Spectral efficiency
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Spectral efficiency or spectrum efficiency refers to the amount of information that can be transmitted over a given bandwidth in a specific digital 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).
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[edit] Link spectral efficiency
The link spectral efficiency is measured in bit/s/Hz, and is the channel capacity or maximum throughput of a logical point-to-point link with a given modulation method. If a forward error correction code is combined with the modulation, a "bit" refers to a user data bit; FEC overhead is always excluded.
A transmission technique using one kilohertz of bandwidth to transmit 1000 bits/second has a spectral efficiency of 1 bit/s/Hz.
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 − 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.
The maximum possible spectral efficiency of any modulation scheme without FEC is given by the Nyquist sampling theorem as follows. For a signaling alphabet with M symbols, each symbol represents N = log2 M bits and the spectral efficiency cannot exceed 2N bits/s/Hz without intersymbol interference. For example, if the alphabet size is M=8 symbols, with N=3 bits/symbol, the spectral efficiency cannot exceed 2N = 6 bits/sec/Hz.
If a forward error correction code is used, the spectral efficiency is reduced by the FEC code rate from the uncoded figure. For example, if FEC with code rate 1/2 is added, meaning that the encoder input 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 errors in a channel with a certain SNR, if ideal error coding and modulation is used, 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.
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, spectrum spreading and FEC reduce the spectral efficiency (in bits/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 bits/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.
[edit] System spectral efficiency
In wireless networks, the system spectral efficiency in bit/s/Hz/area unit, bit/s/Hz/cell or bit/s/Hz/site 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 in hertz. 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 capacity of a cellular network may also be measured as the maximum number of simultaneous phone calls over 1 MHz frequency spectrum in Erlangs//MHz/cell, Erlangs/MHz/sector, Erlangs/MHz/site, or Erlangs/MHz/km². This measure is also affected by the source coding (data compression) scheme, and may be used in analog cellular networks as well.
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/sectoris 1/12 of the link spectral efficiency.
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 spectrally 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: 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).
The spectral efficiency can be improved by radio resource management techniques such as efficient fixed or dynamic channel allocation, power control and link adaptation.
[edit] Comparison table
Examples of numerical spectral efficiency values of some common communication systems can be found in the table below.
| Service | Standard | Net bitrate R per frequency channel
(Mbit/s) |
Bandwidth B per frequency channel
(MHz) |
Link spectral efficiency R/B
(bit/s/Hz) |
Typical frequency reuse factor K | System spectral efficiency
Approximately R/B/K (bit/s/Hz/site) |
|---|---|---|---|---|---|---|
| 2G cellular | GSM | 0.013•8 timeslots = 0.104 | 0.2 | 0.52 | 3 | 0.17 [1] |
| 2.75G cellular | GSM + EDGE | Max 0.384 Typ 0.20 | 0.2 | Max 1.92 Typ 1.00 | 3 | 0.33 [1] |
| 2.75G cellular | IS-136HS + EDGE | Max 0.384 Typ 0.27 | 0.2 | Max 1.92 Typ 1.35 | 3 | 0.45 [1] |
| 3G cellular | WCDMA FDD | Max 0.384 per mobile | 5 | Max 0.077 per mobile | 1 | |
| 3.5G cellular | HSDPA | Max 14.4 per mobile | 5 | Max 2.88 per mobile | ||
| 3.5G cellular | HSOPA OFDMA | Max 100 per mobile | 20 | Max 5 per mobile | ||
| 3G cellular | CDMA2000 1x | Max 0.144 per mobile | 1.25 | Max 0.115 per mobile | 1 | |
| Wi-Fi | IEEE 802.11b | Max 11 | 20 | Max 0.55 | ||
| Wi-Fi | IEEE 802.11a/g | Max 54 | 20 | Max 2.7 | ||
| Wi-Fi | IEEE 802.11n | Max 540 | 20 | Max 27 | 1 | 27 |
| WiMAX | IEEE 802.16 | Max 75 | 20 (1.75, 3.5, 7...) | Max 3.75 | ||
| Digital radio | DAB | 0.576 to 1.152 | 1.712 | 0.34 to 0.67 | 4 | 0.08 to 0.17 |
| Digital radio | DAB with 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 | 5 | 0.55 |
| Digital TV | DVB-T with SFN | Max 31.67 Typ 22.0 | 8 | Max 4.0 Typ 2.8 | 1 | 2.75 |
| Digital TV | DVB-H | 5.5 to 11 | 8 | 0.68 to 1.4 | 5 | 0.14 to 0.28 |
| Digital TV | DVB-H with SFN | 5.5 to 11 | 8 | 0.68 to 1.4 | 1 | 0.68 to 1.4 |
| North American Digital Cable TV | 256-QAM | 38 | 6 | 6.33 | N/A | N/A |
[edit] Notes
- ^ a b c Anders Furuskär, Jonas Näslund and Håkan Olofsson, "Edge—Enhanced data rates for GSM and TDMA/136 evolution", Ericsson Review no 1, 1999, [1]
