Example 5: The downlink of a V.92 modem uses a pulse-amplitude modulation with 128 signal levels, resulting in N = 7 bit/symbol. In practice, ATSC transfers a gross bit rate of 32 Mbit/s over a 6 MHz wide channel, resulting in a modulation efficiency of 32/6 = 5.3 (bit/s)/Hz. Since it can be described as nearly single-side band, the modulation efficiency is close to 2 N = 6 (bit/s)/Hz. Example 4: The 8VSB (8-level vestigial sideband) modulation scheme used in the ATSC digital television standard gives N=3 bit/symbol or bpcu. Since QAM is a form of double sideband passband transmission, the spectral efficiency cannot exceed N = 4 (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 2 W and an attainable modulation efficiency of 2 N (bit/s)/Hz.Įxample 3: A 16QAM modem has an alphabet size of M = 16 alternative symbols, with N = 4 bit/symbol or bpcu. 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. 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. Thus, the spectral efficiency can not exceed 2 N (bit/s)/Hz in the baseband transmission case. 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 2 B symbols/s in view to avoid intersymbol interference. N is the modulation efficiency measured in bit/symbol or bpcu. 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.Īn 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 = log 2 M bits. 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. 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. The modulation efficiency in bit/s is the gross bit rate (including any error-correcting code) divided by the bandwidth.Įxample 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. In the latter case, a "bit" refers to a user data bit FEC overhead is always excluded. 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. 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. 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. 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 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). 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. Information rate that can be transmitted over a given bandwidth
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