Research on the modulation and demodulation of BPSK and BDPSK simulator based on Matlab

Yu Tang1,2 1. College of Information

ZhongKai University of Agriculture and Engineering Guangzhou, China

tangyu_mycauc@163.com

Xiao-lan Lv 2 2. School of Electronic and Information Engineering

South China University of Technology Guangzhou, China 29090137@qq.com

Abstract—The paper introduces the basic modulation and demodulation principle of BPSK and BDPSK. Based on the Matlab, we study on the two kinds of modulation demodulations under the different noises. We mainly research the SNR and BER of BPSK coherent demodulation BDPSK coherent demodulation and BDPSK incoherent demodulation. The simulation indicates the BER of BDPSK coherent demodulation is higher than BPSK coherent demodulation. If we adopt the same demodulation, the BER of coherent demodulation is lower than the incoherent demodulation under the same SNR.

Keywords-BPSK; BDPSK; BER; SNR

I. INTRODUCTION Recently, as the low cost micro controller’s appearance and

civil mobile phone communication introduction, the digital modulation technology popularized day by day. The digital modulation has microprocessor's analog modulation all merits [1 2]− . In the digital modulation system, communication link's any insufficiency may eradicate by using software. The digital modulation information can be realized not only encrypted, but through error correction technology, the received data more reliable. In addition the help of DSP, we can reduce the equipment assigned to each user's limited bandwidth. Then, the frequency utilization can be improved. In the same with the analog modulation, the digital modulation may also divide into the amplitude modulation, the frequency modulation and the phase modulation. Because the frequency modulation and the phase modulation are better to noise abatement, thus become the most preferred communication equipment [2 4]− . We mainly research the SNR and BER of BPSK coherent demodulation BDPSK coherent demodulation and BDPSK incoherent demodulation.

II. THE PRINCIPLES OF BPSK MODULATION AND DEMODULATION

BPSK, which the signal element “0”, “1” uses two different starting phases separately 0 and π expressed, is binary phase shift keying. Binary phase shift keying amplitude and frequency remain unchanged. Its expression is [3 5]− :

0

0

cos 0( )

cos (t phase

s tt phase

ωω π

=−

send" 1"send" 0"

(1)

The BPSK modulation has two kinds [5 8]− : multiplication and selection method. The principles of BPSK modulation show in Figure 1. The main Demodulation is coherent demodulation, as shown in Figure 2.

Figure 1. The principles of BPSK modulation

Figure 2. The coherent demodulation of BPSK

III. THE PRINCIPLES OF BDPSK MODULATION AND DEMODULATION

In the BPSK signaling system has the phase uncertainty, and will create the receive element “0” and “1” the inversion, has the error code. This issue will directly affect the BPSK

Local Carrier

(a) Multiplication

s(t) A(t)

Carrier

Phase shift π

Selector

A(t)

s(t)

(b) Selection method

s(t) Band-pass

filter Low-pass

filter

Local Carrier Sampling Decision A(t)

Time pulse

1239978-1-4244-8165-1/11/$26.00 ©2011 IEEE

signals for long distances. To overcome this shortcoming, we propose a binary differential phase shift keying.

BDPSK is the use of adjacent symbols before and after the relative phase shift of the carrier digital signal transmission, also known as the relative phase shift keying. Suppose θΔ is the phase difference between the current symbol and the previous symbol [4 7]− .

0 "0"1 "1"

sendsend

θΔ = (2)

Then the signal element may express is [6 8]− :

0( ) cos( ) 0s t t t Tω θ θ= + + Δ < ≤ (3)

The BDPSK modulation is the first binary numeral baseband signal differential coding, transforms the basic code into the relative code, then carries on the absolute phase modulation, as shown in Figure 3. The main methods are coherent demodulation and non-coherent demodulation, as shown in Figure 4.

Figure 3. The principle of BDPSK modulation

Figure 4. The principle of BDPSK demodulation

IV. SIMULATION RESULTS AND ANALYSIS

Assuming the initial 0f is 10Hz, sampling frequency sf is

100Hz, symbol rate BR is 1Bd. The initial signal altogether has 25 symbols. They are:

x= [1 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1] (4)

Now let initial signals through different intensity of Gaussian noise channels. Its expression is:

(1, 2600)y x randnλ= + ∗ (5)

Using Matlab simulation studies in different noise environments, BPSK coherent demodulation and BDPSK coherent and non-coherent demodulation of the bit error rate, as shown in Table 1.

Table 1 Data of BER

λ The coherent

demodulation of BPSK

The coherent demodulation of

BDPSK

The incoherent demodulation of

BDPSK

0.01 0 0 0

0.1 0 0 0

0.2 0 0 0

0.5 0 0 0.04

1 0 0 0.12

2 0 0 0.24

5 0 0.08 0.36

10 0.16 0.32 0.48

20 0.48 0.56 0.60

Because we used the Gauss stochastic sequence to have the noise, the noise power was unable to determine. We can only by changing the amplitude of Gaussian random sequence to enhance the power of Gaussian random noise. We use the Matlab simulation of the coherent BPSK demodulation, BDPSK coherent demodulation and non-coherent demodulation of the relationship between BER and SNR, the simulation results shown in Figure 5.

(a) BPSK coherent demodulation

Carrier

Phase shift π

s(t)

A(t)

s(t)

A(t)

Band-pass filter

Local Carrier

Low-pass filter

Sampling Decision

Time pulse

Inverse code transformation

(a) BDPSK coherent demodulation

s(t) Band-pass

filter Low-pass

filter

Sampling Decision

Time pulse

A(t) Delay T

(b) BDPSK non-coherent demodulation

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(b) BDPSK coherent demodulation

(c) BDPSK non-coherent demodulation

Figure 4. The relationship of BER and SNR

From Figure 5 (a), (b), (c), we know when the noise level becomes larger, three demodulated signal to noise ratio decreased and bit error rate increases. When they have the same signal to noise ratio, the BDPSK coherent demodulation's error rate is higher than the BPSK coherent demodulation. But, the BDPSK coherent demodulation's error rate is lower than BDPSK non- coherent demodulation. In the case of large SNR, BPSK coherent demodulation has the lowest error rate.

V. CONCLUSION Binary phase shift keying and binary differential phase shift

keying are at present the very mature digital modulation demodulation technology. The paper from the BER and SNR, has studied the advantages and disadvantages of the two kind of digital modulation demodulation technology. This provides the digital modulation demodulation plan for the modern civil mobile phone and the satellite communication.

ACKNOWLEDGMENT This paper is supported by Guangdong Science and

Technology Plan Program (2010B020315028), Natural Science foundation of Zhongkai University of Agriculture and Engineering (G3092509).

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