频谱效率（spectralefficiency）

频谱效率
频谱效率（Spectral efficiency、Spectrum efficiency）是指在数位通信系统中的带宽限制下，可以传送的资料总量。

在有限的波频谱下，物理层通信协议可以达到的使用效率有一定的限度。

链路频谱效率
数字通信系统的链路频谱效率（Link spectral efficiency）的单位是
bit/s/Hz，或(bit/s)/Hz（较少用，但更准确）。

其定义为净比特率（有用信息速率，不包括纠错码）或最大吞吐量除以通信信道或数据链路的带宽（单位：赫兹）。

调制效率定义为净比特率（包括纠错码）除以带宽。

频谱效率通常被用于分析数字调制方式的效率，有时也考虑前向纠错码（forward error correction, FEC）和其他物理层开销。

在后一种情况下，1个“比特”特指一个用户比特，FEC的开销总是不包括在内的。

例1：1kHz带宽中可以传送毎秒1000bit的技术，其频谱效率或调制效率均为1 bit/s/Hz。

例2：电话网的V.92调制解调器在模拟电话网上以56,000 bit/s的下行速率和48,000 bit/s的上行速率传输。

经由电话交换机的滤波，频率限制在300Hz到3,400Hz之间，带宽相应为 3400 − 300 = 3100 Hz 。

频谱效率或调制效率为56,000/3,100 = 18.1 bit/s/Hz（下行）、48,000/3,100 = 15.5 bit/s/Hz（上行）。

使用FEC 的架空调变方式可达到最大的频谱效率可以利用标本化定理来求得，信号的字母表(计算机科学)利用符号数量M来组合、各符号使用 N = log2 M bit来表示。

此情况下频谱效率若不使用编码间干涉的话，无法超过2N bit/s/Hz 的效率。

举例来说，符号种类有8种、每个各有3bit 的话，频谱效率最高不超过6 bit/s/Hz。

在使用前向错误更正编码的情形时频谱效率会降低。

比如说使用1/2编码率的FEC时，编码长度会变为1.5倍，频谱效率会降低50%。

频谱效率降低的同时FEC可以改善信号的SN比(并非一定会有改善)。

对某个SN比通信回来说、在完全没有传输错误，且编码与调变方式皆处于理想的状况时，其频谱效率的上限可哈特利定理得出。

比如说SN比1即分贝为0时，无论编码与调变方式如何变
化，频谱效率不会超过1 bit/s/Hz。

Goodput（应用层情报使用的量）比一般在此计算的吞吐量还小，其原因为有封包再次传送、超传输协议的架空造成的。

频谱效率这个用语，会产生数值越大的话可以使周波数频谱产生更有效的误解产生。

比如手机因为频谱扩散与使用FEC技术使得频谱效率低下，但SN比不好有时还是可以正常通信。

因此可以使用到比周波带宽数还多的链结、以整体来看其效果可以弥补频谱效率低下的缺点还有过之。

如同后面会提到的，具有较为合适尺度代表”单位带宽利用率”单位的bit/s/Hz存在，这是属于分码多工(CDMA)的技术并已成为数位手机的基本构成技术。

但是电话线路与有线电视网等由于没有频道相互干扰的问题，其使用的基本上皆为其SN比下最大频谱效率。

系统频谱效率
无线网络是以系统频谱效率'在有限的无线周波数带宽下可以同时支援的客户数与服务进行量化。

其单位为bit/s/Hz/area unit、bit/s/Hz/cell、
bit/s/Hz/site 等进行计量。

有可以把系统能同时支援使用者的吞吐量与goodput的总量以通信回路的带宽(Hz)来表示。

这并不单影响使用单一通信回路的技术，多元连接手法与无线资源管理技术也受到影响，特别是动态无线资源管理可以得到改善。

定义最大goodput时，会排除掉通信回路间的相互干渉与冲突，高阶通讯协定的架空也是忽略不计的。

手机网络的容量也是以1 MHz 周波数带宽上可以同时最大连接线数来表示，即Erlang/MHz/cell、Erlangs/MHz/sector、Erlangs/MHz/km²等单位。

这个数值也影响到讯息编码技术（数据压缩）、在类比电话网络也有使用。

例: 以频分多址 (FDMA)与固定频道分配(FCA)为基础的手机系统在频率再利用系数是 4的时候、各基地局可以利用的是所有频谱的1/4。

根据此推算、最大系统频谱效率（bit/s/Hz/site）是链结频谱效率的 1/4。

各基地局使用3个扇形天线将讯号分为3扇区时，被称为4/12再利用模式。

各部份可以使用全频谱的1/12，因此系统的频谱效率（bit/s/Hz/cell 或 bit/s/Hz/sector）为链结频谱效率的1/12。

即使链结频谱效率（bit/s/Hz）偏低，以”系统频谱效率”的観点来看，并不一定代表编码效率不好。

例如、分码多工(CDMA) 频谱扩散为单一通信回路(即只有依未使用者)时，
频谱效率是不好的，但是由于在同一带宽中有复数的通信回路存在，因次系统频谱效率非常好。

例: 以W-CDMA 3G 手机系统来说、打电话时最大压缩8,500 bit/s 时、会造成 5 MHz 带宽的扩散，此时此连接的吞吐量为8,500/5,000,000 = 0.0017 bit/s/Hz 。

在这情形下同扇区内可以有同时容纳100通电话(有声音)的进行。

由于各基地局以3个方向的扇形天线区分为3个扇区，在频谱扩散后、频率再利用系数会变的比1还小。

此时的系统频谱效率为 1 · 100 · 0.0017 = 0.17 bit/s/Hz/site 亦或 0.17/3 = 0.06 bit/s/Hz/cell （也可换算成 bit/s/Hz/sector ）。

频谱效率可以使用固定/动态频道分配、电力控制、 即被称为Link Adaptatio 的无线资源管理技术来进行改善。

比较表如下
表1：一般通信系统的频谱效率数值 一般通信系统
的频谱效率服
务 规格 每秒频道的带宽R (Mbit/s) 频道的带宽B (MHz) 链结频谱效率 R/B (bit/s/Hz) 典型的频率再利用系数 1/K 系统频谱效率 一般 R/B/K 数值 (bit/s/Hz/site) 第二世代手
机(2G) GSM1993
0.013·8 时隙 = 0.104
0.2 0.52 1/7 0.17 2.75G GSM+ EDGE 最大 0.384
通常 0.20
0.2
最大 1.92 通常 1.00 1/7 0.33 2.75G IS-136HS + EDGE 最大 0.384
通常 0.27
0.2
最大 1.92 通常 1.35 1/7 0.45 第三世代手机(3G) W-CDMAFDD 1997 传到手机时
最大 0.384
5
传到手机时最大 0.077 1/7 0.51 3.5G HSDPA2007 传到手机时最大 14.4 5
传到手机时
最大 2.88
1/7 0.71 3.5G HSOPAOFDMA 传到手机时10
传到手机时1/7 0.71
最大 100
最大 5 第三世代携
帯电话(3G)
CDMA20001x
传到手机时最大 0.144 1.25 传到手机时最大 0.115 1/7 0.51 Wi-Fi IEEE
802.11a/g2003
最大 54
20 最大 2.7 1/3 0.9 Wi-Fi IEEE 802.11n
Draft 2.0 2007
最大 144.4 20
最大 7.22 1/3 2.4 WiMAX
IEEE
802.162004 96 20
(1.75, 3.5,
7...)
4.8 1/4 1.2 数位广播 DAB
0.576
～ 1.152
1.712 0.34 ～ 0.67 1/5 0.08 ～ 0.17 数位广播 DAB+ SFN
0.576
～ 1.152
1.712 0.34 ～ 0.67 数位电视 DVB-T 最大 31.67
通常 22.0 8
最大 4.0 通常 2.8
1/5 0.55 数位电视 DVB-T+ SFN 最大 31.67 通常 22.0 8 最大 4.0
通常 2.8
数位电视 DVB-H 5.5 ～ 11 8
0.68 ～
1.4
1/5 0.14 ～ 0.28
数位电视 DVB-H+ SFN 5.5 ～ 11 8
0.68 ～ 1.4
光纤用数位
电视TV 256-QAM
38 6 6.33 1 6.33
Spectral efficiency
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).
Link spectral efficiency
The link spectral efficiency of a digital communication system is measured in
bit/s/Hz,[1] 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.
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 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 or Hartley's law as follows: For a signaling alphabet with M alternative symbols, each symbol represents N = log2M 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.
Example 3:An 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 (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 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 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, 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 (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/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 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.
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 per unit area, (bit/s)/Hz per cell, 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 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.
Example 8: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 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 may also be expressed as the maximum number of simultaneous phone calls per area unit over 1 MHz frequency spectrum in E/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, 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 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 per cell or sector.
The spectral efficiency can be improved by radio resource management techniques such as efficient fixed or dynamic channel allocation, power control, link adaptation and diversity schemes.
A combined fairness measure 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.
Spectral efficiency of common communication systems.
Service Standard La unc hed yea r Net bitrate R pe r carrier (Mbit/s) Bandwid
th B per carrier (MHz) Link spectral
efficiency
R/B
((bit/s)/Hz)
Typical reuse factor 1/K System
spectr
al
efficie
ncy Appro x. ((R /B )/K ) ((bit/s)
/Hz
per
site)
1Gcellular NMT 450 198
1 0.001
2 0.025 0.45 1⁄7 0.064
1Gcellular AMPS 198
3
0.0096[citatio
n needed]
0.030 0.32 1⁄7[2]0.046
2Gcellular GSM 199
1
0.013 ×8
timeslots =
0.104
0.2 0.52
1⁄
9
(1⁄3[3]in
1999)
0.17[3]
2Gcellular D-AMPS 199
1
0.013 ×3
timeslots =
0.039
0.030 1.3
1⁄
9
(1⁄3[3]in
1999)
(0.45[3]
in
1997)
2.75Gcellu
lar CDMA200
01× voice
200
Max.
0.0096 per
mobile
1.2288
0.0078 per
mobile
1
0.172
(fully
loaded)
2.75Gcellu
lar GSM+
EDGE
200
3
Max.:
0.384;
Typ.: 0.20;
0.2
Max.: 1.92;
Typ.: 1.00;
1⁄
3
0.33[3]
2.75Gcellu
lar IS-136HS +
EDGE
Max.:
0.384;
Typ.: 0.27;
0.2
Max.: 1.92;
Typ.: 1.35;
1⁄
3
0.45[3]
3Gcellular WCDMAF
DD
200
1
Max.:
0.384 per
mobile;
5
Max.: 0.077
per mobile;
1[4]0.51
3Gcellular CDMA200
01x PD
200
2
Max.:
0.153 per
mobile;
1.2288
Max.: 0.125
per mobile;
1
0.1720
(fully
loaded)
3Gcellular CDMA200
01×EV-DO
Rev.A
200
2
Max.:
3.072 per
mobile;
1.2288
Max.: 2.5
per mobile;
1
1.3
averag
e
loaded
sector
Fixed WiMAX
IEEE
802.16d
200
4
96
20 (1.75,
3.5, 7, ...)
4.8 1⁄4 1.2
3.5G cellular HSDPA
200
7
Max.: 21
per
mobile;[5]
5
Max.: 2.88
per mobile;
1[4] 4.2
3.9GMBW
A iBurstHC-
SDMA
200
5
Max.: 3.9
per carrier;
0.625
Max.: 7.23
per
carrier;[6]
1 7.23
3.9Gcellul
ar LTE
200
9
Max.:
326.4 per
mobile;
20
Max.: 16.32
per mobile;
1
Max.:
16.32;
Wi-Fi
IEEE
802.11a/g
200
3
Max.: 54; 20 Max.: 2.7; 1⁄30.9
Wi-Fi
IEEE
802.11nDra
ft 2.0
200
7
Max.:
144.4;
20 Max.: 7.22; 1⁄3 2.4
TETRA ETSI 199
8
4 timeslots
= 0.036
0.025 1.44
Digital radio DAB
199
5
0.576 to
1.152
1.712 0.34 to 0.67 1⁄5
0.08 to
0.17
Digital radio DABwith
SFN
199
5
0.576 to
1.152
1.712 0.34 to 0.67 1
0.34 to
0.67
Digital TV DVB-T 199
7
Max.:
31.67;
Typ.: 22.0;
8
Max.: 4.0;
Typ.: 2.8;
1⁄
5
0.55
Digital TV DVB-Twith
SFN
199
6
Max.:
31.67;
8
Max.: 4.0;
Typ.: 2.8;
1
Max.:
4.0;
Typ.: 22.0; Typ.:
2.8;
Digital TV DVB-H 200
7
5.5 to 11 8 0.68 to 1.4 1⁄5
0.14 to
0.28
Digital TV DVB-Hwit
h SFN
200
7
5.5 to 11 8 0.68 to 1.4 1
0.68 to
1.4
Digital cable TV DVB-C256-
QAMmode
38 6 6.33 N/A N/A
Broadban d modem ADSL2dow
nlink
12 0.962 12.47 N/A N/A
Telephone modem V.92downli
nk
199
9
0.056 0.004 14.0 N/A 14。