11
ISI, or intersymbol interference, means different things in the context of PSK and OFDM signals. In PSK signals the symbols almost always have tails that extend, in the time-domain, into the times of other symbols. This is what they mean by "intersymbol interference".
Unfortunately they have to do this to reduce the bandwidth of the signal. They ...
8
Regarding you're general question about how symbol sychronization is done in OFDM systems:
One of the most popular and frequently used techniques is the transmission of one or several pilot symbols that are known in the receiver. A pilot symbol is a complete OFDM symbol where the value of each subcarrier is predefined and known in transmitter and receiver. ...
8
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).
Let me try to explain this a bit more general, without going into coherence bandwidth and flat fading. To my understanding, explaining it with $B_c$ and flat ...
7
Interleaving is not specific to OFDM. It is an age old technique used for improving error correcting codes.
Basically, most error correction coding techniques are good at suppressing bit-wise errors which are independent and random. However, when channels are not memoryless, there could be burst errors. i.e. several bit errors are likely to see in close by ...
7
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 inquality is what you have said, to avoid ISI between OFDM symbols and to convert linear convolution to circular convolution so that we can use single-tap ...
7
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 by correlation operation is used (cell search for example).
Allow including identity in sequence by changing the value of sequence initialization. For example, ...
7
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 discrete-time OFDM symbol s[n], and increase the
sampling rate (defined by the time interval between successive samples
of s[n]), then the OFDM symbol ...
6
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.
...
6
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 ...
6
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.
$$y[n] = \sum_{l=0}^{L-1} x[n-l] h_l + w[n]$$
where $L$ is the number of channel taps. $L$ depends on the relation between the bandwidth of basis waveform and the ...
6
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 both FDD and TDD are defined.
Historically, people want to utilize efficiently the precious spectrum. FDD needs two bands while TDD needs only one.
...
5
How is a pilot tone found?
The location of pilot tones in terms of sub-carriers is defined by the signal protocol. For instance, in the case of 802.11a the pilot sub-carriers are -21, -7, 7, and 21.
What makes it different than the regular data on a sub-carrier?
It is different in that the receiver knows exactly what the pilot tone contains. There is no ...
5
Synchronization is an important task in practical communication systems but it is not directly related to the theory of OFDM.
Frame Synchronization
Practical communication systems (such as IEEE 802.11 or 802.3) exchange so-called frames, which consist of several fields, which in turn accomplish different, specific tasks.
Typically, the first field of a ...
5
To answer your first question, what they mean is that the first training symbol only encodes data on the even-numbered subcarriers. The other subcarriers are set to zero. That is, the frequency-domain,
$$
X[k] =
\begin{cases}
s_k, &k \text{ mod } 2 = 0 \\
0, &\text{otherwise}
\end{cases}
$$
The symbols to encode on the even-numbered subcarriers $...
5
Either of your suggested approaches would work (adapting modulation/coding scheme on a per-subcarrier basis or changing all subcarriers at once). There's no theoretical constraint that prevents you from doing that; it's simply a question of whether the added efficiency of tuning individual subcarriers is worth the increased system complexity.
5
In a pure AWGN channel there is no benefit from OFDM because the noise will affect the received signal in the same way regardless of whether sent as a higher bandwidth serial stream or lower rate parallel streams. Similarly, there isn't much benefit in a flat fading environment either because, by definition, each constituent stream of the OFDM signal will be ...
5
The basic concept of OFDM is to divide a high-bitrate datastream into $N$ low-bitrate datastreams and to multiplex these low-bitrate datastreams in frequency. That is, every datastream is assigned to a distinct frequency band (so-called subcarrier) that does not interfere with the other frequency bands. Orthogonality allows the frequency bands to be packed ...
5
The DC subcarrier is normally omitted because in a zero-IF receiver it overlaps with DC offsets in the hardware which are very difficult to remove.
5
There are two major approaches for cyclic extension in OFDM systems - CP (cyclic prefix) and ZP (zero padding, also called Trailing Zeros, TZ). Generally they show the same performance, I mean in AWGN or Fading channel. CP method is the simplest one so it is preferred in the most cases. ZP approach leads to slightly less transmission power level for obvious ...
5
If you'd like to think analog, an OFDM signal can be written as a sum of weighted complex sinusoidals:
$$
x(t)=\sum_{k=0}^{N-1}X_k \exp{\left( \mathrm j 2\pi\frac{kf_\mathrm{s}}{N}t \tag{1}\right)},
$$
where $N$ is the number of subcarriers, $f_\mathrm{s}$ is the sampling frequency and $X_k$ denotes the subcarrier values. For a digital implementation, (1) is ...
5
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 symbol and create the signal
$$x(t) = \sum_{k=0}^{N-1} s_k \exp(j2\pi f_kt).$$
Contrast this with the definition of the inverse discrete Fourier transform:
$$x[n] =...
5
In general, it means several waveforms will coexist in 5G ecosystem.
In the context of LTE-based 5G (up to now), several subcarrier spacings (hence CP) coexist. The first and foremost motivation for this is to support not only mobile broadband but also other use-cases such as mMTC and URLLC.
Some of benefits of mixed numerology are flexible scheduling and ...
5
Generally the relationship between the sampling frequency $f_s$ and the frequency spacing of each bin $\Delta f$ is given by:
$$\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 ...
4
If I understand the question properly, then it sounds like the difference between time-domain multiplication and frequency domain multiplication.
Windowing is a time-domain multiplication operation. As such, it is equivalent to convolving the spectrum with the window kernel, which will operate all frequencies the same way. On the other hand, filtering is (...
4
I understand your confusion because the equation is barely understandable from the information given in the book. It becomes more clear from the original paper by Classen and Meyr [1] from which it has been taken. They propose a two stage frequency offset estimation that consists of an acquistion stage and a tracking stage. The equation you've cited ...
4
The Hermitian symmetry is used to obtain a real-valued time-domain signal. It is a special case of OFDM called discrete multitone (DMT). It exploits a property of the discrete Fourier transform (DFT), namely that the DFT of a real-valued signal has Hermitian symmetry. The motivation is usually the channel: if the signal shall be transmitted over a low-pass ...
4
Definitely yes. But after IFFT operation data block is CP extended before transmission.
Each sample of OFDM symbol from the output of IFFT is weighted sum of all QAM/PSK modulated subcarriers from the input of IFFT.
In the MIMO case all spatial-time algorithms are applied in the frequency domain. So in transmitter you should do encoding with QAM subcarriers ...
4
Yes. Cyclic Prefix and windows(prefix and postfix for pulse shaping) are added to the OFDM symbol, but windows are only for overlap-and-add for pulse shaping, so the effective length is M+CP_length only. I've mentioned Windowing since it is an important thing to take into consideration if you want to design and test an OFDM transmitter.
Each OFDM sample is ...
4
You need as many samples as you have subcarriers. If you have 64 carriers, then you need 64 samples.
4
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 is Zero padded instead of cyclic prefix, ISI due to adjacent symbol still gets eliminated, but it cannot be modeled using circular convolution. Circular ...
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