The condition of no code-to-code crosstalk is as long as the impulse response waveform h(t) of the baseband transmission system has a maximum value only at the sampling time of the symbol and is 0 at the sampling time of other symbols, thereby eliminating inter-symbol interference. . That is, if h(t) is sampled at time t=kTs (where it is assumed that the delay caused by the channel and the reception filter is t0=0), the following expression holds:
Equation (1) above is referred to as a time domain condition without inter-code crosstalk. That is, if the sample value of h(t) is not zero except at t=0, it is zero at all other sampling points and there is no intersymbol interference.
1, ideal low-pass characteristics
There are many ways to meet Nyquist's first criteria. One of the limit conditions is the ideal low-pass type.
When h(t) is equal to positive and negative kTs (k is not equal to 0), there are periodic zeros. When the time interval of the transmission sequence is Ts, these zeros are used neatly as long as the receiver samples at time t=kTs. , you can achieve codeless crosstalk.
Unfortunately, although the ideal low-pass transmission characteristic achieves the limit transmission rate and the limit bandwidth utilization of the baseband system, this characteristic cannot be physically realized. Moreover, its impulse response h(t) is still unsuitable as a transmission waveform.
Cosine roll-off characteristics
In order to solve the problem of the ideal low-pass characteristic, it is possible to make the edge of the ideal low-pass filter characteristic to slowly fall, which is called roll-off. As long as H(w) exhibits an oddly symmetrical amplitude characteristic at the center frequency of the roll-off segment, the Nyquist first criterion can be satisfied inevitably, thereby achieving crosstalk-free transmission between codes. This design can also be regarded as the result of an ideal characteristic roll-off with an Nyquist bandwidth centered on an odd symmetry condition. The key parameter for the design is the roll-off factor.
The frequency bandwidth occupied by this system is twice that of the ideal low-pass system.
Verification of conditions for crosstalk without codesUse matlab simulation to verify the condition of crosstalk without codes, draw relevant waveforms and eye diagrams, and draw BER curves with noise
Fundamental
Inter-code crosstalk
The transmission of digital signals will cause mutual overlapping of the waveforms of adjacent digital signals in time, that is, the so-called crosstalk between codes. Due to the existence of crosstalk between codes, it may cause an error at the decoding decision of the receiving end. In addition, the condition of crosstalk without code is given in the textbook, which is Nyquist's first criterion. Through this experiment, we can deepen the understanding of intersymbol crosstalk and Nyquist's first criterion.
2, eye profile
In order to measure the merits of the baseband transmission system performance, the oscilloscope is usually used to observe the waveform of the received signal to analyze the effects of crosstalk and noise between codes. This is the eye diagram analysis method, as shown in the following figure.
When the signal distortion is small: the eyes are big eyes, single eyelids;
When the signal distortion is large: The eyes are small eyes and have many eyelids.
Simulation results and analysis
Program running results:
1. Curve of the actual value of sampling points before passing through a raised cosine baseband transmission system
2, eye diagram
3, BER curve
The above four graphs are the actual values ​​of the sampling points before passing the raised cosine baseband transmission system through the raised cosine baseband transmission system, the eye diagram and the BER curve, and Figure 5 shows the correlation of the program operation. information. From the BER curve, we can find that within a certain range, the larger the SNR, the smaller the BER of the corresponding channel transmission.
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