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Spectral efficiency

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Spectral efficiency

Spectral efficiency (alternatively, spectrum efficiency or bandwidth efficiency) refers to the information rate that can be transmitted over a given bandwidth in a specific communication system. It is a measure of how efficiently a limited frequency spectrum is utilized by the physical layer protocol, and sometimes by the medium access control (the channel access protocol).

The link spectral efficiency of a digital communication system is measured in bit/s/Hz, or, less frequently but unambiguously, in (bit/s)/Hz. It is the net bit rate (useful information rate excluding error-correcting codes) or maximum throughput divided by the bandwidth in hertz of a communication channel or a data link.

Alternatively and less commonly, spectral efficiency may be measured in bit/symbol, which is equivalent to bits per channel use (bpcu). This can be calculated by dividing the net bit rate by the symbol rate (modulation rate).

Link spectral efficiency is typically used to analyze the efficiency of a digital modulation method or line code. Spectral efficiency calculations may or may count bits used for forward error correction (FEC) code and other physical layer overhead. If FEC overhead is excluded, a "bit" refers to a user data bit only.

The modulation efficiency in bit/s is the gross bit rate, which includes any bits used for FEC, divided by the bandwidth.

An upper bound for the attainable modulation efficiency is given by the Nyquist rate or Hartley's law as follows: For a signaling alphabet with M alternative symbols, each symbol represents N = log2 M bits. N is the modulation efficiency measured in bit/symbol or bpcu. In the case of baseband transmission (line coding or pulse-amplitude modulation) with a baseband bandwidth (or upper cut-off frequency) B, the symbol rate can not exceed 2B symbols/s in view to avoid intersymbol interference. Thus, the spectral efficiency can not exceed 2N (bit/s)/Hz in the baseband transmission case.

In the passband transmission case, a signal with passband bandwidth W can be converted to an equivalent baseband signal (using undersampling or a superheterodyne receiver), with upper cut-off frequency W/2. If double-sideband modulation schemes such as QAM, ASK, PSK or OFDM are used, this results in a maximum symbol rate of W symbols/s, and in that the modulation efficiency can not exceed N (bit/s)/Hz. If digital single-sideband modulation is used, the passband signal with bandwidth W corresponds to a baseband message signal with baseband bandwidth W, resulting in a maximum symbol rate of 2W and an attainable modulation efficiency of 2N (bit/s)/Hz.

If a forward error correction code is used, the spectral efficiency is reduced from the uncoded modulation efficiency figure.

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