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 media 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 bitrate (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 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 analyse 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 bitrate (including any error-correcting code) 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.
Note that the goodput (the amount of application layer useful information) is normally lower than the maximum throughput used in the above calculations, because of packet retransmissions, higher protocol layer overhead, flow control, congestion avoidance, etc. On the other hand, a data compression scheme, such as the V.44 or V.42bis compression used in telephone modems, may however give higher goodput if the transferred data is not already efficiently compressed.
The link spectral efficiency of a wireless telephony link may also be expressed as the maximum number of simultaneous calls over 1 MHz frequency spectrum in E/MHz (erlangs per megahertz). This measure is also affected by the source coding (data compression) scheme. It may be applied to analog as well as digital transmission.
In wireless networks, the link spectral efficiency can be somewhat misleading, as larger values are not necessarily more efficient in their overall use of radio spectrum. In a wireless network, high link spectral efficiency may result in high sensitivity to co-channel interference (crosstalk), which affects the capacity. For example, in a cellular telephone network with frequency reuse, spectrum spreading and forward error correction reduce the spectral efficiency in (bit/s)/Hz but substantially lower the required signal-to-noise ratio in comparison to non-spread spectrum techniques. This can allow for much denser geographical frequency reuse that compensates for the lower link spectral efficiency, resulting in approximately the same capacity (the same number of simultaneous phone calls) over the same bandwidth, using the same number of base station transmitters. As discussed below, a more relevant measure for wireless networks would be system spectral efficiency in bit/s/Hz per unit area. However, in closed communication links such as telephone lines and cable TV networks, and in noise-limited wireless communication system where co-channel interference is not a factor, the largest link spectral efficiency that can be supported by the available SNR is generally used.
In digital wireless networks, the system spectral efficiency or area spectral efficiency is typically measured in bit/s/Hz/area unit [(bit/s)/Hz per unit area], bit/s/Hz/cell [(bit/s)/Hz per cell] or bit/s/Hz/site [(bit/s)/Hz per site]. It is a measure of the quantity of users or services that can be simultaneously supported by a limited radio frequency bandwidth in a defined geographic area. It may for example be defined as the maximum throughput or goodput, summed over all users in the system, divided by the channel bandwidth. This measure is affected not only by the single user transmission technique, but also by multiple access schemes and radio resource management techniques utilized. It can be substantially improved by dynamic radio resource management. If it is defined as a measure of the maximum goodput, retransmissions due to co-channel interference and collisions are excluded. Higher-layer protocol overhead (above the media access control sublayer) is normally neglected.
The system spectral efficiency of a cellular network may also be expressed as the maximum number of simultaneous phone calls per area unit over 1 MHz frequency spectrum in (E/MHz)/cell (erlangs per megahertz per cell), (E/MHz)/sector, (E/MHz)/site, or (E/MHz)/km². This measure is also affected by the source coding (data compression) scheme. It may be used in analog cellular networks as well.
Low link spectral efficiency in (bit/s)/Hz does not necessarily mean that an encoding scheme is inefficient from a system spectral efficiency point of view. As an example, consider Code Division Multiplexed Access (CDMA) spread spectrum, which is not a particularly spectral efficient encoding scheme when considering a single channel or single user. However, the fact that one can "layer" multiple channels on the same frequency band means that the system spectrum utilization for a multi-channel CDMA system can be very good.
Examples of numerical spectral efficiency values of some common communication systems can be found in the table below.
|Net bitrate R per carrier
|Bandwidth B per carrier
|Link spectral efficiency R/B
|Typical reuse factor 1/K||System spectral efficiency
((bit/s)/Hz per site)
|1G cellular||NMT 450||1981||0.0012||0.025||0.45||1/7||0.064|
|1G cellular||AMPS||1983||0.0096||0.030||0.32||1/7 ||0.046|
|2G cellular||GSM||1991||0.013•8 timeslots = 0.104||0.2||0.52||1/9 (1/3 in 1999)||0.17 |
|2G cellular||D-AMPS||1991||0.013•3 timeslots = 0.039||0.030||1.3||1/9 (1/3 in 1999)||(0.45 in 1997)|
|2.75G cellular||CDMA2000 1x voice||2000||Max 0.0096 per mobile||1.2288||0.0078 per mobile||1||0.172 (fully loaded)|
|2.75G cellular||GSM + EDGE||2003||Max 0.384 Typ 0.20||0.2||Max 1.92 Typ 1.00||1/3||0.33 |
|2.75G cellular||IS-136HS + EDGE||Max 0.384 Typ 0.27||0.2||Max 1.92 Typ 1.35||1/3||0.45 |
|3G cellular||WCDMA FDD||2001||Max 0.384 per mobile||5||Max 0.077 per mobile||1 ||0.51|
|3G cellular||CDMA2000 1x PD||2002||Max 0.153 per mobile||1.2288||Max 0.125 per mobile||1||0.1720 (fully loaded)|
|3G cellular||CDMA2000 1xEV-DO Rev.A||2002||Max 3.072 per mobile||1.2288||Max 2.5 per mobile||1||1.3 average loaded sector|
|Fixed WiMAX||IEEE 802.16d||2004||96||20 (1.75, 3.5, 7...)||4.8||1/4||1.2|
|3.5G cellular||HSDPA||2007||Max 14.4 per mobile||5||Max 2.88 per mobile||1 ||2.88|
|3.9G MBWA||iBurst HC-SDMA||2005||Max 3.9 Mbit/s per carrier||0.625||Max 7.23 per carrier ||1||7.23|
|3.9G cellular||LTE||2009||Max 326.4 per mobile||20||Max 16.32 per mobile||1||16.32 max|
|Wi-Fi||IEEE 802.11a/g||2003||Max 54||20||Max 2.7||1/3||0.9|
|Wi-Fi||IEEE 802.11n Draft 2.0||2007||Max 144.4||20||Max 7.22||1/3||2.4|
|TETRA||ETSI||1998||4 timeslots = 0.036||0.025||1.44|
|Digital radio||DAB||1995||0.576 to 1.152||1.712||0.34 to 0.67||1/5||0.08 to 0.17|
|Digital radio||DAB with SFN||1995||0.576 to 1.152||1.712||0.34 to 0.67||1||0.34 to 0.67|
|Digital TV||DVB-T||1997||Max 31.67 Typ 22.0||8||Max 4.0 Typ 2.8||1/5||0.55|
|Digital TV||DVB-T with SFN||1996||Max 31.67 Typ 22.0||8||Max 4.0 Typ 2.8||1||Max 4.0 Typ 2.8|
|Digital TV||DVB-H||2007||5.5 to 11||8||0.68 to 1.4||1/5||0.14 to 0.28|
|Digital TV||DVB-H with SFN||2007||5.5 to 11||8||0.68 to 1.4||1||0.68 to 1.4|
|Digital cable TV||DVB-C 256-QAM mode||38||6||6.33||N/A||N/A|
|Broadband modem||ADSL2 downlink||12||0.962||12.47||N/A||N/A|
|Telephone modem||V.92 downlink||1999||0.056||0.004||14.0||N/A||14|
N/A means not applicable.