Spectral efficiency, 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). Link spectral efficiency 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, the spectral efficiency may be measured in bit/symbol, which is equivalent to bits per channel use (bpcu), implying that the net bit rate is divided by the symbol rate (modulation rate) or line code pulse rate. Link spectral efficiency is typically used to analyze the efficiency of a digital modulation method or line code, sometimes in combination with a forward error correction (FEC) code and other physical layer overhead. In the latter case, a "bit" refers to a user data bit; FEC overhead is always excluded. The modulation efficiency in bit/s is the gross bit rate (including any error-correcting code) divided by the bandwidth. Example 1: A transmission technique using one kilohertz of bandwidth to transmit 1,000 bits per second has a modulation efficiency of 1 (bit/s)/Hz. Example 2: A V.92 modem for the telephone network can transfer 56,000 bit/s downstream and 48,000 bit/s upstream over an analog telephone network. Due to filtering in the telephone exchange, the frequency range is limited to between 300 hertz and 3,400 hertz, corresponding to a bandwidth of 3,400 − 300 = 3,100 hertz. The spectral efficiency or modulation efficiency is 56,000/3,100 = 18.1 (bit/s)/Hz downstream, and 48,000/3,100 = 15.5 (bit/s)/Hz upstream. 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