The design of an improved matched filter in DSSS-GMSK system

This paper introduces the principle of DSSS-GMSK system, analyses the superiority of GMSK modulation over MSK modulation. Accord that the method of de-spread before demodulation can effectively improve the capability of the system with spread spectrum gain, this paper researches an improved method with matched filter to de-spread and demodulate the DSSS signals. The local PN code is modulated with GMSK modulation before being correlated with received signal, then we can get the synchronous PN code, de-spread and demodulate the signal. MATLAB simulation shows that this method is more efficient than the method of demodulation before despread in low SNR environment.


Principle of DSSS-GMSK modulation
GMSK(Gaussian-filtered minimum-shift keying)is a kind of modulation scheme with constant envelope, which develops from MSK. The principle of GMSK modulation is that the signals go through a Gaussian low-pass filter before MSK modulation. The impulse response of the Gaussian filter is defined as follows: Where ln 2 2 B a = ， B is the 3dB bandwidth of the Gaussian filter. If the width of a pulse is T, then BT is the normalized 3dB bandwidth. We can obtain the frequency impulse signal of the Gaussian filter: ( ) Suppose that the transmitting data multiplied by PN sequence is ( a a Î -， then the phase of the modulated signals is shown as follows: The frequency of the carrier wave is c f , then the GMSK modulated signal is produced after IF modulation:

Capability analysis of GMSK modulated signals
GMSK is an improvement on MSK. Figure 1 gives the BER performances and frequency spectrum for GMSK and MSK modulated signals. Although the error rate performance of GMSK modulated signal is less than MSK modulated signal, but the gap is quite small. Figure 2 shows that with respect to MSK modulated signals, GMSK modulated signals have a more compact spectrum and faster band attenuation. So GMSK has a broader development prospect.  Normalized 3dB bandwidth is a very important parameter of GMSK modulated signals. From figure 2 we can see that the spectrum structure of GMSK modulated signals is closely related to BT value. The smaller the BT value, the more compact the frequency spectrum. When BT ® +¥ , the GMSK modulated signals change into MSK modulated signals. BT value will also have an impact on the error rate of GMSK modulated signals. Figure 1 also shows that the BER performance will be getting worse as BT value decreases. So, BT value usually is 0.3 in GSM system.

Improved method with matched filter to de-spread and demodulate the DSSS signals
Two methods are used for the signal processing at the receiving terminal of the DSSS system: de-spread before demodulation and demodulation before de-spread. In high SNR environment, the two methods both have good BER performances. But in low SNR environment, the method of de-spread before demodulation has a better BER performance because this method could effectively use the spread spectrum gain. At the receiving terminal, we must get the the synchronous PN code before despread the received signals. Common methods to get synchronous PN code are sliding correlation and matched filter. The principle of matched filter is that we use the PN code as the coefficients of the filter to filter the received signals. The result will be sent to the threshold decider. If the result is larger than the threshold value, the PN code is synchronous.
In DSSS-BPSK system, signals at the receiving terminal is shown as follows: We can not find the correlation peak from formula(8), then we can not get the synchronous PN code and despread the received signals. To solve this problem, this paper researches an improved method with matched filter to de-spread and demodulate the DSSS signals. Figure 3 shows the process of the method.  Figure 3. Process of the improved method.
Assume that the carrier is synchronous, after DDC, the GMSK In-phase data and Quadrature data of the signals are that: If ( ) z t is larger than threshold value, then the local PN code is synchronous. According to the correlation peak values in each symbol period, we can demodulate the received signals.

Simulation results
Assume that signal transmission rate (1)The output of the matched filter is shown as Figure 4.
From Figure 4 we can see the correlation peak clearly. Then we can get the synchronous PN code by setting a suitable threshold value.  (2) Figure 5 shows the correlation peak after de-spread. Since every symbol has 1536 sampling points, the correlation peak will appear every 1536 sampling points. We can get the sending signals through the positive and negative of every peak value.  Figure 6 shows the BER performances of the two methods. The method this paper researched has a better BER performance than the method of demodulation before de-spread in low SNR environment.

Summary
This paper introduces the principle of DSSS-GMSK system, analyses the GMSK modulated signals. According to the special form of the GMSK modulated signals, with the thought of de-spread before demodulation, this paper improves the matched filter. Simulation results show that we can get the correlation peak from the filter output and despread the signals. When input SNR is 6dB -, the BER can be 5 10 -.