Spectral efficiency 1652911 222286274 2008-06-28T14:48:28Z Dicklyon 869314 adjust template and change section name to references '''Spectral efficiency''', '''spectrum efficiency''' or '''bandwidth efficiency''' refers to the amount of information that can be transmitted over a given [[Bandwidth (signal processing)|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). == Link spectral efficiency == The '''link spectral efficiency''' of a digital communication system is measured in '''[[bit]]/[[Second|s]]/[[Hz]]'''<ref>{{cite book | title = Principles of Digital Transmission: With Wireless Applications | author = Sergio Benedetto and Ezio Biglieri | isbn = 0306457539 | year = 1999 | publisher = Springer | url = http://books.google.com/books?id=thfj9S8cbdoC&pg=RA1-PA219&dq=%22spectral+efficiency%22+(bit/s)/Hz&lr=&as_brr=3&ei=ZHSuR4XrIo6IswPtrIH-BQ&sig=KvPGYnsRaQVXQ2AtXXPvPA2c5H8 }}</ref>, or less frequently but unambiguously (bit/s)/Hz. It is the [[net bitrate]] or [[maximum throughput]] divided by the [[Bandwidth (signal processing)|bandwidth]] in hertz of a [[communication channel]] or a [[data link]]. Spectral efficiency is typically used to analyse the efficiency of a [[digital modulation]] method, 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. <blockquote>'''Simple example:''' A transmission technique using one [[kilohertz]] of bandwidth to transmit 1000 bits per second has a spectral efficiency of 1 (bit/s)/Hz.</blockquote> <blockquote>'''Telephone modem example:''' 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 3400 &minus; 300 = 3100 hertz. The spectral efficiency is 56,000/3,100 = 18.1 (bit/s)/Hz downstream, and 48,000/3,100 = 15.5 (bit/s)/Hz upstream. </blockquote> The maximum possible spectral efficiency of any modulation scheme without FEC is given by the [[Nyquist rate]] or [[Shannon–Hartley theorem|Hartley's law]] as follows. For a signaling alphabet with ''M'' alternative symbols, each symbol represents ''N'' = log<sub>2</sub> ''M'' bits. For a [[baseband signal]] with bandwidth (or upper cut-off frequency) ''B'' that is higher than the carrier frequency, the [[symbol rate]] can not exceed 2''B'' symbols/s in view to avoid [[intersymbol interference]]. Thus, the spectral efficiency can not exceed 2''N'' (bit/s)/Hz . However, a [[passband]] signal with bandwidth ''W'' can be converted to an equivalent baseband signal (using [[undersampling]] or a [[superheterodyne receiver]]), with upper cut-off frequency ''W''/2. This results in a maximum symbol rate of ''W'' symbols/s, and in that the spectral efficiency can not exceed ''N'' (bit/s)/Hz in the passband case. <blockquote>'''Numerical example:''' A 8PSK modem has an alphabet size is ''M''=8 alternative symbols, with ''N''=3 bits/symbol, resulting in that the spectral efficiency cannot exceed 2''N'' = 6 (bit/s)/Hz in the base band case, and ''N'' = 3 (bit/s)/Hz in the pass band case.</blockquote> If a [[forward error correction]] code is used, the spectral efficiency is reduced from the uncoded figure. For example, if FEC with [[code rate]] 1/2 is added, meaning that the encoder input bit rate is one half the encoder output rate, the spectral efficiency is 50% of the uncoded value. In exchange for this reduction in spectral efficiency, FEC usually (but not always) enables operation at a lower [[signal to noise ratio]] (SNR). An upper bound for the spectral efficiency possible without [[bit error]]s in a channel with a certain SNR, if ideal error coding and modulation is assumed, is given by the [[Shannon-Hartley theorem]]. For example, if the SNR is 1, expressed as a ratio and corresponding to 0 [[decibel]], the link spectral efficiency can not exceed 1 bit/s/Hz regardless of the modulation and coding. 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. With 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 term "spectral efficiency" can be somewhat misleading, as larger values are not necessarily more efficient in their overall use of radio spectrum. For example, in a [[cellular telephone]] network with frequency reuse, [[spread spectrum|spectrum spreading]] and FEC reduce the spectral efficiency in (bit/s)/Hz but substantially lower the required signal-to-noise ratio. This can allow for much denser geographical frequency reuse that more than compensates for the lower link spectral efficiency. As discussed below, a more relevant measure would be bit/s/Hz '''per unit area''', and this is the principle behind [[CDMA]] digital cellular. However, in closed communication links such as telephone lines and cable TV networks where co-channel interference is not a factor, the largest spectral efficiency that can be supported by the available SNR is generally used. == System spectral efficiency or area spectral efficiency == In digital [[wireless network]]s, 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 site|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 spectral efficiency of a [[cellular network]] may also be measured as the maximum number of simultaneous phone calls over 1 MHz frequency spectrum in ([[Erlang unit|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. <blockquote>'''Example:''' In a cellular system based on [[frequency-division multiple access]] (FDMA) with a [[fixed channel allocation]] (FCA) cellplan using a [[frequency reuse factor]] of 4, each base station has access to 1/4 of the total available frequency spectrum. Thus, the maximum possible '''system spectral efficiency''' in bit/s/Hz/'''site''' is 1/4 of the '''link spectral efficiency'''. Each base station may be divided into 3 cells by means of 3 sector antennas, also known as a 4/12 reuse pattern. Then each cell has access to 1/12 of the available spectrum, and the system spectral efficiency in bit/s/Hz/'''cell''' or bit/s/Hz/'''sector'''is 1/12 of the link spectral efficiency. </blockquote> 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 [[CDMA|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. <blockquote>'''Example:''' In the [[W-CDMA]] 3G cellular system, every phone call is compressed to a maximum of 8,500 bit/s (the useful bitrate), and spread out over a 5 MHz wide frequency channel. This corresponds to a link throughput of only 8,500/5,000,000 = 0.0017 (bit/s)/Hz. Let us assume that 100 simultaneous (non-silent) simultaneous calls are possible in the same cell. [[Spread spectrum]] makes it possible to have as low a frequency reuse factor as 1, if each base station is divided into 3 cells by means of 3 directional sector antennas. This corresponds to a system spectrum efficiency of over 1 · 100 · 0.0017 = 0.17 bit/s/Hz/site, or 0.17/3 = 0.06 bit/s/Hz/cell (or bit/s/Hz/sector).</blockquote> The spectral efficiency can be improved by [[radio resource management]] techniques such as efficient fixed or dynamic [[channel allocation]], [[power control]] and [[link adaptation]]. == Comparison table == Examples of numerical spectral efficiency values of some common communication systems can be found in the table below. {| class="wikitable" |+ Spectral efficiency of common communication systems. ! Service ! Standard ! [[Net bitrate]] ''R'' per frequency channel (Mbit/s) ! [[Bandwidth (signal processing)|Bandwidth]] ''B'' per frequency channel (MHz) ! Link spectral efficiency ''R/B'' ((bit/s)/Hz) ! Typical [[frequency reuse factor]] ''1/K'' ! System spectral efficiency Approximately (''R''/''B'')/''K'' ((bit/s)/Hz per site) |- ! [[1G]] cellular ! [[AMPS]] | 0.0096 | 0.030 | 0.32 | 1/7 {{Fact|date=June 2008}} | |- ! [[2G]] cellular ! [[GSM]] 1993 | 0.013•8 timeslots = 0.104 | 0.2 | 0.52 | 1/7 | 0.17 <ref name="furuskär"> Anders Furuskär, Jonas Näslund and Håkan Olofsson (1999), "[http://www.ericsson.com/ericsson/corpinfo/publications/review/1999_01/files/1999014.pdf Edge—Enhanced data rates for GSM and TDMA/136 evolution]", Ericsson Review no. 1</ref> |- ! [[2G]] cellular ! [[D-AMPS]] 1990 | 0.013•3 timeslots = 0.039 | 0.030 | 1.3 | 1/7 | |- ! [[2.75G]] cellular ! [[GSM]] + [[Enhanced Data Rates for GSM Evolution|EDGE]] | Max 0.384 Typ 0.20 | 0.2 | Max 1.92 Typ 1.00 | 1/7 | 0.33 <ref name="furuskär">[http://www.ericsson.com/ericsson/corpinfo/publications/review/1999_01/files/1999014.pdf ER 1/99 EDGE 23/2 JM<!-- Bot generated title -->]</ref> |- ! [[2.75G]] cellular ! [[IS-136]]HS + [[Enhanced Data Rates for GSM Evolution|EDGE]] | Max 0.384 Typ 0.27 | 0.2 | Max 1.92 Typ 1.35 | 1/7 | 0.45 <ref name="furuskär">[http://www.ericsson.com/ericsson/corpinfo/publications/review/1999_01/files/1999014.pdf ER 1/99 EDGE 23/2 JM<!-- Bot generated title -->]</ref> |- ! [[3G]] cellular ! [[CDMA2000]] 1x voice | Max 0.0096 per mobile | 1.2288 | 0.0078 per mobile | 1 | 0.172 (fully loaded) |- ! [[3G]] cellular ! [[CDMA2000]] 1x PD | Max 0.153 per mobile | 1.2288 | Max 0.125 per mobile | 1 | 0.1720 (fully loaded) |- ! [[3G]] cellular ! [[CDMA2000]] 1xEV-DO | Max 2.4576 per mobile | 1.2288 | Max 2.0 per mobile | 1 | 1.1 average loaded sector |- ! [[3G]] cellular ! [[WCDMA]] FDD 1997 | Max 0.384 per mobile | 5 | Max 0.077 per mobile | 1/7 {{Fact|date=September 2007}} |0.51 <!-- 0.077 if only one high speed user--> |- ! 3.5G cellular ! [[HSDPA]] 2007 | Max 14.4 per mobile | 5 | Max 2.88 per mobile | 1/7 {{Fact|date=September 2007}} | 0.71 |- ! 4G cellular ! [[Long Term Evolution|LTE]] | Max 326.4 per mobile | 20 | Max 16.32 per mobile | 1 | 16.32 max |- ! [[Wi-Fi]] ! [[IEEE 802.11|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 |- ! [[WiMAX]] ! [[IEEE 802.16]] 2004 | 96 | 20 (1.75, 3.5, 7...) | 4.8 | 1/4 | 1.2 |- ! [[Digital radio]] ! [[Digital audio broadcasting|DAB]] | 0.576 to 1.152 | 1.712 | 0.34 to 0.67 | 1/5 | 0.08 to 0.17 |- ! [[Digital radio]] ! [[Digital audio broadcasting|DAB]] with [[Single-frequency network|SFN]] | 0.576 to 1.152 | 1.712 | 0.34 to 0.67 | 1 | 0.34 to 0.67 |- ! [[Digital TV]] ! [[DVB-T]] | Max 31.67 Typ 22.0 | 8 | Max 4.0 Typ 2.8 | 1/5 | 0.55 |- ! [[Digital TV]] ! [[DVB-T]] with [[Single-frequency network|SFN]] | Max 31.67 Typ 22.0 | 8 | Max 4.0 Typ 2.8 | 1 | Max 4.0 Typ 2.8 |- ! [[Digital TV]] ! [[DVB-H]] | 5.5 to 11 | 8 | 0.68 to 1.4 | 1/5 | 0.14 to 0.28 |- ! [[Digital TV]] ! [[DVB-H]] with [[Single-frequency network|SFN]] | 5.5 to 11 | 8 | 0.68 to 1.4 | 1 | 0.68 to 1.4 |- ! [[Digital Cable TV via fiber optical nodes]] ! [[256-QAM]] | 38 | 6 | 6.33 | N/A | N/A |- ! [[ADSL2]] downlink ! [[OFDM]] | 12 | 0.962 | 12.47 | N/A | N/A |- ! [[V.92]] modem downlink ! [[V.92]] | 0.056 | 0.004 | '''14.0''' | N/A | N/A |} N/A means not applicable. ==References== {{Refimprove|date=January 2008}} <references/> ==See also== * [[Baud]] * [[Channel capacity]] * [[Comparison of mobile phone standards]] * [[Goodput]] * [[Radio resource management]] (RRM) * [[Spatial capacity]] * [[Throughput]] [[Category:Network performance]] [[Category:Wireless networking]] [[Category:Information theory]] [[Category:Communication theory]] [[Category:Radio resource management]] [[de:Spektrale Effizienz]] [[ja:スペクトル効率]] [[nl:Spectrale efficiëntie]] [[sv:Spektrumeffektivitet]]