# Tag Info

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The OFDM signal as a whole is affected by frequency selective filtering. It is usually designed such that the subcarrier bandwidth is smaller than the channel coherence bandwidth. This yields you frequency flat fading for each subcarrier which can be described by a single complex multiplication and equalization can equally done with just one tap. ...

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By using cyclic prefix and its associated demodulation techniques, LTE OFDM (nearly) eliminates the inter-symbol inteference (ISI). The intra-block inteference, if I understand well your question, refers to intra-carrier inteference (ICI) when the orthogonality between sub-carriers is not maintained due to Doppler, delay spread too large, synchronisation ...

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The key idea in spread-spectrum communications is to use much more bandwidth than the minimum required for the signal being sent. Multipath effects occur when the sent signal $s(t)$ and a delayed, attenuated version of it interfere at the receiver: $$r(t) = s(t) + \alpha \cdot s(t-\tau)$$ If $s(t)$ is really narrow band (a sinusoid), and $\alpha = 1$, ...

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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 $... 3 This is an idealized case of the echogram that simply depicts the times of arrival and energy of reflections. You can see this type of plot in literature and as an output in modelling software such as CATT-A and ODEON. If you have a real-life impulse response then you can obtain information about reflections by representing the IR in logarithmic scale, i.e.... 3 These are not the codes you are looking for... As I mentioned in the comments, there are quite a number of ways to do robust TDOA. (Cross-correlation with Linear Chirps, Exponential Chirps, and CDMA-type methods). You have already built a TDOA system utilizing codes, (and that is indeed a good choice over linear-chirps if you need robustness to doppler), ... 3 There are three reasons to avoid ISI through pulse shaping rather than correcting it via channel correction methods. As Bruce pointed out, it is a simpler solution and requires fewer computations. Channel correction usually amplifies the received noise. Received noise will corrupt the channel model, making the ISI removal imperfect to some degree. 2 @MohammedFatehy If you put up -exactly- what you currently know and have, we can help you more. Generally speaking, let us say you have a signal x[n]. And lets say your sampling rate is 1 Hz. So you take one sample every second. Now you want to construct a channel for multipath. Right off the bat, your multipath channel is going to be an FIR filter btw. ... 2 Multi-path is a property of the communication channel (mostly the wireless channel). The received signal$r(t)$is the sum of delayed and weighted versions of the transmit signal$x(t)$: $$r(t) = \sum_{i} a_i x(t-\tau_i)$$ Transmit diversity is a property of the transmitter. It describes a technique using multiple transmit antennas, thus creating multiple ... 2 Quasi-static is almost-static. In other words, for a block (or window) period of time, you could assume that your channel is static. Below, i attach a figure that depicts this scenario. As you can see the channel could be assumed static for around 100 ms. 2 Quasi-static channels can be said as "block-wise" time (in)variant. For example, your channel has no variations over time (not in delay domain) for some time-period, e.g., 1 ms, but the channel may change after 1 ms. 2 There are three different kinds of synchronization in a passband digital communications system: Carrier synchronization: the receiver needs to know the exact frequency and phase of the carrier used by the transmitter. Symbol synchronization: the receiver needs to know the optimum instants to sample the matched filter's output. Frame synchronization: the ... 2 So you have a complex impulse response, and the real and imaginary parts of each tap are modeled as i.i.d. zero mean Gaussian variables with variance$\sigma^2/2$(correct me if I'm wrong). The DFT of the impulse response is a weighted sum of the filter taps: $$H[k]=\sum_{n=0}^{N-1}h[n]e^{-j2\pi nk/N}\tag{1}$$ where I assume$N\ge L$(where$L$is the ... 2 Generally, any matched filtering would be done before equalization, since there is no practical advantage that I am aware of to applying a matched filter afterwards. Most textbooks that I've read present an architecture in which a matched filter is applied first, the signal is sampled at 1 sample/symbol, then an equalizer is applied at 1 sample/symbol. But ... 2 What's labeled$(1)$in your question is a special case, the flat channel. It can be represented as a single coefficient. In general, channels aren't flat, and we then need to apply$(2)$instead. That's no different from acoustics. So, your claim that$(1)$generally applies to SISO channels is plain wrong. However, when naming something "SISO", one ... 2 Yes indeed it will be (although we could argue that it may not be necessarily for all distances since the phase is cyclical!). In free space the signal propagates at the speed of light, therefore this sets the wavelength in distance based on the frequency transmitted according to: $$\lambda = c/f$$ Where$c$is the speed of light in meters/second (or ... 1 The channel impulse response represent the weighted gains and phases at different delays, so yes this is a multipath channel. You can simulate the channel (in Matlab as you requested, what I show below was done in Octave with compatible results) by first creating the complex channel weights: channel = [c1, c2, c3, c4, c5, c6, c7]; where$c1 = -.005 - j0....

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I assume by "shift" you mean "shift in time". No, the first correlation peak should not be shifted in time, you should just get multiple peaks, assuming the time difference of arrival is not much shorter than the chirp length. If it is shorter then you will get "blurring" of the cross-correlation peak. Having said that, there are a couple of other ...

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One approach is to upsample the signal, then delay it, then downsample (or, if feasible, you can do the rest of the processing at the higher sampling rate). This general approach to modeling multipath is correct. However, you need to make sure that your model is realistic and/or useful for your purpose. A few things to consider: If you add delayed/...

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Let's say we have a function that we transmit which is: $$x(t)$$ Transmitting the function is kinda easy part. We assume there is just the function we are trying to send. However things are a little bit ugly in the air. Let's look at the receiver part. What we generally consider first is the AWGN. Which is: $$r(t) = y(t) + n(t)$$ $r(t)$ is our received ...

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I don't fully understand your question, since you correctly state $\tau_i$ are delays of the multipath therefore, $\tau_1$ is simply the delay incurred by the shortest path. And no, $\tau_{i\ge2}$ are not relative delays; look at the formula: you just add up different independent paths with different delays; every path has its own delay, which is ...

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Never done this but it might work. Record the audio simultaneously using multiple microphones located in the neighborhood of your main recording position. If the cross-correlations between signals from different pairs of microphones show peaks at different time lags than the autocorrelation, then there must be either multiple sources or multiple paths. Be ...

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LTE uses OFDM. OFDM with a long enough cyclic prefix turns multipath distortion into a large number of flat fading channels at slightly different frequencies. An OFDM system can either dynamically re-assign channels that have faded below some allowed S/N, or use some sort of redundancy (an ECC or error correcting code) across channels.

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Definition of Excess delay : Relative delay of $i^{th}$ path with respect to the first received component. This excess delay is defined for each multipath. So, the plot you have posted might be giving a picture of how the received power is changing as excess delay is increasing. It can be interpreted as follows: Sort all the multipaths based on Excess ...

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In the multi-path scenario we have occurrence energy from (typically) all directions, and a channel could be a Rayleigh fading channel; no LOS component or Rician fading channel; a strong LOS component is present. The figure you referred to contains a dominant component with a delay spread of 130 ns and with responses from other paths occurring with ...

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Wav files expect values from -1 to +1. You are probably exceeding those limits when you filter the signal through the channel model. After the channel filter add the following: after_channel = after_channel / max(abs(after_channel)); I suspect, though, that you will still have a problem. I believe that wavwrite ignores the imaginary part of complex ...

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I'm not sure Jim's answer is quite correct here: My understanding is that "fixed" refers to a situation where the transfer function is time-invariant, i.e. transmitter and receiver are stationary and the environment doesn't change. An example for that would be a radio station and a home radio receiver. The opposite of fixed would be variable, such as a car ...

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Your "h" is a valid multipath channel impulse response. It is a special case, though, in that it represents a multipath delay that is an exact multiple of your sample period. Usually the delay will not be an exact multiple of the sample period. I am not an expert on multipath channels, so hopefully someone else can chime in, but I think that the easiest ...

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A strong LOS component, i.e. a high Rician factor, will always improve receiver performance. If $K$ denotes the Rician factor, i.e. the ratio between the power of the LOS component and the power of the other (scattered) components, then for $K\rightarrow\infty$ you have no multipath propagation at all and you get a simple AWGN channel. For $K=0$ you have a ...

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