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It's often said that pulse compression gives you a gain proportional to the time-bandwidth product (otherwise known as the pulse compression ratio, or $PCR$). This is a really misleading statement, and it had me confused enough to sit down and think about it for awhile. I thought I'd share some of my findings that I pieced together from both reading the ...


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You also see this on Spectrum Analyzers; "video bandwidth" for the same reason: the video is the output voltage from the power detector used to drive the vertical on a display (when the horizontal is the sweep), or in the case of the polar displays used to drive the radius where the sweep drives the angle. Since it is used for the display signal it is ...


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The answer is yes but one has to specify $B_n$ properly to avoide possible confusions. In case if one uses a pulse compression, the bandwidth through which the receiver collects the noise will normally be $B_n = \beta_c$. Then, the "new" signal-to-noise ratio should be written as: $SNR = \dfrac{P_TG_TG_R\lambda^2\sigma{P_g}}{(4\pi)^3R^4(kT_{sys}\beta_c)} = \...


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Note that these definitions of effective duration and effective bandwidth are only useful for very specific signals, namely for (real-valued) low-pass signals that are even and centered around $t=0$. This implies that their Fourier transform is also real-valued, even and centered around $\omega=0$, and, consequently, the same definition of width can be used. ...


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So, to give you something to read up on first, the channel you describe is a Rician or Rayleigh channel, depending on whether you have a dominant line-of-sight path or not. So, as a first approach, to delay something in time, you don't have to shift it by a whole sample – you can also do it in frequency domain, by DFT'ing your signal, multiplying it with a $...


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The ambiguity function is used in radar systems to get the distance and the relative speed of a moving object with respect to the transmitter. Is called ambiguity because it also tells about the ability to distinguish objects that are close between them and with a similar vector velocity. The ideal ambiguity function is a Delta function in both domains. ...


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If we wanted to add a nuance, the "gate" is the actual switching on of the receiver for the duration of observing the reflected signal (which can be as narrow as a single sample, which even a single sample for analog to digital conversions is an integrated observation over a sample time), while the range bin is which "gate" you are in. (Imagine a receiver ...


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Its very simple: The time domain signal per range gate should be windowed (e.g. hamming, blackman-harris, etc.) to avoid ringing, then a FFT per range gate should be calculated. All that is left is to arrange everything in a matrix where each row is a frequency bin and each column is a range bin. (or vice versa).


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Remember that phase is usually only defined on the $[0;2\pi[$ interval (or on $[-\pi;+\pi[$). When you do that $\mod 2\pi$ operation on your graphs, you'll notice that there's no significant difference between your two plots.


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The two most obvious things you can try are: Fitting a Gaussian to your data and then clustering their parameters Estimate the similarity of waveforms directly and then try to cluster that Since you know that the return waveform conforms to a Gaussian, it is better to use a method that takes this into account. So, basically, for every pixel time course, ...


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Definitions: $\tau$: round-trip delay. $\Delta \tau$ = delay resolution. $r$: range. $r=c\tau/2$. Range resolution $\Delta r = c \Delta \tau / 2$. $B$: chirp bandwidth $T$: chirp sweep time $R$: chirp rate. $R=B/T$ Basic steps: We estimate the delay by estimating the frequency shift between the received and transmitted signal. Typically the ...


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The Ambiguity Function is just a name for 2D Correlator. It is known that given a shifted 1D Signal the optimal estimator for the shift (Range in RADAR / LIDAR, etc...) it the correlation with the signal. What if our signal had 2 parameters and both are shifted? In the case of RADAR we have a shift of the signal due to the range (Time Shift) and due to ...


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The "best" detector is a highly subjective subject, and there is (in my opinion) not a definitive answer here. I work in radar processing and I've used everything that you've mentioned in one form or another. All of these CFAR methods are tools, and all of them have good/bad applications. For instance, asking what the "best" wrench is in the toolbox highly ...


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Radar designer here: It sounds like you’re talking about pulse-Doppler (PD) radar systems. For PD radars, the process is essentially as you described: Generate a waveform (typically at IF) and then convert to RF Transmit the waveform at RF Receive the waveform at RF, and eventually mix it down to IF. Apply IQ demodulation (for digital receivers a Hilbert ...


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Part of your misunderstanding comes from the fact that there are many ways in which the radar signal processing chain is implemented. Depending on the type of radar, targets of interest, hardware, etc., some methods are more appropriate than others. We will consider pulsed-Doppler radar here. In the chain you describe: In modern pulse-Doppler systems using ...


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The range resolution is normally some fraction bandwidth of the pulse. The fraction will depend on how you measure it i.e. null to null, 3dB points, 6 dB points etc. Also the windowing (Hamming, Kaiser) used will reduce the resolution i.e. increase the number. For a chirp pulse with the bandwidth you stated the null to null width is given by $$ \delta r = \...


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If you mean that you want a time-varying delay then the whole system becomes time-varying, which means that there is no such thing as a frequency response in the conventional sense. Only linear time-invariant systems can be described by a frequency response. There are of course ways to describe time-varying systems, but the question is what it exactly is ...


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Magnitude |H(z)| is always defined as an absolute value of your transfer function H(z) values which are complex. What you are plotting is the vector that contains complex numbers. You need to take their absolute value and that will give you magnitude. If you call the angle function then you are going to get phase. Transfer function H(z) is always complex. ...


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I'll provide a slightly different perspective. Detection is usually measured against the noise and/or clutter statistics, so you end up with a detection probability which is a function of Signal to Noise Ratio. You will also have a probability of false alarm, which is a function of the noise/clutter statistics and the chosen threshold. In some radars ...


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If you can detect the target separately , you have resolved the targets. If you resolved two targets, you have detected them too. In general you are totally right, radar can detect targets and in some cases can resolve several closely targets. Are radar resolution and detection capabilities not very tightly related? Usually they are related, but none of ...


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Resolution is (usually) referred to as the ability to distinguish two closely separated returns, not targets. The distinction is how far along the processing chain of the radar you are, resolution, given by the inverse of the bandwidth is often limited by the hardware (waveform generation, filters, amplifiers, sampling..) and the environment. While Radar ...


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Two suggestions that may independently, or combined, help to solve your problem. Consider using a different window/weighting function for your FFT processing. There are window functions with low uniform sidelobes such as the Chebyshev window. This window function allows for selection of a constant sideline level response. It sounds like you are using a ...


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That depends a bit on the constraints: are you out of code space or data space or both? Anyway, the typical way of dealing with space problems is to use external memory in conjunction with a fast access internal cache. An alternative would be something like this http://www.ti.com/lsds/ti/processors/dsp/c6000_dsp/c66x/overview.page with a few gigs of DDR ...


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How is angle of arrival estimated? The estimation of angle in linear array antenna is based on the relative phase variation between the target location and antenna elements. This phase variation in spatial dimension between antenna elements will provide you with the location of the target (in terms of angle). Thus, the basic approach to obtain an angle ...


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As for this question 2 months have been passed but it would be helpful for the users looking for the relevant information, There are couple of factors which are related to the sweep time, Maximum velocity after successive chirp Fourier transform. The sweep time should be at least 10 to 20 times the maximum round trip time to have enough samples also from ...


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I refer to the graph you presented at your original post. The interpretation of the graph is as follows: the wider the yellow part of the graph, the more immune to Doppler your system is. Normally it is desirable to have the system immune to the relative speed between source and target, for example when you do not know the targets speed. Therefore, the more ...


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