The structure of the time division multiplexed digital optimal frequency band transmission system is shown in Figure 1. It consists of multiple signal inputs, a time division multiplexer, a transmission pulse shaping filter with the square root characteristic of the raised cosine spectrum, a digital modulator. Besides, it is composed of communication channel, digital demodulator, receiving matched filter with square root characteristics of raised cosine spectrum, sampling

decision circuit, time division multiplexer, and multiple signal output.

In the circuit structure of the transmission system shown in Figure 1, the band-pass transmission system is composed of a digital modulator, a communication channel, and a digital demodulator. In order to achieve the best reception of the digital frequency band transmission system, the receiving filter should be designed as a matched filter, and the pulse shaping transmission filter before the digital modulator should be designed as a filter with the square root characteristic of the raised cosine spectrum.

Principle analysis: Let G_T(f) be the transfer function of the pulse-shaping filter, G_R(f) is the transfer function of the receiving filter, C(f) is the transmission characteristic of the digital modulation and demodulation band communication channel, under ideal conditions C(f) = 1; The total transfer function of the system composed of G_T(f), G_R(f) and C(f) H(f) = G_T(f) ∙G_R(f)∙C(f); To eliminate inter-code crosstalk, H(f) must meet Nyquist’s first criterion. At the same time, to achieve the best reception, G_R(f) must be the complex conjugate relationship of G_T(f), that is, |G_R(f)|= |G_T(f)*| So the expressions of |G_R(f)|, G_T(f) satisfy formula (1) [3] [4]

| H ( f ) | = | G R ( f ) | ⋅ | C ( f ) | ⋅ | G T ( f ) | = | G R ( f ) | 2 = | G T ( f ) | 2 (1)

can be written as:

| G R ( f ) | = | G T ( f ) | = | H ( f ) | (2)

Therefore, Formula (2) shows that the transmit and receive filters are designed with the square root characteristics of the raised cosine spectrum to achieve the best reception.

The system composed of pulse shaping transmitting filter, bandpass transmission system, and receiving matched filter can be called equivalent baseband channel transmission system. This equivalent baseband channel transmission system achieves the best reception with the maximum output signal-to-noise ratio at the output of the matched filter, and the total transmission function of its corresponding digital frequency band transmission system conforms to the Nyquist criterion, which means that Therefore, the crosstalk between the sampled time codes is zero. At the same time, the total transfer function H(f) of the system is designed as a raised cosine roll-off transfer function, which is physically achievable. If the channel is not an ideal channel, the inter-symbol crosstalk of the transmission system is not completely eliminated, and an equalizer can be added to further eliminate the inter-symbol crosstalk. Therefore, the data of multiple signal sources are connected to high-speed data through time division multiplexing, the system, which is then transmitted through the optimal frequency band transmission system, is the Time-division multiplexing digital optimal frequency band transmission system, which eliminates inter symbol interference and achieves optimal reception.

In the design, the input signal of the Time-division multiplexing is a four-way signal, which is designed to be a square wave, a sawtooth wave and two sine waves with different amplitudes, and then set their parameters. Using the Subsystem module, the simulation model of the designed Time-division multiplexing module is shown in Figure 2.

This module realizes that the four input signals are extracted and digitized sequentially according to time, and then the signals extracted from different time slots are merged into a multi-channel signal through the merging module. At the receiving end, the multiplexed signal will be separated into the original four signals through the Subsystem1 module, and the multiplexed and demultiplexed waveforms will be displayed on the oscilloscope.

The digital modulation/demodulation method is designed as 2PSK, in which the 2PSK signal is first generated by keying method, and then demodulated by coherent demodulation method [5] [6] [7] [8] The modulated signal and the Additive white Gaussian noise signal are then added together to produce a modulated signal with noise, and the input signal is a time division multiplexing signal. The simulation circuit model of the designed digital modulator/demodulator is shown in Figure 3.

Parameter setting:

Carrier signal parameters: Amplitude 3, initial phase “0” and “180”; Sampling time 0.001 s.

1) Transmission filter and matched filter adopt Discrete Filter module filter

with square root raised cosine characteristics, its parameters are set to “Numerator” to “rcosine (1, 10, ‘fir/sqrt’, 0.5, 10)”, where 0.5 is the roll-off factor, “Denominator” is “1”, “Sample time” is “0.001”.

2) The Channel “AWGN Channel” module uses an additive white Gaussian noise channel with parameters “EB/No (dB)” “15” and “Symbol period” is “0.001”.

3) The sampling decision is made up of “Product”, “Relay”, “Enabled and Triggered Subsystem”, in which “Relay” parameter “Output w’ hen on” is “3”, “Output when off” is “−3”, sampling time is the frequency of multiplex signal sequence.

The simulation circuit model of Time Division multiplex digital optimal band Transmission System is composed of Time-division multiplexing module, transmit filter module, 2PSK modulation module, channel, 2PSK demodulation module, matched receiving filter module, time division multiplexing module, etc., the model block diagram is shown in Figure 4.

Four-way source input signal parameter setting: First, amplitude 3, period 2, no delay square wave; second, amplitude 3, period pi sine wave; third, Amplitude 2, period 2 sawtooth wave; fourth, amplitude 2, period 2 * pi sine wave.

The time domain waveform is shown in Figures 5(a)-(d). The other main modules according to the unit module design parameters, and then adjust the debugging simulation system. Adjustment complete, running simulation results.

System simulation in the corresponding oscilloscope display results, oscilloscope display results: The input time-domain waveform of the signal is shown in Figures 5(a)-(d). The output time-domain waveform after TDM is shown in Figure 6. The time-domain waveform of the modulated signal is shown in Figure 7. The optimal sampling time of the matched filter is shown in Figure 8, the

demultiplexing output time domain waveform of the system is shown in Figures 9(a)-(d).

The simulation results show that the waveform of the original signal is the same as that of the input signal. The bit error rate (Ber) of the simulation system is 0, and the eye diagram of the simulation system is clear, which shows that the matched filter can restrain the noise and ISI to some extent. So we can see that the design of the whole system is reasonable and the digital frequency band transmission system achieves the best receiving state. The simulation results verify that the designed time-division multiplexing has completed its functions and met its design requirements. The simulation research results of this article will help us understand how to optimize and design the time division multiplexed digital optimal frequency band transmission system in practical applications, it has important application value.