Gmsk modulation and demodulation matlab how to achieve _ two gmsk modulation and demodulation methods to achieve

First, the principle of continuous phase modulation

1, CPM signal model

Real-domain math expressions for CPMC signals:

In the above formula, A represents the symbol energy, fc represents the carrier frequency, and I is the transmitted symbol data

T represents the symbol period, Bears the symbol information to be transmitted, indicating the time-varying phase function of the CPM baseband signal. The initial phase of the signal. The phase of the CPM baseband signal differs from the finite discrete value of the baseband phase of the PSK signal. It is a continuous function of time. The following gives the continuous phase function of the CPM signal The expression:

In the above equation, h is the modulation index of the CPM signal, which determines the phase variation of the CPM signal in each symbol period. The larger the modulation index h is, the larger the phase change in a symbol period is, and the easier it is to distinguish between time domain and frequency domain: q(t) is called the phase shaping impulse function, and is obtained by integrating a pulse function g(t) with a finite duration. :

So the pulse function g(t) is also called frequency shaping pulse.

The frequency pulse function g(t) has a non-zero value only in the interval [0, LT], where L is called the correlation length, and the frequency pulse function g(t) has the following characteristics:

Therefore, the phase shaping pulse function q(t) satisfies the following relationship:

From the above equations, the modulation index h, the frequency shaping pulse function g(t), the correlation length L, and the base number M of the baseband symbol determine the variation of the phase of the CPM baseband signal with time, and select different modulations. The exponential can get different continuous phase modulation signals, and this kind of CPM signal has similar properties. From the integral form of (2.4), it can be seen that the phase shaping pulse function q(t) is a continuous function of time, which guarantees the phase function of the CPM baseband signal

Continuity, and the frequency pulse function g(t) also determines the waveform of the phase pulse function q(t); from Equation (2.8), it can be seen that the correlation length L affects the coding characteristics of the phase pulse function, and the larger the L is introduced, The more obvious the coding effect is.

2, CPM continuous phase formation

The CPM signal is still essentially a phase modulation. The CPM modulation maps the original to-be-transmitted binary information to the continuous phase of the CPM baseband signal and then performs phase modulation with the carrier. CPM baseband signal phase The formation process is a linear weighted sum of all transmitted symbol symbols for the phase shaping pulse function q(t), as can be seen from expression (2.4). The formation process is similar to the convolution process. So you can The formation process is seen as a similar convolution of all the symbol symbols to be sent and the phase shaping pulse function q(t), ie, the baseband symbol symbols to be transmitted are shaped and filtered by the phase shaping pulse function q(t), so that the band is limited . The following is a detailed analysis of the baseband phase of the CPM signal.

The analysis will be performed during the Nth symbol symbol period, where N is an integer, and , the current moment . The continuous phase expression for rewriting the CPM baseband signal is as follows:

From equation (2.8), we can see that the pulse shaping function q(t) is 0 at t《=0 and fixed value 1/2 at t》=LT, so equation (2.14) can be expanded by the following form:

among them, The fixed phase part of the CPM baseband signal, called the fixed phase, is the linear accumulation of all symbol symbols in the interval (negative infinity, NL) and the corresponding phase. Its value is fixed in one symbol period and is h*pi. Integer times; It is the part where the CPM baseband signal continuously changes, which is called the correlation phase, and is obtained by class convolution of the L-symbol symbol and the time-varying part of the phase pulse. The phase forming process of the CPM baseband signal is shown in the figure. Can be expressed as:

Based on the MSK signal, in order to improve the sidelobe attenuation performance of the signal, the idea of ​​adding a filter at the front end of the MSK modulator for pre-modulation is proposed, and the idea of ​​minimum Gaussian frequency shift keying (GMSK) is derived. After passing through a Gaussian low-pass filter, the bipolar pulse sequence has a smoother signal waveform. After being modulated by the MSK modulator, the resulting modulated signal has a smoother phase path and better sidelobe attenuation performance of the power spectrum. The following mainly describes the implementation of GMSK modulation and Matlab simulation.

Figure 2.5 Implementation of GMSK Modulator

Figure 2.5 shows the block diagram of the GMSK modulator. The Gaussian filter in GMSK modulation is usually determined by the filter's BT product, 3db bandwidth B, and symbol duration T. Gaussian filter impulse response is

among them,

The transmitted information bit bi(0/1) is differentially encoded and then changed to the symbol ai = +/-1. These symbols are then filtered by the filter with impulse response g(t)

Which represents the convolution,

The phase of the modulation signal is:

H=1/2 in GMSK modulation.

As can be seen from Figure 2.6, although the domain of the impulse response function g(t) is from negative infinity to positive infinity, it can be ignored in the interval of |t|

Assume that g(t)=0 in the interval of |t|"2T. From formula (3) we can see that g(t) is non-causal and unachievable. Therefore, assuming g(t)=0 in the interval of |t|"2T, delaying g(t) by 2T makes g(t) causal.

Mtlab code:

Clc;

Clear all;

Close all;

Burst = sign(randn(1, 1000));

Tb = 1/19200;

OSR= 16;

BT = 0.3;

Ts = Tb/OSR;

PTV = -2*Tb:Ts:2*Tb;

RTV = -Tb/2:Ts:Tb/2;

Sigma = sqrt(log(2))/(2*pi*BT);

Gauss = (1/(sqrt(2*pi)*sigma*Tb))*exp(-PTV.^2/(2*sigma^2*Tb^2));

Rect = 1/(2*Tb)*ones(size(RTV));

G_TEMP = conv(gauss,rect);

% TRUNCATING THE FUNCTION TO 3xTb

G = G_TEMP(OSR+1:4*OSR);

% TRUNCATION IMPLIES THAT INTEGRATING THE FREQUENCY PULSE

% FUNCTION WILL NOT EQUAL 0.5, HENCE THE RE-NORMALIZATION

G_FUN = (GG(1)). /(2*sum(GG(1)));

% CALCULATE RESULTING PHASE PULSE

Q_FUN = cumsum(G_FUN);

Using FX489 to Implement GMSK Signal Modulation and Demodulation

FX489 is a chip of CML Company for GMSK modulation and demodulation. It includes a Gaussian filter, shaping circuit and other ancillary circuits. The Gaussian filter has a BT value of 0.3 or 0.5 to choose from. The transmission rate is 4bps to 19.2kbps, which provides the transmit clock and receive clock. Figure 2 shows the function of FX489.

Figure 2FX489 features

Using FX489 to achieve GMSK signal modulation and demodulation shown in Figure 3. The symbol transmission rate is determined by the internal partial frequency coefficients of the FX489's external crystal oscillator (logic levels of pins 3 and 4) (Table 1). The selection of the Gaussian filter BT value is determined by the foot 15 of FX489. When the 15th pin is "1", the BT value is 0.5; when it is "0", the BT value is 0.3. In Fig. 3, the negative feedback circuit that constitutes the internal amplifier of FX489; The low-pass filter that is composed is the gain adjusting circuit, should satisfy:

Table I

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