Editing Orthogonal frequency-division multiplexing (section)

== Idealized system model ==
This section describes a simple idealized OFDM system model suitable for a time-invariant [[AWGN]] channel.

=== Transmitter ===
[[File:OFDM transmitter ideal.png|center|754px]]

An OFDM carrier signal is the sum of a number of orthogonal subcarriers, with [[baseband]] data on each subcarrier being independently modulated commonly using some type of [[quadrature amplitude modulation]] (QAM) or [[phase-shift keying]] (PSK). This composite baseband signal is typically used to modulate a main [[radio frequency|RF]] carrier.

<math>s[n]</math> is a serial stream of binary digits. By [[inverse multiplexing]], these are first demultiplexed into <math>N</math> parallel streams, and each one mapped to a (possibly complex) symbol stream using some modulation constellation ([[QAM]], [[phase-shift keying|PSK]], etc.). Note that the constellations may be different, so some streams may carry a higher bit-rate than others.

An inverse [[fast Fourier transform|FFT]] is computed on each set of symbols, giving a set of complex time-domain samples. These samples are then [[Quadrature phase|quadrature]]-mixed to passband in the standard way. The real and imaginary components are first converted to the analogue domain using [[digital-to-analogue converter]]s (DACs); the analogue signals are then used to modulate [[cosine]] and [[sine]] waves at the [[carrier signal|carrier]] frequency, <math>f_\text{c}</math>, respectively. These signals are then summed to give the transmission signal, <math>s(t)</math>.

=== Receiver ===
[[File:OFDM receiver ideal.png|center|800px]]

The receiver picks up the signal <math>r(t)</math>, which is then quadrature-mixed down to baseband using cosine and sine waves at the [[carrier frequency]]. This also creates signals centered on <math>2 f_\text{c}</math>, so low-pass filters are used to reject these. The baseband signals are then sampled and digitised using [[analog-to-digital converter]]s (ADCs), and a forward [[fast Fourier transform|FFT]] is used to convert back to the frequency domain.

This returns <math>N</math> parallel streams, each of which is converted to a binary stream using an appropriate symbol [[detector (radio)|detector]]. These streams are then re-combined into a serial stream, <math>\hat{s}[n]</math>, which is an estimate of the original binary stream at the transmitter.