Spectral efficiency
Encyclopedia
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
Physical layer
The physical layer or layer 1 is the first and lowest layer in the seven-layer OSI model of computer networking. The implementation of this layer is often termed PHY....

 protocol, and sometimes by the media access control
Media Access Control
The media access control data communication protocol sub-layer, also known as the medium access control, is a sublayer of the data link layer specified in the seven-layer OSI model , and in the four-layer TCP/IP model...

 (the channel access protocol).

Link spectral efficiency

The link spectral efficiency of a digital communication system is measured in bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

/s
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

/Hz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....

, 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
Data link
In telecommunication a data link is the means of connecting one location to another for the purpose of transmitting and receiving information. It can also refer to a set of electronics assemblies, consisting of a transmitter and a receiver and the interconnecting data telecommunication circuit...

. Alternatively, the spectral efficiency may be measured in bit/symbol, which is equivalent to bits per channel use
Channel use
Channel use is a quantity used in signal processing or telecommunication related to symbol rate and channel capacity. Capacity is measured in bits per input symbol into the channel . If a symbol enters the channel every Ts seconds the channel capacity in bits per second is C/Ts...

(bpcu), implying that the net bit rate is divided by the symbol rate
Symbol rate
In digital communications, symbol rate is the number of symbol changes made to the transmission medium per second using a digitally modulated signal or a line code. The Symbol rate is measured in baud or symbols/second. In the case of a line code, the symbol rate is the pulse rate in pulses/second...

 (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
Line code
In telecommunication, a line code is a code chosen for use within a communications system for baseband transmission purposes...

, sometimes in combination with a forward error correction
Forward error correction
In telecommunication, information theory, and coding theory, forward error correction or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels....

 (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.
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
V.92
V.92 is an ITU-T recommendation, titled Enhancements to Recommendation V.90, that establishes a modem standard allowing near 56 kb/s download and 48 kb/s upload rates. With V.92 PCM is used for both the upstream and downstream connections; previously 56K modems only used PCM for downstream...

 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
Nyquist rate
In signal processing, the Nyquist rate, named after Harry Nyquist, is two times the bandwidth of a bandlimited signal or a bandlimited channel...

 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
Pulse-amplitude modulation
Pulse-amplitude modulation, acronym PAM, is a form of signal modulation where the message information is encoded in the amplitude of a series of signal pulses....

) with a baseband bandwidth (or upper cut-off frequency) B, the symbol rate
Symbol rate
In digital communications, symbol rate is the number of symbol changes made to the transmission medium per second using a digitally modulated signal or a line code. The Symbol rate is measured in baud or symbols/second. In the case of a line code, the symbol rate is the pulse rate in pulses/second...

 can not exceed 2B symbols/s in view to avoid intersymbol interference
Intersymbol interference
In telecommunication, intersymbol interference is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have similar effect as noise, thus making the communication less reliable...

. 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
Undersampling
In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass filtered signal at a sample rate below the usual Nyquist rate In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass filtered signal at a sample rate...

 or a superheterodyne receiver
Superheterodyne receiver
In electronics, a superheterodyne receiver uses frequency mixing or heterodyning to convert a received signal to a fixed intermediate frequency, which can be more conveniently processed than the original radio carrier frequency...

), 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
Single-sideband modulation
Single-sideband modulation or Single-sideband suppressed-carrier is a refinement of amplitude modulation that more efficiently uses electrical power and bandwidth....

 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.
Example 3: A 16QAM modem has an alphabet size of M = 16 alternative symbols, with N = 4 bit/symbol or bpcu. Since QAM is a form of double sideband passband transmission, the spectral efficiency cannot exceed N = 4 (bit/s)/Hz.

Example 4: The 8VSB
8VSB
8VSB is the modulation method used for broadcast in the ATSC digital television standard. ATSC and 8VSB modulation is used primarily in North America; in contrast, the DVB-T standard uses COFDM....

 (8-level vestigial sideband) modulation scheme used in the ATSC digital television standard gives N=3 bit/symbol or bpcu. Since it can be described as nearly single-side band, the modulation efficiency is close to 2N = 6 (bit/s)/Hz. 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.

Example 5: The downlink of a V.92 modem uses a pulse-amplitude modulation with 128 signal levels, resulting in N = 7 bit/symbol. Since the transmitted signal before passband filtering can be considered as baseband transmission, the spectral efficiency cannot exceed 2N = 14 (bit/s)/Hz over the full baseband channel (0 to 4 kHz). As seen above, a higher spectral efficiency is achieved if we consider the smaller passband bandwidth.


If a forward error correction
Forward error correction
In telecommunication, information theory, and coding theory, forward error correction or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels....

 code is used, the spectral efficiency is reduced from the uncoded modulation efficiency figure.
Example 6: If a forward error correction (FEC) code with code rate
Code rate
In telecommunication and information theory, the code rate of a forward error correction code is the proportion of the data-stream that is useful...

 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 modulation efficiency. In exchange for this reduction in spectral efficiency, FEC usually reduces the bit-error rate, and typically enables operation at a lower signal to noise ratio (SNR).


An upper bound for the spectral efficiency possible without bit errors in a channel with a certain SNR, if ideal error coding and modulation is assumed, is given by the Shannon-Hartley theorem.
Example 7: If the SNR is 1 times expressed as a ratio, corresponding to 0 decibel
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...

, the link spectral efficiency can not exceed 1 (bit/s)/Hz for error-free detection (assuming an ideal error-correcting code) according to Shannon-Hartley regardless of the modulation and coding.


Note that the goodput
Goodput
In computer networks, goodput is the application level throughput, i.e. the number of useful information bits, delivered by the network to a certain destination, per unit of time. The amount of data considered excludes protocol overhead bits as well as retransmitted data packets...

 (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 erlangs per megahertz, or E
Erlang unit
The erlang is a dimensionless unit that is used in telephony as a statistical measure of offered load or carried load on service-providing elements such as telephone circuits or telephone switching equipment. It is named after the Danish telephone engineer A. K...

/MHz
. 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
Spread spectrum
Spread-spectrum techniques are methods by which a signal generated in a particular bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider bandwidth...

 and forward error correction
Forward error correction
In telecommunication, information theory, and coding theory, forward error correction or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels....

 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.

System spectral efficiency or area spectral efficiency

In digital wireless network
Wireless network
Wireless network refers to any type of computer network that is not connected by cables of any kind. It is a method by which homes, telecommunications networks and enterprise installations avoid the costly process of introducing cables into a building, or as a connection between various equipment...

s, the system spectral efficiency or area spectral efficiency is typically measured in (bit/s)/Hz per unit area, (bit/s)/Hz per cell
Cell site
A cell site is a term used to describe a site where antennas and electronic communications equipment are placed, usually on a radio mast, tower or other high place, to create a cell in a cellular network...

, or (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
Throughput
In communication networks, such as Ethernet or packet radio, throughput or network throughput is the average rate of successful message delivery over a communication channel. This data may be delivered over a physical or logical link, or pass through a certain network node...

 or goodput
Goodput
In computer networks, goodput is the application level throughput, i.e. the number of useful information bits, delivered by the network to a certain destination, per unit of time. The amount of data considered excludes protocol overhead bits as well as retransmitted data packets...

, 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
Radio resource management
Radio resource management is the system level control of co-channel interference and other radio transmission characteristics in wireless communication systems, for example cellular networks, wireless networks and broadcasting systems...

 techniques utilized. It can be substantially improved by dynamic radio resource management
Radio resource management
Radio resource management is the system level control of co-channel interference and other radio transmission characteristics in wireless communication systems, for example cellular networks, wireless networks and broadcasting systems...

. 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
Media Access Control
The media access control data communication protocol sub-layer, also known as the medium access control, is a sublayer of the data link layer specified in the seven-layer OSI model , and in the four-layer TCP/IP model...

 sublayer) is normally neglected.
Example 8: In a cellular system based on frequency-division multiple access
Frequency-division multiple access
Frequency Division Multiple Access or FDMA is a channel access method used in multiple-access protocols as a channelization protocol. FDMA gives users an individual allocation of one or several frequency bands, or channels. It is particularly commonplace in satellite communication. FDMA, like...

 (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 per 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 per cell or (bit/s)/Hz per sector is 1/12 of the link spectral efficiency.


The system spectral efficiency of a cellular network
Cellular network
A cellular network is a radio network distributed over land areas called cells, each served by at least one fixed-location transceiver known as a cell site or base station. When joined together these cells provide radio coverage over a wide geographic area...

 may also be expressed as the maximum number of simultaneous phone calls per area unit over 1 MHz frequency spectrum in E
Erlang unit
The erlang is a dimensionless unit that is used in telephony as a statistical measure of offered load or carried load on service-providing elements such as telephone circuits or telephone switching equipment. It is named after the Danish telephone engineer A. K...

/MHz per cell, E/MHz per sector, E/MHz per site, or (E/MHz)/m2. 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
Spread spectrum
Spread-spectrum techniques are methods by which a signal generated in a particular bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider bandwidth...

, 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.
Example 9: In the W-CDMA
W-CDMA
W-CDMA , UMTS-FDD, UTRA-FDD, or IMT-2000 CDMA Direct Spread is an air interface standard found in 3G mobile telecommunications networks. It is the basis of Japan's NTT DoCoMo's FOMA service and the most-commonly used member of the UMTS family and sometimes used as a synonym for UMTS...

 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) calls are possible in the same cell. Spread spectrum
Spread spectrum
Spread-spectrum techniques are methods by which a signal generated in a particular bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider bandwidth...

 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 per site, and 0.17/3 = 0.06 (bit/s)/Hz per cell or sector.


The spectral efficiency can be improved by radio resource management
Radio resource management
Radio resource management is the system level control of co-channel interference and other radio transmission characteristics in wireless communication systems, for example cellular networks, wireless networks and broadcasting systems...

 techniques such as efficient fixed or dynamic channel allocation, power control
Power control
Power control, broadly speaking, is the intelligent selection of transmit power in a communication system to achieve good performance within the system. The notion of "good performance" can depend on context and may include optimizing metrics such as link data rate, network capacity, geographic...

, link adaptation
Link adaptation
Link adaptation, or adaptive coding and modulation , is a term used in wireless communications to denote the matching of the modulation, coding and other signal and protocol parameters to the conditions on the radio link Link adaptation, or adaptive coding and modulation (ACM), is a term used in...

 and diversity scheme
Diversity scheme
In telecommunications, a diversity scheme refers to a method for improving the reliability of a message signal by using two or more communication channels with different characteristics. Diversity plays an important role in combatting fading and co-channel interference and avoiding error bursts...

s.

A combined fairness measure
Fairness measure
Fairness measures or metrics are used in network engineering to determine whether users or applications are receiving a fair share of system resources. There are several mathematical and conceptual definitions of fairness.-TCP fairness:...

 and system spectral efficiency measure is the fairly shared spectral efficiency.

Comparison table

Examples of numerical spectral efficiency values of some common communication systems can be found in the table below.

See also

  • Baud
    Baud
    In telecommunications and electronics, baud is synonymous to symbols per second or pulses per second. It is the unit of symbol rate, also known as baud rate or modulation rate; the number of distinct symbol changes made to the transmission medium per second in a digitally modulated signal or a...

  • CDMA spectral efficiency
    CDMA spectral efficiency
    CDMA spectral efficiency refers to the system spectral efficiency in bit/s/Hz/site or Erlang/MHz/site that can be achieved in a certain CDMA based wireless communication system...

  • Channel capacity
    Channel capacity
    In electrical engineering, computer science and information theory, channel capacity is the tightest upper bound on the amount of information that can be reliably transmitted over a communications channel...

  • Comparison of mobile phone standards
    Comparison of mobile phone standards
    -Issues:Global System for Mobile Communications and IS-95 were the two most prevalent 2G mobile communication technologies in 2007...

  • Goodput
    Goodput
    In computer networks, goodput is the application level throughput, i.e. the number of useful information bits, delivered by the network to a certain destination, per unit of time. The amount of data considered excludes protocol overhead bits as well as retransmitted data packets...

  • Radio resource management
    Radio resource management
    Radio resource management is the system level control of co-channel interference and other radio transmission characteristics in wireless communication systems, for example cellular networks, wireless networks and broadcasting systems...

     (RRM)
  • Spatial capacity
    Spatial capacity
    Spatial capacity is an indicator of "data intensity" in a transmission medium. It is usually used in conjunction with wireless transport mechanisms. This is analogous to the way that lumens per square meter determine illumination intensity....

  • Throughput
    Throughput
    In communication networks, such as Ethernet or packet radio, throughput or network throughput is the average rate of successful message delivery over a communication channel. This data may be delivered over a physical or logical link, or pass through a certain network node...

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