Comparative Study of Bit Error Rate of Different M-ary Modulation Techniques in AWGN Channel

: This paper focuses on various digital modulation schemes and their effect on bit error rate (BER); and to ascertain which has the lowest bit error rate. Further analysis includes: to compare bit error rates of various digital modulation schemes using the M-ary modulation technique, analyse the effect of varying signal energy per bit to Noise ratio (E b /N o ) on the error rate of various digital modulation schemes, analyse graphically the relationship between E b /N o and BER, analyse graphically the relationship between BER and M-ary number. A model-based design methodology was employed in the research using MATLAB/SIMULINK. The comparison between different M-ary (M-PAM, M-PSK, and M-QAM) (M = 2, 4, 8, 16, 32, and 64) modulation schemes in normal AWGN channel was done. By analysing the graphical illustration of E b /N o vs BER of these M-PSK schemes it was strongly observed that increase in the value of M causes a correspondent increase in the error rate. Therefore, as the error rate increases with increasing M; lower level should be used for long distance communication and vice versa. High level modulation techniques are always preferred for high data rate.


Introduction
Digital communication is employed for signals that are essentially analog and continuous-time, such as speech and images; and signals that are essentially digital such as text files [14]. In digital modulation, the baseband (modulating) signal is converted to a digital signal. It is preferred over analogue modulation for the following reasons: Greater noise immunity and robustness to channel impairments; accommodation of digital error control codes with detect/correct transmission errors. The basic digital modulation techniques are: Frequency shift keying, Phase shift keying, BPSK, QPSK and QAM. The choice of a particular digital modulation scheme depends on the quality factors such as: provision of low bit error rates at low received signal-to-noise ratios; good performance interference, multipath and fading environments; bandwidth occupation; easy and cost effective implementation [1][2][3][4]14]. This paper focuses on various digital modulation schemes and their effect on bit error rate (BER) and to ascertain which has the lowest bit error rate. The objectives include: to compare bit error rates of various digital modulation schemes using the M-ary modulation technique, Analyse the effect of varying signal energy per bit to Noise ratio (E b /N o ) on the error rate of various digital modulation schemes, analyse graphically the relationship between E b /N o and BER, Analyse graphically the relationship between BER and M-ary number.

Theoretical Background
S 1 (t) and S 2 (t) are the pairs of signals used to represent binary in BPSK system.
and E b is the energy transmitted signal energy per bit [5][6] The average probability of symbol error or, equivalently, the bit error rate for BPSK is

M-ary PSK
The modulated waveform of the carrier phase in an M-ary PSK system can be expressed as: 0 t T ≤ ≤ Equation (5) can be rewritten as: Where I = 1, 2...., M Average symbol error probability of an M-ary PSK system [7][8] is given by

M-ary QAM
Quadrature Amplitude Modulation (QAM) is a popular system of attaining high data rates in bandwidth channels that are limited. It is characterized by two data signals that are 90° out of phase with each other [6] [9]. M-ary QAM has become dominant over the years [10]: The general expression of an M-ary QAM signal can be defined as: Where E min is the energy of the signal with the lowest amplitude and a i and b i are a pair of independent integers. Specific values of S i (t) is detected with higher probability than others because the energy per symbol of an M-ary QAM is not constant.
The average probability of error in an AWGN channel for M-ary QAM, using coherent detection: In terms of average signal energy E avg :

Bit Error Rate (BER)
Bit Error Rate (BER) is the number of bit errors that occur for a given number of bits transmitted. It is related to the error probability because it is the ratio of bit errors to bits transmitted. The energy per bit is the amount of power in a digital bit for a given amount of time [10][11].

AWGN (Additive White Gaussian Noise)
The presence of Additive White Gaussian Noise (AWGN) in a channel distorts the quality of the received signal. The deviation of the received symbols with respect to the constellation set increases with respect to higher variance of the noise. And this leads to higher probability, demodulating a wrong symbol to make errors [12][13].

Model-Based Design Methodology
Three M-ary modulation schemes where considered in this work, namely: M-ary PAM, M-ary PSK and M-ary QAM. The model was designed using Simulink. Additional Sinks sub-folder. The entire design is as shown in Figure 1.    Fig. (2) ii. Design steps for QPSK a Select the Random Integer Generator module from the Random data source block set b Select QPSK Modulator Baseband module and QPSK Demodulator Baseband module from Digital Baseband Modulation block set. The Simulink model for QPSK is shown in Fig (3) iii. Design steps for M-PSK Model was designed using Simulink.

Design Steps for M-ary PAM
(1) Select the Random Integer Generator module.  Fig (4)

Results and Discussion
This section contains the designed systems experimentation, simulation and result analysis

Simulation Results of M-ary PAM
The BER for M-ary PAM for different values of E b /N o of the AWGN channel as obtained in this work is as shown in Table 1 below. The modified form is shown in Table 2.

Simulation Results from M-ary PSK Model
(1) BPSK: The BER for M-ary BPSK for different values of E b /N o of the AWGN channel is shown in Table 3 below.
(2) QPSK: The BER for Q-PSK for different values of E b /N o of the AWGN channel is shown in Table 4 below.  Table 5 below.

Simulation Results from M-ary QAM Model
The BER for M-QAM for different values of E b /N o of the AWGN channel is shown in Table 7 below.

Discussion of Results
In all the digital modulation schemes experimented on, it is observed from tables 1 -8 and figures 6 -11, BER decreases with the increase in the E b /N o value. Increasing the E b /N o value means increasing the signal power with respect to noise energy. The error rate is increasing as the value of M increases for the same E b /N o value that is, BER of 64-PSK is higher than BER of 32-PSK, BER of 16-QAM is higher than BER of 8-QAM and so on i.e. BER 64-PSK ≥ BER 32-PSK ≥ BER 16-PSK ≥ BER 8-PSK ≥ BER 4-PSK ≥ BER 2-PSK for the same E b /N o value. This also applies to the other M-ary modulation schemes considered in this report. The error rate becomes constant after a certain value of E b /N o in all the modulation schemes considered for this study through the normal AWGN channel. The value of M increases means more number of bits are combined to make a symbol and these bits are packed more closely in signal constellation. From this experiment, it is proven that between the different M-ary modulation schemes experimented with, M-PAM has the lowest bit error rate within the same E b /N o value of the AWGN channel used with the other modulation schemes considered in the study. Between BPSK, QPSK, and M-PSK, BPSK has the lowest bit error rate within the same E b /N o values. Based on the results obtained from this research, for digital amplitude modulation, M-PAM offers a better BER than M-QAM. This in turn, translate to better transmission of the integrity of the signal.

Conclusion
This paper has successfully dealt with the digital modulation schemes and their effect on bit error rate (BER); and to ascertain which has the lowest bit error rate. The bit error rates of various digital modulation schemes using the M-ary modulation technique were compared, the effect of varying signal energy per bit to Noise ratio (E b /N o ) on the error rate of various digital modulation schemes was analysed. From this research, M-PAM and BPSK offer better BER and better coverage integrity of the signal as it is transmitted along an AWGN channel.