User:Ryan Cooley/COFDM

The account of this former contributor was not re-activated after the server upgrade of March 2022.

COFDM

Coded, Orthogonal, Frequency Division, Multiplexing

Multiplexing refers to combining multiple independent bits of data into one large single datastream. This is necessary for carrying multiple independent signals over a single data channel at the same time.

Frequency Division refers to how the independent signals are segregated. In time division, any signal can use up the entire bandwidth, but only for a fixed amount of time, before it must stop, and allow a different signal to transmit. In frequency division, any signal can take up as much time as it needs, but is restricted to a smaller frequency range to avoid interference with other signals.

With frequency division multiplexing, however, the side-bands of each signal would cause unwanted interference between one another if no special steps are taken. In traditional FDM, this is handled by the use of guard-bands, unused bandwidth between any two signals to avoid possible overlap and interference. This is terribly inefficient use of a communications channel, however, as a significant amount of the potential bandwidth is wasted as guard-bands. An alternative to guard-bands is orthogonality.

Orthogonality is the mathematical property of two signals that can co-exist without interference to one another. In practical terms, that means two waves which are 90 degrees opposed, or delayed relative to one another by a factor of one-half the peak-to-peak period. This ensures that they will overlap and interfere for the absolute minimum possible period. In practice, dozens of orthogonal signals may overlap to offer the most efficient use of the spectrum. As long as each signal is precisely out of phase with the next, so that any signal only ever overlaps another at 90 degrees opposed, all can be decoded successfully.

Coding is a method of error protection and correction.

OFDM, and COFDM in particular, are desirable because they allow a communications channel to be utilized efficiently, while being robust against inter-symbol interference. A single carrier utilizing the full bandwidth would have an exceptionally short period-length, and be very susceptible to ISI.

OFDM allows for single frequency networks, because synchronized adjacent transmitters broadcasting the same signal will appear to be simple multipath interference, and the demodulator will simply ignore the weaker signal.

 To enable the signal to be generated using an inverse

FFT, it is preferable that the number of carriers consid-ered in the calculation is a power of two. In practice, it is not always desirable to have the number of real carriers restricted in this way. However, it is conven-ient to make up the actual number chosen to a power of two by setting the amplitudes of those not wanted to zero. This feature also simplifies the design of the anti alias filter after the DAC.