# Tag Info

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Generally the relationship between the sampling frequency $f_s$ and the frequency spacing of each bin $\Delta f$ is given by: $$\Delta f= f_s/N$$ For example if you have 1000 bins and the sampling rate is $f_s = 1$ KHz, then each bin is spaced by 1 Hz given by $f_s/N$. So if the frequencies $f_1, f_2, ..., f_N$ (using the OP's indexing) were associated ...

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I checked your code in my PC, you need just to delete the delay added before the filter. For example, you can use: U_aft_fil = U_aft_fil(fil_delay+1:end); Then when filtering it again at the receiving side, you delete it again : U_r_fil = U_r_fil(fil_delay+1:end); Good luck

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Not necessary. In DRM (Digital Radio Mondaile) specification, for some channels number of careers are not the power of 2. Power of 2 makes the implementation of FFT and IFFT simpler.

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Implementing an IFFT and FFT engine which is a power of $2$ is easier in hardware and hence if an OFDM system is talked about, it is talked about in $2^k$ length FFT. All practical Communication system based on OFDM use $2^k$ length FFT-IFFT engines. However, for OFDM in principle, it is not required to have FFT-IFFT in power of $2$. There are different ...

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Sorry for late reply .. I was little bit busy. you have mistakes in your code. Although mythology is right, you have mistakes in some parameters. Check this paper "Low-Complexity Equalization of Orthogonal Signal-Division Multiplexing in Double-Selective Channels" Then, Modify your code following part II in that paper. It's with details there, if you ...

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Traditionally, OFDM became popular in WiFi and LTE because the channel model consisted of multi-path. That is, the radio signal transmitted in 1-6GHz frequencies bounced from various obstacles (walls, trees, cars, humans) at the receiver. Of course this is time varying because obstacle position or transmitter/receiver position also changes. But to simplify ...

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As specified in documentation, using 'ParityCheckMatrix' you can configure the Parity Check Matrix (PCM) during the constructions of the encoder/decoder objects. The syntax is encoder = comm.LDPCEncoder('ParityCheckMatrix',pcm) or simply encoder = comm.LDPCEncoder(pcm); where pcm is the desired PCM which must be sparse type. An example for (probably poor ...

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The channel which you have created is having 4-Taps and all taps are one after the other, meaning roughly there are 4 multi-paths and they are very close to each other. How close depends on what is the Sub-Carrier Spacing you would have assumed. Anyway, the point is only 3 samples of Cyclic Prefix would be enough and even with 0 or 2 samples of CP will not ...

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You can simply send the message multiple ($N$) times and if all N messages were received at the same SNR you would coherently average the messages for a processing gain in SNR equal to $10\log_{10}(N)$ in dB. This is effectively trading bandwidth for SNR as you are using more resources to send the same message. To coherently add you remove the complex ...

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Below is a short code to do this for 1024 samples. "phi" array below is the required phase for each samples N=1024; %number of samples phi=zeros(1,N); phi(1,1) = pi/4;. %initial phase, could be set to zero if the phase is set to zero by the front end processing Phase_snr=10; %snr in phase estimation,equivalent to 1db for n=1:N-1 phi(1,n+1)=phi(1,n) + (1/...

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For a given OFDM symbol, no subcarrier can be assigned to two users simultaneously. Each subcarrier is uniquely assigned to a unique user. Else you have to implement an Interference cancellation at receiver (which would require having channel knowledge of other users as well, meaning global CSI) or at the transmitter and extremely complex interference ...

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w = conv(u,v) returns the convolution of vectors u and v. If u and v are vectors of polynomial coefficients, convolving them is equivalent to multiplying the two polynomials. (from MATLAB documentation) Both expressions are correct. In 2., whenever an addend of a convolution operation calls randn in a convolution computation procedure, the callee returns ...

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According to my reading, LDPC is almost the best channel coding we can use for channel coding, but I have a question regarding that kind of coding. Mentally, something being "the best" should always instantly raise a mental flag for you, saying "under which conditions, according to which measure". It is right that iterative LDPC decoders ...

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I am not a specialist of the 4G LTE, but worked on other OFDM waveform similar to it. OFDM signal is made of symbols. Each symbol in frequency domain is made of a number of subcarriers. Some of subcarriers are mapped with data and other with pilots. Pilots have known defined values (usually scrambled BPSK symbols). The sampling frequency offset results in ...

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Because when a quantity can be complex, and even when it is just real, the absolute squared difference $|f-g|^2$ can be expressed in both domain (complex and real) as: $$|f-g|^2 = (f-g)^H(f-g)$$ and of course this is correct as well for reals. This setting is often related to Hilbert spaces.

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Hint: you could convert zero padded ofdm into cyclic ofdm at the receiver, and use the same equalization. Though there will be more noise on this scheme. I had asked a puzzle some time back on this topic: Modelling zero padded OFDM as circular convolution between channel and FFT frame

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In simulation, we do upsample to simulate the "analog" signal which is a continuous signal in reality but we represent it as a high-time-resolution in our digital/discrete simulation. When we upsample our data before going through the channel, we should also upsample the "impulse response" (IR) of the channel. It means that the timing-...

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µ-law is defined for real-valued PCM signals only. You will either need to produce a real-valued signal containing OFDM as passband signal, either by mixing it to a carrier frequency, or by modifying your OFDM system to only produce symmetrical spectrum baseband, or by u-law coding I and Q separately (but that makes little sense, since a high PAPR happens ...

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However, when I add an AWGN channel, I get pretty low BER of 10^-5 in passband as compared to around 10^-4 BER in baseband under same AWGN channel of SNR 10 dB. Why is it happening? You've got a bug in either passband channel or baseband channel model, or in how you transform your noise or your signal – end of story! I thought that there would be more ...

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For a SISO channel, assuming you have estimated channel coefficients for each sub-carrier $k$, the MMSE equalizer is $$\hat{h}_k=\frac{h_k^*}{|h_k|^2 + \frac{\sigma_x^2}{N_0}}$$ So you can see already there is a multiplication in the numerator ($h_k^*$), and then there is a division by a term in the denominator. So for all $N$ subcarrier, this itself will ...

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OFDM subcarriers are packed relatively tightly together. If you look at the original OFDM signal in the frequency domain, you may wonder why adjacent subcarriers are not interfering with each other. The answer is that subcarriers are orthogonal to each other. Even adjacent subcarriers, have 0 influence on each other, and are independent in that sense. It ...

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It is most convenient for implementation of the IFFT and FFT, that the number of subcarriers is a power of 2. However, it is not necessary. Even in practical systems, it may not be a power of 2. In LTE, for example, there are 6 allowed bandwidths, ranging from 1.4 MHz to 20 MHz. For the 15 MHz deployment bandwidth, the number of subcarriers is 1536. See ...

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First value is from cyclic prefix and last value is the last sub-carrier which you are messing up by windowing of 1 sample. As a result of this, the frequency orthogonality of the sub-carriers is lost. And this inter-carrier interference is causing your QAM sliced symbols to randomly change phase and amplitude around true value. The way actually windowing ...

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CP based Symbol Boundary detection algorithm which is fundamentally based on correlation will still work. You just need to do a timing recovery before FFT operation. A small offset in sampling times will cause a small phase rotation in pilots and these small rotations are used to compute the timing offset. Once you have a good timing offset estimate, you ...

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It is possible if the system supports MU-MIMO.

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In both cases, you need to interpolate the channel between the pilots you've got. Both cases are typically suboptimal, since they'd only work perfectly for (a) actual block-fading (which is a convenient model, but doesn't look like reality) or (b) for a channel that is perfectly interpolatable from just a few points of observation in frequency (but that ...

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To expand on jithin's answer: The whole point of OFDM is, as they say, to avoid equalization in time domain! Equalization in time domain requires you to have the same amount of channel state information, but inherently reverses a convolution, and is hence quadratically complex with channel size (i.e. impulse response length in samples), whereas the OFDM ...

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What you mean might be circulant matrix instead of toeplitz matrix. See section 3.4.4 in https://web.stanford.edu/~dntse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter3.pdf about how the circular convolution in OFDM is represented by matrix operations (eq 3.130 onwards). First, in almost all standard OFDM systems, you can assume $D \le L$. The ...

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Zero padded OFDM (i.e.) adding zeros after IFFT is used to combat Inter symbol interference, suppose that there is multi path in the system that spans over L samples then atleast L zero samples are prefixed at the transmitter after IFFT so that these can be thrown away at the receiver and then recover ISI free IFFT frame / OFDM symbol. The advantage of ...

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