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2

As a hint consider if you are using non-coherent demodulation techniques of which this waveform is designed for, where you multiply each symbol with the previous symbol: observe how you are multiplying two independent identically distributed Gaussian random variables (since the noise in each symbol will be independent to the noise in the adjacent symbols (...


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The sentences you've mentioned in your question all have a quite different meaning. Let me try to explain them one by one: Clearly, it is not true that all $2^n$ sequences of length $n$ have the same probability. This refers to the example of a sequence of binary i.i.d. random variables. If $p(1)\neq p(0)$ then it is clear that sequences with different ...


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There is no requirement that Direct Sequence Spread Spectrum (DSSS) have an integer number of chips per symbol, nor for the repetition rate of the code to be synchronous with the data (although this is often done). So in this case you have a spreading sequence with a code of some particular length that is running at 6.138Mcps that is multiplied by your data ...


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The training sequence should be at the same spacing as the equalizer. Adaptive algorithms converge to the least square solution based on the error between the received sequence and the transmitted sequence (known when a training sequence is used). Further, the equalizer can only determine a solution where channel energy is present (for example, if you ...


2

Consider using a Gardner Timing Error Detector which in the following form is usable for higher order QAM: $$TED = I_n(I_{n+1}-I_{n-1}) + Q_n(Q_{n+1}-Q_{n-1})$$ Where $I_{n-1}$,$Q_{n-1}$, $I_{n}$, $Q_{n}$ and $I_{n+1}$, $Q_{n+1}$ are the early, prompt and late QAM samples at 2 samples per symbol. The TED will drive the prompt sample to zero error at the ...


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Because we have to know the phase of elements in the channel matrix first before we do the EGC,however,the channel should be randomly generated every second,so I wonder that if we can do EGC in the real world or not? Yeah, so you continuously have to estimate the channel. You need to do that anyway, no matter whether you use any combining method or not, ...


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Your channel has 3 taps, your EQ has 9 taps which means that your cascaded response has 11 taps. You only force the middle 9 taps of the response to be a unit impulse. If you convolve the channel with your EQ, you see that the middle is indeed a unit impulse but the first and the last sample are very non-zero. The actual inverse your channel would be an IIR ...


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The answer is to NOT down-select to one sample per symbol until after using the Gardner Timing recovery since the TED requires 2 samples per symbol. If the equalizer is running at 2 samples per symbol, that is perfect for use with the Gardner; why would you down-select to one sample per symbol after the equalizer? You can downselect after timing recovery ...


1

I give an explanation that avoids the pejorative comments of Engineer. First question: can you explain me these two definitions of perfect code? Those are not two definitions of perfect codes but rather a single somewhat poorly-phrased definition of a perfect code. It should read A perfect (binary) $t$-error-correcting code of block length $n$ is a ...


2

The OP stated he was interested in $\pi/4$-DQPSK (not QPSK), so phase synchronization is presumably not an issue for him. As far as the actual implementation is concerned, you'll save yourself some time if you become familiar with the bottom of pages 29 (symbol mapping) and 37 (differential detection) in this student paper. Ignore all the old TI DSP-chip ...


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I don't know how WCDMA does it, but CDMA2000 encodes the data twice or three times (it's been a while): once with a "long code" (42 or 43 bits, so it takes days to cycle through even at chip rates in the MHz), once with a "short code" (16 bits, with zero-stuffing so that the cycle is exactly 65536 chips long, and the spectrum is flat), and IIRC once with a ...


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First question: The perfect code definition is just what you wrote down, it is just a definition. But don't let it fool you, a perfect code is not always a good code. For example, no coding at all is a "perfect code" for $t=0$, and actually the $(7, 4)$ Hamming code is a perfect code but not all that great. A bit pattern is just a pattern of bits. For $n$ ...


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In most cases the codes for CDMA specifically are predetermined and set the "channel" to use. This is no different than FDMA where each frequency within a coverage area is assigned for a particular use (whether it be user or data packet etc; it is how the medium is divided and used among multiple users). GPS is a good simple example of CDMA in practice: ...


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No. Your question neglects the fact that a mixer can't transfer the whole received power to baseband (mixers are typically active, and most of the baseband energy comes from the LO that the device has to generate itself). You can use any nonlinear device, even one without an external power source, but the mixed output's energy will always be way lower than ...


1

Small scale fading results from a superposition of a large number of propagation paths between TX and RX, which can be constructive or desctructive depending on their phase offset. As the phase offset varies rapidly with the propagation distance, the phase offsets between different paths are likely to vary rapidly too, leading to a pseudo-random behaviour of ...


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The OFDM-MIMO channel can be modeled as: $ \mathbf{y} = \mathbf{H} \mathbf{x} + \mathbf{w} $ where $\mathbf{y}$ is $M_RN \times 1$, $\mathbf{H}$ is $NM_R \times (N+N_{CP})M_T$, $\mathbf{x}$ is $M_T(N+N_{CP}) \times 1$, and $\mathbf{w}$ is $M_RN \times 1$. Lets break down each one now: $\mathbf{y}$: the received $N$ symbols for each $M_R$ antenna. $\...


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In 5G NR or 4G LTE, Multiple Input-Multiple Output (MIMO) transmission is a key technology specifically in downlink. Signals transmitted from gNB/eNB via different antennas or signals subjected to different and for the receiver unknown, multiple antenna precoding will experience different radio channels even if the MIMO antennas are located at the same site. ...


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From the diagram in the Algorithms section of the documentation you can see how the different quantities are computed: Note that $z$ in the diagram is an estimate of the output power.$^1$ The error signal $e$ is computed by comparing the reference value $A$ to $\ln(z)$. So if you choose $$A=\ln(P)\tag{1}$$ then the average output power will be adjusted to ...


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Sounds pretty solid to me. It's not necessarily MRC>EGC>SC, you'd need to write $\geq$ technically, since for the special case where all $|h_k|$ are equal you have MRC=EGC and for the special case of a single branch (antenna), they are all equal.


1

If by "oversampling", you mean interpolating more frequency samples between your existing frequency samples, then in this case this would have the effect of zero padding your time domain waveform. Therefore the duration of your signal itself doesn't change, but the duration of time over which the DFT is performed would, with the addition of zero padding to ...


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In case somebody is still interested in this: A mathematical approach can be found in https://ieeexplore.ieee.org/document/890336. It is shown, that CPM Modulations with integer modulation indexes contain tones, which you can observe as spikes in the spectrum


5

Three reasons to increasing the sampling rate further are 1) To relax the requirements of the post D/A conversion filtering for image rejection. 2) Increase signal SNR by spreading quantization noise for a fixed number of DAC bits across a wider frequency range. 3) Minimize passband droop in the D/A reconstruction. Reason 1 is the most dominant one in my ...


3

My first inclination is to say this is a meaningless question. The concept of "instantaneous" frequency really only pertains to a single pure tone with a slightly varying frequency. In this light, one may construct a definition saying "The instantaneous frequency at time $t$ is the same as that of a pure tone which matches the function (sum) in the ...


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From an audio point of view, I would determine if the reciprocal of the least common multiple of a1,a2,a2 were within the range perceivable as pitch to a human; and, if so and stationary for about 6 periods or more, call that reciprocal the instantaneous pitch frequency.


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Eventhough Laurent has given a broader sense of the answer, let me put here the communications theory sense ot it. The concept of instantaneous freqency emerges when you consider Frequency Modulation or Phase Modulation systems, where the message is embedded into the change of the frequency or phase of a carrier signal. This carrier is typically a single ...


2

The notion of instantaneous frequency is (hopefully) consistent with the monochromatic wave model: $$x(t)=a \cos 2\pi \nu t\,,$$ where $a$ is the amplitude and $ \nu$ the frequency. It would be tempting to compute a similar formula for evolving amplitude and frequency cases, something like: $$x(t)=a(t) \cos \left(\phi(t)\right)\,.$$ However, this is not ...


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You are doing transmit beamforming and choosing your vector $\mathbf{f}_A$ so that you beamforming in the "best" direction. So you transmit the signal: $\mathbf{z}=\sqrt{P} \mathbf{f}_A x$, where $\mathbf{z}$ is a length $N_T$ vector. Now you receive the signal: $\mathbf{y} = \sqrt{P}\mathbf{H}\mathbf{f}_A x + \mathbf{n}$, which is a length $N_R$ vector. ...


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