軟件無線電第九章

1、Software RadioPulse Shaping and Receive FilteringSee first that the design is wise and just: that ascertained, pursue it resolutely; do not for one repulse forego the purpose that you resolved to effect. William ShakespearePulse Shaping and Receive Filtering Pulse and Pulse Amplitude Modulated Messa

2、ge Spectrum Eye Diagram Nyquist Pulses Matched Filtering Matched, Nyquist Transmit and Receive Filter CombinationPulse Shaping and Receive Filtering We will focus on the situation where up and down-conversion have been flawlessly performed and the effect of transmission from baseband PAM message wav

3、eform to received signal is presumed described by a linear transfer function and the addition of interferers, in particular spectrally flat broadband noise. Pulse Shaping and Receive FilteringPulse Shaping and Receive Filtering Pulse SpectrumPulse Shaping and Receive Filtering Pulse SpectrumPulse Sp

4、ectrumPulse Shaping and Receive Filtering Pulse SpectrumPulse SpectrumPulse Shaping and Receive Filtering Pulse Spectrum One-symbol wide Hamming blip pulse shape (with 10 samples per symbol) and frequency response (from freqz)Pulse SpectrumPulse Shaping and Receive Filtering Pulse Spectrum Spectrall

5、y flat 4-PAM symbol sequence triggering baud-spaced 10-times oversampled Hamming blip pulse shape as (baseband) output of pulse shaping filterPulse SpectrumPulse Shaping and Receive Filtering Pulse Spectrum Triple-wide Hamming blipPulse SpectrumPulse Shaping and Receive Filtering Pulse Spectrum Spec

6、trally flat 4-PAM symbol sequence triggering three-baud-wide 10-times oversampled Hamming blip pulse shape as (baseband) output of pulse shaping filterPulse SpectrumPulse Shaping and Receive Filtering Pulse Spectrum Compare message with single-baud-wide Hamming pulse to observe how inter-symbol inte

7、rference of triple-baud-wide Hamming pulse can cause decision errors.Pulse SpectrumPulse Shaping and Receive Filtering Pulse Spectrum Eye diagram is a popular robustness evaluation tool. For 4-PAM, single-baud-wide Hamming blip with additive broadband channel noise, retriggering oscilloscope after e

8、very 2 baud intervals producesEye DiagramPulse Shaping and Receive Filtering Eye DiagramEye DiagramPulse Shaping and Receive Filtering Eye Diagram Observe illustrative vertical (amplitude) and horizontal (timing) margins for correct decision at sample times.Eye DiagramPulse Shaping and Receive Filte

9、ring Eye Diagram Reconsider multiple-baud-wide Hamming pulse example.Eye DiagramPulse Shaping and Receive Filtering Eye Diagram Top: Double open-eye Middle: Triple partial eye closure Bottom: Quintuple fully closed eyeEye DiagramPulse Shaping and Receive Filtering Eye Diagram The impulse response of

10、 a Nyquist pulse creating no ISI at other sample times is zero at those instants and nonzero only at the one particular sample time.Nyquist PulsesPulse Shaping and Receive Filtering Nyquist PulsesNyquist PulsesPulse Shaping and Receive Filtering Nyquist PulsesNyquist PulsesPulse Shaping and Receive

11、Filtering Nyquist PulsesNyquist PulsesPulse Shaping and Receive Filtering Nyquist PulsesNyquist PulsesPulse Shaping and Receive Filtering Nyquist PulsesNyquist PulsesPulse Shaping and Receive Filtering Nyquist PulsesNyquist PulsesPulse Shaping and Receive Filtering Nyquist Pulses Raised-cosine pulse

12、 Time and Frequency Plots:Nyquist PulsesPulse Shaping and Receive Filtering Nyquist Pulses The sum of the frequency responses of a Nyquist pulse shape and its replicas shifted by an integer multiple of the symbol frequency (i.e. the inverse of the symbol period) is a real constant. Consider a candid

13、ate Nyquist pulse v(t) that is nonzero at time zero and zero for all other times that are integer multiples of the symbol period T.Nyquist PulsesPulse Shaping and Receive Filtering Nyquist PulsesNyquist PulsesPulse Shaping and Receive Filtering Nyquist PulsesNyquist PulsesPulse Shaping and Receive F

14、iltering Nyquist PulsesNyquist PulsesPulse Shaping and Receive Filtering Nyquist Pulses Suppose the channel simply adds broadband noise n(t). The symbol to reconstructed downsample system is described byMatched FilterPulse Shaping and Receive Filtering Matched FilterMatched FilterPulse Shaping and R

15、eceive Filtering Matched FilterMatched FilterPulse Shaping and Receive Filtering Matched FilterMatched FilterPulse Shaping and Receive Filtering Matched FilterMatched FilterPulse Shaping and Receive Filtering Matched FilterMatched FilterPulse Shaping and Receive Filtering Matched FilterMatched Filte

16、rPulse Shaping and Receive Filtering Matched FilterMatched FilterPulse Shaping and Receive Filtering Matched FilterMatched FilterPulse Shaping and Receive Filtering Matched Filter Example:Matched FilterMinimum for causality of matched filter ispulse width for pulse initiated at t = 0.Pulse Shaping a

17、nd Receive Filtering Matched Filter A preferred receive filter impulse response (in the absence of channel ISI but with broadband channel noise) (i) will match the reversed impulse response of the transmitter pulse shape and (ii) when convolved with the transmitter pulse shape will form a Nyquist pu

18、lse.Matched Nyquist Transmit and Receive Filter CombinationsPulse Shaping and Receive Filtering Matched Nyquist Transmit and Receive Filter Combinations Want convolution of candidate pulse shape g(t) and its matched filter g(t ) to equal even symmetric Nyquist pulse p(t). Since convolution of two ev

19、en symmetric pulse shapes is even symmetric, presume g(t) is even symmetric, so with particular , g(t) = g( t).Matched Nyquist Transmit and Receive Filter CombinationsPulse Shaping and Receive Filtering Matched Nyquist Transmit and Receive Filter CombinationsMatched Nyquist Transmit and Receive Filter CombinationsPulse Shaping and Receive Filtering Matched Nyquist Transmit and Receive Filter CombinationsMatched Nyquist Transmit and Receive Filter Combinationswhich ha