Struct Ofdm

Source

pub struct Ofdm {
    pub n_fft: usize,
    pub n_active: usize,
    pub oversampling: usize,
    pub n_cp: usize,
    pub dc_null: bool,
    pub dft_spread: bool,
    pub sample_rate: Hertz,
}

Expand description

An OFDM (or DFT-spread OFDM) modulator and demodulator.

Fields§

§n_fft: usize

Size $N$ of the subcarrier grid.

§n_active: usize

Number $K$ of active (modulated) subcarriers, centred on the carrier.

§oversampling: usize

Oversampling factor $L$ (IFFT of size $L N$).

§n_cp: usize

Cyclic prefix, in Nyquist-rate samples ($L N_{\mathrm{cp}}$ samples).

§dc_null: bool

Leave the DC subcarrier empty (the active subcarriers skip $k = 0$).

§dft_spread: bool

DFT spreading of the data (localised SC-FDMA).

§sample_rate: Hertz

The rate of the modulated samples, $L N \Delta f$ ($\Delta f$ the subcarrier spacing): the rate of the Signal of Modulate, and the rate Demodulate expects; 1 Hz by default (time in samples).

Implementations§

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impl Ofdm

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pub fn new(n_fft: usize, n_active: usize) -> Result<Ofdm>

$K$ active subcarriers out of $N$, oversampling 4, no prefix, at the sample rate 1 Hz.

§Errors

comnum_core::Error::Config unless $1 \le K \le N$.

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pub fn check(&self) -> Result<()>

Validate the configuration.

§Errors

comnum_core::Error::Config for an empty or overfull grid, a zero oversampling or a sample rate that is not positive and finite.

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pub fn fft_len(&self) -> usize

Size of the IFFT, $L N$.

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pub fn block_len(&self) -> usize

Samples per block, prefix included, $L (N + N_{\mathrm{cp}})$.

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pub fn subcarrier(&self, i: usize) -> isize

Subcarrier index $k$ of the active subcarrier i.

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pub fn bin(&self, i: usize) -> usize

FFT bin of the active subcarrier i (fft::centred_bin, one bin further from the subcarrier 0 on with dc_null).

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pub fn pulse(&self, i: usize, n: usize) -> (usize, Vec<C64>)

The transmit pulse of the active subcarrier i of symbol n, prefix included, on its support: (first sample, values), $\frac{1}{\sqrt{LN}} e^{j 2\pi k (t - L N_{\mathrm{cp}})/(LN)}$ for $t = 0, \dots, L(N + N_{\mathrm{cp}}) - 1$ (energy $(N + N_{\mathrm{cp}})/N$); a column of the matrix $\mathbf{G}$ of Nissel, Schwarz & Rupp 2017, eq. (20).

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pub fn window(&self, i: usize, n: usize) -> (usize, Vec<C64>)

The receive pulse (the window of the demodulator) of the active subcarrier i of symbol n: the Ofdm::pulse without its prefix, of unit energy, on its support (first sample, values).

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pub fn is_active_bin(&self, bin: usize) -> bool

Whether an FFT bin carries an active subcarrier.

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pub fn spread(&self, data: &[C64]) -> Vec<C64> ⓘ

The values of the active subcarriers of data (the identity, or the unitary DFT of size $K$ with dft_spread).

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pub fn despread(&self, active: &[C64]) -> Vec<C64> ⓘ

The inverse of Ofdm::spread.

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pub fn to_time(&self, active: &[C64]) -> Result<Vec<C64>>

The time block (without prefix, $L N$ samples) of the values of the active subcarriers.

§Errors

comnum_core::Error::Shape if active does not have $K$ values.

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pub fn to_active(&self, block: &[C64]) -> Result<Vec<C64>>

The values of the active subcarriers of a time block (without prefix).

§Errors

comnum_core::Error::Shape if block does not have $L N$ samples.

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pub fn filter(&self, block: &[C64]) -> Result<Vec<C64>>

Keep only the active subcarriers of a time block (an ideal band-pass filter).

§Errors

As Ofdm::to_active.

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pub fn with_prefix(&self, block: &[C64]) -> Result<Vec<C64>>

Prepend the cyclic prefix to a time block.

§Errors

comnum_core::Error::Shape if the prefix is longer than the block.

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pub fn windowed(&self, samples: &[C64], ramp: usize) -> Result<Vec<C64>>

The raised-cosine window of whole blocks of Ofdm::block_len samples (prefix included): the first ramp samples of every prefix rise as

$$ w[n] = \frac{1}{2}\left(1 - \cos\frac{\pi (n + 1/2)}{R}\right), \qquad n = 0 \dots R - 1, $$

a cyclic postfix of $R$ samples of the block falls as $1 - w$ and overlaps the ramp of the next block (the postfix of the last block wraps onto the first: the stream stays periodic), so the output has the length of the input and the FFT part of every block is untouched. The pulse of a block then lasts $L(N + N_{\mathrm{cp}}) + R$ samples with $(1 - \cos)$ edges: the raised-cosine impulse shape of windowed OFDM (Saul, Proc. IEEE VTC2004-Fall, 2004, eq. (1): a guard interval and a roll-off of 11.1 %), whose out-of-band sidelobes fall as $f^{-3}$ instead of the $f^{-1}$ of the rectangular pulse. ramp = 0 returns the samples unchanged.

§Errors

comnum_core::Error::Config if ramp exceeds the prefix $L N_{\mathrm{cp}}$, comnum_core::Error::Shape for a partial block.

§Examples

use comnum_waveform::ofdm::Ofdm;
use comnum_math::C64;
let ofdm = Ofdm { n_cp: 4, oversampling: 1, ..Ofdm::new(16, 16).unwrap() };
let data: Vec<C64> = (0..32).map(|k| C64::new(if k % 3 == 0 { 1.0 } else { -1.0 }, 0.0)).collect();
let x = ofdm.modulate(&data).unwrap();
let y = ofdm.windowed(&x, 4).unwrap();
assert_eq!(y.len(), x.len());
// the FFT part of every block is untouched
assert!(y[4..20].iter().zip(&x[4..20]).all(|(a, b)| (a - b).norm() < 1e-12));