Radio Transmission: OFDM Intro – Transcript:

• To start this discussion we should recap the main issue with the wireless channel – multipath fading
• As we remember from the „radio channel” part, the radio signal is received through multipath copies, being a separate channel „taps”
• When we transmit a single rectangle symbol, it shhows up at the receiver as a combination of (in this case 3 copies) that are differently delayed and attenuated
• When there are multiple consecutive symbols one right next to the other one – this resuts in interference from the previous symbol to the next – ISI.

• Lets look at the example of the actual impairments – lets assume we have 3 symbols within 1 second (so 3 sym/second) (each carying a single bit (or multiple bits as in the case of QPSK/QAM mapping)
• They go through a channel with 3 „taps” that results in a spread symbols with a duration longer than the individual symbol – resulting in ISI
• When the symbols are long, – meaning low thrpt – the ISI is small, i.e. we are able to decode the signal as majority of the power is received without interference
• Now, we want to transmit more symbols within this 1s – in the second example we have 6 symbols – meaning they are shorter in time, but getting us higher thrpt (2x)
• The channel does not change only due to the transmission characteristic of the symbol
• So the same symbol dispersion (smeering out) is seen, but the symbols are shorter – thus the impairment is more severe – i.e. larger part of the symbol is spreading out to subsequent symbols – so as we could see – the green symbol is pretty much impaired along its whole way (by blue and red) – so we are not having any part of the symbol being „clear from interferenfce”

• If we now take a look on the other dimension of the transmission i.e. frequency
• As we discussed in the „signal” theory part – long symbols result in narrow BW (BW = 1/T)
• The multipath channel response is always selective
• In the frequency domain we multiply each individual frequency „tap” of the signal with the corresponding frequency tap of the channel response
• In this case if the symbol is lng – the signal can be modified, but only amplified or attenuated, but shape stays still the same (this means that the channel is flat)
• Now if we take the second example – we are transmitting faster, which (by the same principle BW = 1/T) means, that the symbol/system BW is wider
• The signal also goes through the same channel – and thus all the individual components are modified accordingly to the shape of the channel – so the resulting received signal shape is destroyed, and make it harrd to revoke the original shape without complex estimators and receiveing algorithms

• SO on one hand we want long symbols – because long symbols mean low impact of the ISI and also low impact of the frequency selectivity – BUT in the same time we would like to have high throughput – which is not possible through single carrier modulation, where data symbols (bits/QPSK/QAM) are transmitted one after another – because of increasing impact of the channel.
• IT IS IMPORTANT TO NOTICE, that the long or short symbols are always with respect to the channel impulse response (and its dispersion) – which means that a short symbol in mountain environment (where the channel impuullse response is long) can be „perceioved” as long in the office environemnt – that does not impact the signal that much due to short CIR
• So the OFDM si here a solution, that combines both requirements – where the usable bandwidth is divided into a large number of smaller bandwidths, or “subcarriers” (SCs). The high-speed information is divided onto multiple lower-speed signals, transmitted simultaneously on different frequencies in parallel
• We have both – long symbols – decreasing ISI, narrow BWs – (decreased frequency seletivity)

• Now lets look at the analogy between single carrier and multi carrier transmission
• An example analogy is to the shipment goods via trucks
• When we transmit a wideband signal (one after another), this is analogous, to a big truck carying several packages
• In contrary multi carrier transmission is analogous to shipment goods using several smaller cars, each carying a single package
• now, when the channel goes through the „fading channel” the signal is distorted, as explained before, that can be seen as a road accident, if the same road accident happens to both types of transmission, in the case of a truck the whole transport is destroyed, whil ein the case of smaller cars carying the separate packages, only one will be destroyed
• So in the case of a deep fade only one subcarrier (part of data) is destroyed (i.e. not receivable)