Spectral efficiency

Spectral efficiency, spectrum efficiency or bandwidth efficiency refers to the amount of information 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).

Link spectral efficiency

The link spectral efficiency of a digital communication system is measured in bit/s/Hz, or less frequently but unambiguously (bit/s)/Hz. It is the net bitrate or maximum throughput divided by the 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.

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.

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 rate or Hartley's law as follows. For a signaling alphabet with M alternative symbols, each symbol represents N = log₂ 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 2B symbols/s in view to avoid intersymbol interference. Thus, the spectral efficiency can not exceed 2N (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.

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 2N = 6 (bit/s)/Hz in the base band case, and N = 3 (bit/s)/Hz in the pass band case.

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 errors 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, 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 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 spectral efficiency of a cellular network may also be measured as the maximum number of simultaneous phone calls 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.

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 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: 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.

Comparison table

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

Spectral efficiency of common communication systems.

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 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 Template:Fact
2G cellular	GSM 1993	0.013•8 timeslots = 0.104	0.2	0.52	1/7	0.17
2G cellular	D-AMPS 1990	0.013•3 timeslots = 0.039	0.030	1.3	1/7
2.75G cellular	GSM + EDGE	Max 0.384 Typ 0.20	0.2	Max 1.92 Typ 1.00	1/7	0.33
2.75G cellular	IS-136HS + EDGE	Max 0.384 Typ 0.27	0.2	Max 1.92 Typ 1.35	1/7	0.45
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 Template:Fact	0.51
3.5G cellular	HSDPA 2007	Max 14.4 per mobile	5	Max 2.88 per mobile	1/7 Template:Fact	0.71
4G cellular	LTE	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
WiMAX	IEEE 802.16 2004	96	20 (1.75, 3.5, 7...)	4.8	1/4	1.2
Digital radio	DAB	0.576 to 1.152	1.712	0.34 to 0.67	1/5	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	1/5	0.55
Digital TV	DVB-T with 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 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

Template:Refimprove

See also

• Baud
• Channel capacity
• Comparison of mobile phone standards
• Goodput
• Radio resource management (RRM)
• Spatial capacity
• Throughput

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