Research Article
Bandwidth Efficient Differentially Encoded 16 Amplitude Phase Shift Keying (16DAPSK) Schemes for Rician Fading Channels
Department of Electrical Engineering, Faculty of Engineermg, Mutah University, AL-Karak, 61710, Jordan
Mobile radio system requires highly bandwidth efficient digital modulation schemes, because the available radio spectrum resources are limited. 16DAPSK is based on 16 star QAM that needs coherent detection[1-3]. However, since the performance of coherent detection is severely affected by fast multi path fading because of the tracking problem experienced by carrier recovery circuits in fast fading environments, differentially coherent detection is preferred.
Frequency flat Rayleigh fading is a typical channel model found in land mobile radio situations. This model is suitable for modelling urban areas that are characterized by many obstructions where a line of sight path does not exist between the transmitter and receiver. In suburban areas, a line of sight path may exist between the transmitter and receiver and this will give rise to Rician fading. Rician fading is characterized by a factor, which is expressed as the power ratio of the specular (line of sight or dominant path) component to the diffused components. This ratio, k, defines how near to Rayleigh statistics the channel is. In fact when k = 0, this means to have Rayleigh fading and there is no fading at all when k = ∞.
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 fdTs where, fd is the maximum Doppler rate and Ts is the symbol duration. For our simulations, the symbol duration is assumed to be 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[1,2].
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 non-flat frequency response, which also varies with time. This type of channel is said to be frequency selective and is usually modelled 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 study, the ratio k for the Rician fading[4,5] path is equal to 15 for all the simulations. Figure 1 shows the simulation model for 16DAPSK system and channel.
The rate of change of the fading is defined by the Doppler rate. To enable comparison between systems we define a normalized Doppler rate given by, fdn = fdTS[6]. Where, fd is the maximum Doppler rate and Ts is the transmitted symbol duration. Figure 2 shows the Rician fading with 16DAPSK model.
Fig. 1: | 16DAPSK system and channel |
Fig. 2: | Rician fading with 16DAPSK model |
Fig. 3: | Basic 16DAPSK system simulation model |
Fig. 4: | 16 level star QAM constellation |
SYSTEM SIMULATION
A basic 16DAPSK system can be simulated as shown in Fig. 3. Firstly the data symbols come from the serial data source to the 16DAPSK modulator . The output of the differentially encoded 16-level amplitude/phase shift keying (16DAPSK) modulator is fed to the channel
In this simulations the outputs of the channel are then differentially coherently demodulated to recover the data. Figure 3 shows the basic 16DAPSK system simulation model.
Differential 16 star QAM (16DAPSK): The majority of this work concerning QAM for mobile radio applications has utilized square QAM constellations. In general 16 QAM (square) requires coherent detection.
Table 1: | Amplitude bit change |
Table 2: | 16 Star QAM phase change |
However, since the performance of coherent detection is severely affected by multipath fading, (mainly because of carrier recovery issues), the 16 Star QAM constellation shown in Fig. 4 combined with differentially coherent detection is preferred[4,7].
Modulator structure for 16DAPSK: The modulator structure for 16DAPSK is shown in Fig. 5. The random data source gives a binary sequence, which is formed into four bit symbols namely, an,bn,cn,dn. The carrier is differentially phase modulated by the last three bit, bn, cn, dn and differentially amplitude modulated by the first bit an. The first bit an is used to determine the transmitted signal amplitude as follows. If the incoming bit an is a binary 1 the amplitude level of the transmitted signal is changed to the other amplitude level. However, if the incoming bit an is a binary 0 the amplitude level of the transmitted signal remains the same as shown in Table 1. The remaining three bits, bn, cn, dn are Gray encoded to give the phase changes shown in Table 2. Consequently it can be seen that a differential 16 star QAM is a combination of independent 8DPSK[8] and 2DASK.
For example, suppose that the current input bits {bn,cn,dn} are 000 and the previous transmitted phase is 0°, it can be seen from Table 2 that the required phase change is zero degrees giving a transmitted phase of 0°.
Detection of a differential 16APSK: Differential detection of a 16APSK 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[1]. The DPD and DARD detectors detect the phase difference and amplitude ratio of the two successive received signals, respectively, as shown in Fig. 6 and their respective outputs are given by:
(1) |
where, * denote the complex conjugate and
Fig. 5: | Modulator structure for 16DAPSK |
Fig. 6: | Demodulator structure for 16DAPSK |
Fig. 7: | The BER results as a function of signal to noise ratio (SNR) for 16DPSK and 8DPSK and 16DAPSK system in AWGN |
Fig. 8: | BER performance of 16DAPSK in the presence of AWGN with various Rician fading channels and a Doppler rate of 0.01 Hz |
Fig. 9: | BER performance of 16DAPSK in the presence of AWGN with various Rician fading channels and a Doppler rate of 0.1 Hz |
(2) |
The decision rule is to find
where,
Which is chosen from:
(3) |
(4) |
(5) |
where, ΔRL1 and ΔRL12 are the decision thresholds for low level and high level of the signal, respectively.
(6) |
The transmitted four bits anbncndn is recovered from
(7) |
k = S/D Where, k is so called k factor of Rician fading, S is the power of the specular component and D is the power of the defuse component and σ2 is the variance.
SIMULATION RESULTS
Performance of Differential Encoded (DE) 16DAPSK IN AWGN: The BER performance of 16DAPSK disturbed by AWGN are compared with 16DPSK and 8DPSK. Figure 7 shows the BER results as a function of Signal To Noise Ratio (SNR) for 16DPSK, 8DPSK and 16DAPSK system, respectively. Clearly the BER performances are not Identical in AWGN.
Performance of 16 Star 16DAPSK in the rician fading channel: The BER performances presented in Fig. 8 compare the sixteen differential amplitude, phase shift keying (16DAPSK) in the Gaussian channel (k =∞) and with various Rician channel with a normalised Doppler rate of 0.01 Hz. The worse results when k = 0. This is because the channel is Rayleigh. However, when we increase k to become k = 20 (Rician channel), the performance of the system becomes better, for the same Doppler rate from 0.01 Hz.
Figure 9 shows the BER performance of 16DAPSK in the presence of AWGN with various Rician fading channels and a Doppler rate of 0.1 Hz. The results shows that the performance of the system is worse than the results shown in Fig. 8, this is due to the increase of the Doppler rate from 0.01 to 0.1 Hz.
In this study, the performance of 16DAPSK has been investigated in AWGN, flat Rayleigh/Rician fading channels. With a specular (k = 20) Rician channel at a normalised Doppler rate of 0.01, the degradation decreases for AWGN performance at a BER of 0.0000001, though a Rayleigh channel (k= 0) gives rise to an unacceptable irreducible BER of about 0.01. However, for the indoor or microcellular environment a direct path is likely to lead to less hostile channels than flat Rayleigh fading. This will improve the performance of the differentially coherent demodulator, especially for 8DPSK system.