Mathematical Description
If sub-carriers are used, and each sub-carrier is modulated using alternative symbols, the OFDM symbol alphabet consists of combined symbols.
The low-pass equivalent OFDM signal is expressed as:
where are the data symbols, is the number of sub-carriers, and is the OFDM symbol time. The sub-carrier spacing of makes them orthogonal over each symbol period; this property is expressed as:
where denotes the complex conjugate operator and is the Kronecker delta.
To avoid intersymbol interference in multipath fading channels, a guard interval of length is inserted prior to the OFDM block. During this interval, a cyclic prefix is transmitted such that the signal in the interval equals the signal in the interval . The OFDM signal with cyclic prefix is thus:
The low-pass signal above can be either real or complex-valued. Real-valued low-pass equivalent signals are typically transmitted at baseband—wireline applications such as DSL use this approach. For wireless applications, the low-pass signal is typically complex-valued; in which case, the transmitted signal is up-converted to a carrier frequency . In general, the transmitted signal can be represented as:
Read more about this topic: Orthogonal Frequency-division Multiplexing
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