10
votes
Accepted
Flat fading criterion of OFDM subcarrier spacing
Your mathematical derivation is correct, your $H[k]$ is the single-tap equalizer (i.e. one tap for each subcarrier, and the subcarriers do not mix with each other. That's the orthogonal in OFDM).
...
- 6,208
8
votes
Coherence bandwidth/delay spread in OFDM
Indeed, the constraint $T_s(N+N_{cp}) \gg T_m$ should be derived as $T_s(N+N_{cp}) \gg T_s N_{cp} \geq T_m$.
The first inequality to make sure that the CP overhead is as small as possible. The second ...
- 6,080
8
votes
Practicality of the assumption of i.i.d. for Rayleigh channels
I am a little late but I post my answer anyway so that someone having the same question will find it interesting and discuss.
The discrete baseband multipath channel can be modeled as a FIR, i.e.
$$...
- 6,080
7
votes
OFDM intra-block multipath interference
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, ...
- 6,080
7
votes
What's the reasoning behind changing pilot tones in OFDM?
Advantage of pilot pseudo-random sequences in standards (with examples are taken from LTE) :
Interference from other sources with different identities (UE ID, Cell ID, ...) are mitigated if detection ...
- 6,080
7
votes
Accepted
How the increasing of sampling frequency in OFDM didn't cause increase on the required channel bandwidth
You can say the null subcarriers have their own bandwidth if you define an alphabet including "zeros" and use null carriers to transmit these "zeros". As the comment of MBaz,
If we start with the ...
- 6,080
6
votes
Effect of cyclic prefix and zero-padding in OFDM
The main idea of using Cyclic prefix in OFDM systems is because of 2 reasons,
1) To eliminate ISI from previous symbol.
2) To model linear convolution as circular convolution
If an OFDM symbol ...
- 555
6
votes
Why is LTE either FDD or TDD?
You are mixing two things modulation and multiple access. SC-FDMA has been chosen because it is battery-friendly modulation. SC-FDMA is used in both FDD and TDD modes.
There are several reasons why ...
- 6,080
6
votes
Sending complex signal over a single wire
Note that signals sent over wires (and over the air, and over any medium) are always real. What quadrature means is that, on a passband channel (wired or otherwise), you can transmit two signals at ...
- 14.9k
6
votes
OFDM use a pulse shaping filter or not?
The purpose of pulse shaping filters is not to overcome ISI as is implied in the OP's question. The only reason for using a pulse shaping filter is spectral efficiency, and in the process ISI can be ...
- 48.9k
5
votes
IFFT-based OFDM system
Say you want to transmit complex symbols $s_0,s_2,\ldots,s_{N-1}$ using frequency-division multiplexing. In the "bank of modulators" approach, you would assign a carrier frequency $f_k$ to each ...
- 14.9k
5
votes
Number of samples in one period of subcarrier after IFFT
If you'd like to think analog, an OFDM signal can be written as a sum of weighted complex sinusoidals:
$$
x(t)=\sum_{k=0}^{N-1}X_k \exp{\left( \mathrm j 2\pi\frac{kf_\mathrm{s}}{N}t \tag{1}\right)},
$$...
- 4,235
5
votes
Subcarrier spacing in OFDM
There are many intepretation of OFDM to answer your question. One way I find intuitive is looking at the resolution of (Discrete) Fourier Transform.
By capturing a signal during time $T$, and by ...
- 6,080
5
votes
What is the mixed numerology in OFDM
In general, it means several waveforms will coexist in 5G ecosystem.
In the context of LTE-based 5G (up to now), several subcarrier spacings (hence CP) coexist. The first and foremost motivation for ...
- 6,080
5
votes
Accepted
What is the difference between (Sample Timing Offset), (Carrier Frequency offset), and (Sampling Frequency Offset)?
I would have the easiest time explaining these briefly with the aid of an eye diagram as depicted in the graphic below.
In this example we see the constellation pattern of a raised cosine QPSK ...
- 48.9k
5
votes
Accepted
Frequency domain samples to time domain without knowing the sampling rate?
Generally the relationship between the sampling frequency $f_s$ and the frequency spacing of each bin $\Delta f$ is given by:
$$\Delta f= f_s/N$$
For example if you have 1000 bins and the sampling ...
- 48.9k
5
votes
Accepted
OFDM time vs. frequency domain channel estimation/equalization
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, ...
- 2,213
5
votes
Accepted
how to design the $\text{sinc}(\cdot)$ filter for OFDM oversampled system
Resampling the transmit OFDM waveform in the frequency domain by zero-padding the FFT prior to taking the IFFT has the advantage of simplicity and maintaining sub-carrier orthogonality (no inter-...
- 48.9k
4
votes
Number of samples in one period of subcarrier after IFFT
You need as many samples as you have subcarriers. If you have 64 carriers, then you need 64 samples.
- 12k
4
votes
Multipath resistance of spread spectrum systems
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, ...
- 25.2k
4
votes
Accepted
The necessity of null subcarrier in OFDM?
The only portion of the spectrum that is "occupied" or "transmitted" are the subcarriers that are actually used (i.e. 10 MHz instead of 15 MHz). The null subcarriers referenced in your question are ...
- 24.5k
4
votes
Difference between Fine and Coarse Frequency Offset in OFDM
If in doubt, read the original Schmidl&Cox Paper Robust Frequency and Timing
Synchronization for OFDM. It's actually a good read, and a good paper with respect to demonstration of state of the art,...
- 29.6k
4
votes
Accepted
Why Convolution between Signal and a Channel Is Not Done Directly in SIMO Channel
I've said, in another comment, convolution using the function conv "i.e in MATLAB" and convolution using the Toeplitx matrix must give the same results. That's ok.
Now, according to your code, the ...
- 1,056
4
votes
Accepted
What is the forward error correction in 802.11a?
From the official standard, IEEE Std 802.11a-1999, Part 11, section 17.3.5.5 Convolutional encoder, see the rate 1/2 code:
The resulting two streams A and B are interleaved bit-alternatingly.
The ...
- 29.6k
4
votes
Accepted
Spectral efficiency of with OFDM vs without OFDM?
The spectral efficiency of OFDM is strictly worse than that of a pulse-shaped QAM signal with the same rate.
OFDM requires a guard interval, on which no useful information is transmitted.
It is ...
- 14.9k
4
votes
Accepted
Can an OFDM waveform be spread (DSSS)?
You can do a lot of things.
Some are sensible!
Remember why you're using OFDM (frequency-domain equalization) and remember that the temporal structure of the OFDM symbol (as the IDFT of the data ...
- 29.6k
4
votes
Accepted
Frequency-domain vs Time-domain OFDM oversampling
Your first method is just not using the subcarriers at the band edges (the ones that you zero-pad). It is hence equivalent to a sinc-interpolation in the time domain. Finally, a cyclic prefix (or ZP, ...
- 29.6k
3
votes
Accepted
OFDM demodulation, how to set the sampling rate?
Your receiver will consist of, apart from synchronization blocks, an FFT. You want that FFT to generate one output bin for each of the subcarriers. Therefore, you should make use of the relationship ...
- 24.5k
3
votes
Accepted
Transmit power of non-orthogonal FDM
In your example, the sinusoids are still orthogonal to one another; the key is that you must integrate over the correct period when calculating $P$. All of the sinusoids have frequencies that are ...
- 24.5k
3
votes
Accepted
OFDM symbol acquisition block in GNU Radio gives rotating constellation even if there is no carrier offset. How is this possible?
Got me at that one! The "OFDM symbol acquisition" block is in fact not from gr-digital (where your other OFDM blocks come frome), but from gr-dtv, where it is used ...
- 29.6k
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