Lab 1：Pulse Shaping and Matched Filtering Introduction Pulse shaping：In electronics and telecommunications, pulse shaping is the process of changing the waveform of transmitted pulses. Its purpose is to make the transmitted signal better suited to its purpose or the communication channel, typically by limiting the effective bandwidth of the transmission. By filtering the transmitted pulses this way, the intersymbol interference caused by the channel can be kept in control. In RF communication, pulse shaping is essential for making the signal fit in its frequency band.Typically pulse shaping occurs after line coding and modulation. Not every filter can be used as a pulse shaping filter. The filter itself must not introduce intersymbol interference — it needs to satisfy certain criteria. The Nyquist ISI criterion is a commonly used criterion for evaluation, because it relates the frequency spectrum of the transmitter signal to intersymbol interference. Examples of pulse shaping filters that are commonly found in communication systems are: Sinc shaped filter：It is also called as Boxcar filter as its frequency domain equivalent is a rectangular shape. Theoretically the best pulse shaping filter would be the sinc filter, but it cannot be implemented precisely. It is a non-causal filter with relatively slowly decaying tails. It is also problematic from a synchronisation point of view as any phase error results in steeply increasing intersymbol interference. Raised-cosine filter：Raised-cosine filters are practical to implement and they are in wide use. They have a configurable excess bandwidth, so communication systems can choose a trade off between a simpler filter and spectral efficiency. Gaussian filter：This gives an output pulse shaped like a Gaussian function. Matched filter： In signal processing, a matched filter is obtained by correlating a known signal, or template, with an unknown signal to detect the presence of the template in the unknown signal.This is equivalent to convolving the unknown signal with a conjugated time-reversed version of the template. The matched filter is the optimal linear filter for maximizing the signal to noise ratio (SNR) in the presence of additive stochastic noise. Matched filters are commonly used inradar, in which a known signal is sent out, and the reflected signal is examined for common elements of the out-going signal. Pulse compression is an example of matched filtering. Nyquist ISI criterion： In communications, the Nyquist ISI criterion describes the conditions which, when satisfied by acommunication channel (including responses of transmit and receive filters), result in nointersymbol interference or ISI. It provides a method for constructing band-limited functions to overcome the effects of intersymbol interference. When consecutive symbols are transmitted over a channel by a linear modulation (such as
ASK, QAM, etc.), the impulse response (or equivalently the frequency response) of the channel causes a transmitted symbol to be spread in the time domain. This causes intersymbol interference because the previously transmitted symbols affect the currently received symbol, thus reducing tolerance for noise. The Nyquist theorem relates this timedomain condition to an equivalent frequency-domaincondition.
Lab results & Analysis： 1.pulse_shaping 1.1 The block diagram
2.Matched filter 2.1 The block diagram
3.1 Set TX Front Panel: Device names: 192.168.10.2 Carrier frequency: 915MHz Gain(dB):10 Active antenna: TX1 Generation mode: continuous
3.2Set RX Front Panel: Device names: 192.168.10.2 Carrier frequency: 915MHz Capture time:20m Gain: 10 Trigger level:10m Bandwidth:40M Active antenna: RX2
4.Result constellation diagram and eye diagrams of TX.
1) constellation diagram and eye diagrams of RX(from top to bottom: factor = 0，0.5， 1)
Fig 1 Factor=0
Fig 2 Factor=0.5
Fig 3 Factor=1 it is easy to see from the chart when the value of factor was larger, the constellation point is more intensive, eye effect is better, that is to say when factor is larger, the received signal effect is better, the smaller error. 2)Frequency domain (from top to bottom: factor = 0, 0.5, 1)
Fig 4 Factor=0
Fig 4 Factor=0.5
Fig 4 Factor=1 It is easy to find that the bandwidth of the signal is the greater as the factor increase. 3)Signal before and after matched filtering with different noise power Factor=0.5 (from top to bottom: Noise power=-Inf, -20dB, -10dB)
Fig 5 Factor=0.5 power=-Inf
Fig 6 Factor=0.5 power=-20
Fig 7 Factor=0.5 power=-10
When the noise power is smaller, the amplitude of the signal in the time domain is greater, we also can see that the effect after the match filtering is better than before the matched filter. 4)Comparison of waveforms before and after matched filtering under different factor values (from top to bottom: factor = 0, 0.5, 1)
Fig 8 Factor=0
Fig 9 Factor=0.5
Fig 10 Factor=1 When the factor is greater, the amplitude of the waveform is larger, the waveform is more obviously, it is easier be demodulation.
5.Q&A Q1：Why we need matched filtering? A1:In signal processing, a matched filter is obtained by correlating a known signal, or template, with an unknown signal to detect the presence of the template in the unknown signal. This is equivalent to convolving the unknown signal with a conjugated time-reversed version of the template. The matched filter is the optimal linear filter for maximizing the signal to noise ratio (SNR) in the presence of additive stochastic noise. Q2: What is the relationship between T and W? What is the maximum symbol rate with a given bandwidth W? A2: W=1/2T;2W. Q3：Does ISI increase or decrease with increasing α and why. A3: Using the square root raised cosine function, as increasing the value of the α, ISI decrease. Q4：What is the benefit from the matched filtering? A4: We can perfectly estimate the signal at lower SNR. The matching filter can improve the signal power and improve the signal-to-noise ratio
Note: Please indicate meaning of the symbols in all expressions. Please indicate the coordinate and unit in all figures.
Experience At first, I do not know how to plot this graph.
And after classmate’s help, I understand that we should plot the signal before filtering and after filtering. And we can
this to plot two signal in one graph.
Score
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