with the problems of multi path reception. It achieves this by transmitting a large number of narrowband digital signals over a wide bandwidth. The consequently longer symbol duration renders the system less susceptible to the effects of inter symbol interference (ISI) induced by a frequency selective channel. To achieve the aim of (MCMT) the subcarrier frequencies are chosen to be spaced at the symbol rate, that is, if the MC symbol duration is T_{s} seconds, the subcarrier frequency spacing is 1/T_{s} Hz (Chang, 1966).
System simulation
A basic (MCMT) system can be simulated as shown in Fig. 1.
Firstly the data symbols from the (16 DEAPSK) modulator are converted from
serial to parallel (S/P) format. In the simulations the output width of the
converter is 16 symbols (complex valued), which corresponds with the number
of parallel carriers in the MCMT signal at the output of the inverse Fast Fourier
transform (IFFT) block. The output of IFFT is the time domain MC signal which
has 16 complex valued samples (Weinstein, 1971; Qatawneh, 2002). These samples
are converted from parallel to serial format before being placed on to the channel.
In the receiver, the incoming signal is converted back to a parallel format
before being processed by the Fast Fourier transform (FFT) which implements
the demodulator. The FFT output represents the parallel demodulated symbols
which are converted back into the original serial format. These symbols are
then differentially coherently demodulated to recover the data. The data formats
employed at the input to the IFFT block will be described where required.
In the presence of intersymbol interference caused by the transmission channel, the properties of orthogonality between the carriers is no longer maintained. However, by preceding each symbol by a guard period it is possible to absorb the intersymbol interference. This is achieved using the optional guard period add block shown in Fig. 1. This guard period is removed at the receiver by the complementary guard period remove block. The guard period must be of limited duration (Shelswell, 1995), because although a longer guard period gives a more rugged system, it imposes a penalty because of the power required for its transmission. If is the guard period, the duration of transmitted signal is given by t_{S}=Δ+T_{S} where is the MC symbol period. In this case the guard period is created by taking the last four samples of the 16 time domain samples at the output of the IFT and then inserting them in front of the 16 original samples. Consequently, there are now 20 samples per M C symbol.
Differential 16 Star QAM
The majority of work concerning QAM for mobile radio applications has utilized
square QAM constellations. In general 16 QAM (square) requires coherent detection.
However, since the performance of coherent detection is severely affected by
multi path fading, (mainly because of carrier recovery issues), the 16 Star
QAM constellation shown in Fig. 2 combined with differentially
coherent detection is preferred (Webb et al., 1991).
Modulator structure for 16 DAPSK
The modulator structure for 16 Star QAM(16DAPSK) is shown in Fig.
3. The random data source gives a binary sequence, which is formed into
four bit symbols namely, a_{n},b_{n},c_{n},d_{n}.
The carrier is differentially phase modulated by the last three bit, b_{n},
c_{n}, d_{n} and differentially amplitude modulated by the first
bit a_{n}. The first bit a_{n} is used to determine the transmitted
signal amplitude as follows. If the incoming bit a_{n} is a binary ‘1’
the amplitude level of the transmitted signal is changed to the other amplitude
level. However, if the incoming bit a_{n} is a binary ‘0’
the amplitude level of the transmitted signal remains the same as shown in Table
1. The remaining three bits, b_{n}, c_{n}, d_{n}
are Gray encoded to give the phase changes shown in Table 2.

Fig. 2: 
16 level star QAM constellation 

Fig. 3: 
Modulator structure for 16 DAPSK (16 Star QAM) 
Table 1: 
Amplitude bit change 

Table 2: 
16 Star QAM phase change 

Consequently it can be seen that a differential 16 star QAM is a combination of independent 8 DPSK and 2 DASK.
For example, suppose that the current input bits {b_{n},c_{n},d_{n}} are “000” and the previous transmitted phase 0° is, it can be seen from Table 2 that the required phase change is zero degrees giving a transmitted phase of 0°.
For example, suppose that the current input bits {b_{n},c_{n},d_{n}} are “000” and the previous transmitted phase is, it can be seen from Table 2 that the required phase change is zero degrees giving a transmitted phase of 0°.
How to detect a differential 16 DEAPSK signal
Differential detection of Differential 16 DEAPSK signal can be split into
two stages: first the differential phase detector (DPD) for the eight PSK signal
and second the differential amplitude ratio detection (DARD) of the two level
amplitude signal. Fig. 4 shows Demodulator structure for 16DEAPSK.
The DPD and DARD detectors detect the phase difference and amplitude ratio of
the two successive received signals, respectively and their respective outputs
are given by :
The * denote the complex conjugate
And
The decision rule is to find

Fig. 4: 
Demodulator structure for 16DEAPSK 

Fig. 5: 
MC16 DEAPSK system and channel 

Fig. 6: 
Rician fading with MC16 DEAPSK model 
Which is chosen from :
where ΔR_{l1} and ΔR_{l2}, arethedecisionthresholds
The transmitted four bit s(a_{n}b_{n}c_{n}d_{n})
is recovered from
, where k is so called k factor of Rician fading, S is the power of the specular
component, D is the power of the defuse component and σ^{2} is
the variance
Flat fading channels
A typical channel model in land mobile radio is known as frequency flat
Raleigh fading. Rician fading may be characterized by a factor which is defined
as the power ratio of the specular (line of sight or direct path) component
to the diffuse components. Fig. 5 shows MC16 DEAPSK system
and channel. The rate of change of the fading is defined by the Doppler rate.
The Doppler rate is proportional to the velocity of the mobile station and the
frequency of operation. The normalized Doppler rate is given by f_{d}T_{s}
where f_{d} is the maximum Doppler rate and T_{s} is the MC
symbol duration. For the considered simulations, the symbol duration is equal
to one second so that the normalized Doppler rate is equal to the Doppler rate.
In general, normalized Doppler rates less than 0.01 are applicable to most systems.
A more complex propagation model includes many discrete scatters, where each propagation path may have a different amplitude, propagation delay and Doppler shift. When the components of a signal are received with different delays, the phase difference between them is a function of the frequency of the components. Thus the transmitted signal will experience a channel with a nonflat frequency response, which also varies with time. This type of channel is said to be frequency selective and is usually modeled as a tapped delay line, where the number of taps is equal to the number of discrete delayed paths. Clearly, the effect of the tapped delay line is to introduce overlap between the transmitted symbols. This form of degradation is known as intersymbol interference (ISI). In this model the first arriving path experiences Rician fading. In this work, the ratio k for the Rician fading path is equal to 15 for all the simulations. Fig. 6 shows the simulation model
Results and BER evaluations
Performance of multi carrier differential encoded 16 DEAPSK and single 16 DEAPSK
in the presence of AWGN
We wish to establish benchmark AWGN for Multi carrier Differential encoded
(DE. 16 DEAPSK and single 16 DEAPSK in the presence of AWGN with differentially
coherent demodulation. In this section the BER performance of Multi carrier
Differential encoded (DE. 16 DEAPSK and single 16 DEAPSK with a guard period
disturbed by AWGN are compared. Fig. 7 shows the BER results
as a function of signal to noise ratio (SNR) for both a single carrier and for
an MC system using differential 16 DEAPSK encoding. Clearly the BER performances
are not identical in AWGN. This is to be expected owing to the noisy phase reference
used in the differential systems.
Also Fig. 8 Compares the BER performance for Multi carrier
16 DE –APSK and single 16 DE–APSK and single 16 DPSK in the presence
of AWGN.
For example the result of Comparison shows that the BER performance for Multi
carrier 16 DE–APSK and single 16 DE –APSK and single 16DPSK in the
presence of AWGN are not the same as shown in Fig. 8. If we
choose SNR ratio for instant 15 dB, then the BER performance for Multi carrier
16 DEAPSK is equal 10^{7} and the BER performance for 16 DPSK is equal
10^{4}, but the BER performance for 16 DEAPSK is equal 7x10^{5}.
Performance of Multi carrier Differential Encoding 16 DEAPSK with Differentially
Coherent Demodulation in Rician Fading Channels
The BER performances presented in Fig. 9 compare Multi
carrier 16 DEAPSK in the Gaussian channel (k=∞) and for various values
of the Rician fading power ratio (k) and a Doppler rate of f_{d}=0.01
Hz. It can be observed that the Rician channel degrades the SNR performance
of the MC systems by about 6 dB compared with that achieved over the Gaussian
channel at a BER of 1x10^{3}.

Fig. 7: 
Multi carrier 16 DEAPSK and single 16 DEAPSK in the presence
of AWGN 

Fig. 8: 
Comparison of Multi carrier 16 DE –APSK and single 16
DE –APSK and single 16 DPSK in the presence of AWGN 

Fig. 9: 
Comparison of Multi carrier 16 DEAPSK in the Gaussian channel
(k=∞) and for various values of the Rician fading power ratio (k)
and a Doppler rate of f_{d}=0.1 Hz 

Fig. 10: 
Performance of Multi carrier 16 DEAPSK in presence of Gaussian
channel (k=∞) and for various values of the Rician fading power ratio
(k) and a Doppler rate of f_{d}=0.01 Hz 
The single channel system performance is some 3 dB worse than the OFDM system at the same BER in the Rician channel. The irreducible BER is also higher for the single channel system.
Fig. 9 compares the performance of Multi carrier 16 DEAPSK in the Gaussian channel (k=∞) and for various values of the Rician fading power ratio (k) and a Doppler rate of f_{d}=0.1 Hz
The simulation results presented in Fig. 10 show the performance of Multi carrier 16 DEAPSK in presence of Gaussian channel (k=∞) and for various values of the Rician fading power ratio (k) and a Doppler rate of f_{d}=0.01 Hz with differentially coherent demodulation It can be seen that the BER become irreducible for all the simulated values of k except for the AWGN case of k=∞.
The BER performance of Rician faded for Multicarrier 16 DEAPSK and single 16 DEAPSK with differentially coherent demodulation in the presence of AWGN is considered. The BER performance was presented for various values of k factor. With a Doppler rate 0.1 Hz and 0.01 Hz. It was shown that the BER performance improves as k factor increases (specular components becomes stronger). When specular component (k=15) Rician channel, the required value of signal to noise ratio(SNR) is 35 dB at BER=2x10^{9} for Doppler rate 0.01 Hz. But for Doppler rate 0.1 Hz, the required value of signal to noise ratio (SNR) equal 35 dB at BER=4x10^{4}.
Acknowledgments
The authors would like to thank Mutah University for their technical and financial support in undertaking the research made for this paper.