Chains

class OFDMTransmitter(N_carrier_data: int, N_cp: int, *, carrier_type: ndarray | CarrierAllocation | None = None, pilots: ndarray | None = None, name: str = 'ofdm_transmitter')

OFDM transmitter chain: allocation, IFFT, cyclic prefix, serialization.

Signal Model

The serial data symbols are split into blocks, allocated to the data subcarriers (pilot and null subcarriers are filled according to the allocation mask), and each allocated block \(X_t[k]\) of length \(N\) is brought to the time domain with the orthonormal IDFT:

\[x_t[n] = \frac{1}{\sqrt{N}} \sum_{k=0}^{N-1} X_t[k] \, e^{i 2 \pi k n / N}, \qquad n = 0, \dots, N-1\]

A cyclic prefix of length \(N_{cp}\) (the last \(N_{cp}\) samples of the block) is prepended to each block, and the extended blocks are serialized into the time-domain signal \(y[m]\).

Axes: declared axis – consumes the serial axis -1 (length \(T \, N_{data}\)), produces a serial time-domain signal of length \(T (N + N_{cp})\) on axis -1.

param N_carrier_data:

Number of data subcarriers \(N_{data}\) per OFDM symbol.

type N_carrier_data:

int

param N_cp:

Length \(N_{cp}\) of the cyclic prefix.

type N_cp:

int

param carrier_type:

Subcarrier allocation mask (e.g. data, pilot, null), passed to CarrierAllocator. Default is an all-data mask of length N_carrier_data.

type carrier_type:

CarrierAllocation or np.ndarray, optional, keyword-only

param pilots:

Pilot values, one per pilot subcarrier of the allocation mask.

type pilots:

np.ndarray or list, optional, keyword-only

param name:

Name of the processor instance. Default is "ofdm_transmitter".

type name:

str, optional, keyword-only

References

R. van Nee, R. Prasad, OFDM for Wireless Multimedia Communications, Artech House, 2000, Chapter 2.

Examples

>>> transmitter = OFDMTransmitter(4, 2)
>>> x = np.arange(8) + 0j  # 2 OFDM symbols of 4 data subcarriers
>>> y = transmitter(x)
>>> print(y.shape)  # 2 blocks of length 4 + 2
(12,)

class OFDMReceiver(N_carrier_data: int, N_cp: int, *, h: ndarray = <factory>, carrier_type: ndarray | CarrierAllocation | None = None, name: str = 'ofdm_receiver')

OFDM receiver chain: prefix removal, FFT, equalization, extraction.

Signal Model

The serial received signal is split into blocks of length \(N + N_{cp}\), the cyclic prefix is discarded, and each block \(r_t[n]\) is brought to the frequency domain with the orthonormal DFT before one-tap zero-forcing equalization:

\[R_t[k] = \frac{1}{\sqrt{N}} \sum_{n=0}^{N-1} r_t[n] \, e^{-i 2 \pi k n / N}, \qquad Y_t[k] = \frac{R_t[k]}{H[k]}\]

where \(H[k]\) is the \(N\)-point DFT of the channel impulse response \(h[l]\). The data subcarriers are then extracted according to the allocation mask and serialized.

Axes: declared axis – consumes the serial axis -1 (length \(T (N + N_{cp})\)), produces the serial data symbols of length \(T \, N_{data}\) on axis -1.

param N_carrier_data:

Number of data subcarriers \(N_{data}\) per OFDM symbol.

type N_carrier_data:

int

param N_cp:

Length \(N_{cp}\) of the cyclic prefix.

type N_cp:

int

param h:

Channel impulse response \(h[l]\) used by the frequency domain equalizer. Default is the ideal channel [1.0].

type h:

np.ndarray or list, keyword-only

param carrier_type:

Subcarrier allocation mask (e.g. data, pilot, null), passed to CarrierExtractor. Default is an all-data mask of length N_carrier_data.

type carrier_type:

CarrierAllocation or np.ndarray, optional, keyword-only

param name:

Name of the processor instance. Default is "ofdm_receiver".

type name:

str, optional, keyword-only

References

R. van Nee, R. Prasad, OFDM for Wireless Multimedia Communications, Artech House, 2000, Chapter 2.

Examples

>>> x = np.arange(8) + 0j
>>> y = OFDMTransmitter(4, 2)(x)
>>> x_est = OFDMReceiver(4, 2)(y)
>>> print(np.round(x_est.real, 6) + 0.0)
[0. 1. 2. 3. 4. 5. 6. 7.]