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In [[digital communications]], a '''turbo equalizer''' is a type of [[Receiver (information theory)|receiver]] used to receive a message corrupted by a [[Channel (communications)|communication channel]] with [[intersymbol interference]] (ISI). It approaches the performance of a [[maximum a posteriori]] (MAP) receiver via iterative [[message passing]] between a [[soft-in soft-out]] (SISO) [[Equalizer (communications)|equalizer]] and a SISO [[decoder]].<ref>R. Koetter, A.C. Singer, and M. Tüchler [http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1267050 ''Turbo Equalization''] IEEE Signal Processing Mag., vol. 21, no. 1, pp. 67–80, Jan. 2004.</ref> It is closely related to [[turbo codes]], as a turbo equalizer may be considered a turbo decoder if the channel is viewed as a [[convolutional code]]. | |||
==History== | |||
In 1993, [[turbo codes]] were introduced by [[Claude Berrou|Berrou]], [[Alain Glavieux|Glavieux]], and [[Punya Thitimajshima|Thitimajshima]].<ref>{{Citation|url=http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=397441 |first=Claude|first2=Alain|first3=Punya|last=Berrou|last2=Glavieux|last3=Thitimajshima|title=Near Shannon Limit Error – Correcting}} International Conference on Communications, 1993.</ref> In 1995, the turbo principle, which was developed for turbo codes, was applied to an equalizer by [[Catherine Douillard|Douillard]], [[Michel Jézéquel|Jézéquel]], and [[Claude Berrou|Berrou]].<ref>{{Citation| url=http://www3.interscience.wiley.com/journal/121408109/abstract |first=Catherine|first2=Michel|first3=Claude|last=Douillard|last2=Jézéquel|last3= Berrou|title=Iterative Correction of Intersymbol-Interference: Turbo-Equalization}} European Transactions on Telecommunications, vol. 6, no. 5, pp. 507-511, September–October 1995.</ref> They formulated the ISI receiver problem as a turbo code decoding problem, where the channel is thought of as a rate 1 convolutional code and the error correction coding is the second code. In 1997, [[Alain Glavieux|Glavieux]], [[Christophe Laot|Laot]], and [[Joël Labat|Labat]] demonstrated that a linear equalizer could be used in a turbo equalizer framework.<ref>A. Glavieux, C. Laot, and J. Labat, [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.6389 “Turbo equalization over a frequency selective channel,”] in Proc. Int. Symp. Turbo Codes, Brest, France, Sept. 1997, pp. 96–102.</ref> This discovery made turbo equalization computationally efficient enough to be applied to a wide range of applications.<ref>M. Tüchler, R. Koetter, and A.C. Singer, “[http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.8619 Turbo Equalization: Principles and New Results],” IEEE Transactions on Communications, vol. 50, no. 5, pp. 754-767, May 2002.</ref> | |||
== Overview == | |||
=== Standard Communication System Overview === | |||
Before discussing turbo equalizers, it is necessary to understand the basic receiver in the context of a communication system. This is the topic of this section. | |||
At the [[transmitter]], information [[bit]]s are [[code|encoded]]. Encoding adds redundancy by mapping the information bits <math>a</math> to a longer bit vector – the code bit vector <math>b</math>. The encoded bits <math>b</math> are then [[forward error correction#Interleaving|interleaved]]. Interleaving permutes the order of the code bits <math>b</math> resulting in bits <math>c</math>. The main reason for doing this is to insulate the information bits from bursty noise. Next, the symbol mapper maps the bits <math>c</math> into [[Modulation|complex symbols]] <math>x</math>. These digital symbols are then converted into analog symbols with an [[Digital-to-analog converter|D/A converter]]. Typically the signal is then [[Radio frequency upconverter|up-converted]] to pass band frequencies by mixing it with a [[Carrier wave|carrier]] signal. This is a necessary step for complex symbols. The signal is then ready to be transmitted through the [[Channel (communications)|channel]]. | |||
At the [[Receiver (information theory)|receiver]], the operations performed by the transmitter are reversed to recover <math>\hat{a}</math>, an estimate of the information bits. The [[Digital down converter|down-converter]] mixes the signal back down to baseband. The [[Analog-to-digital converter|A/D converter]] then samples the analog signal, making it digital. At this point, <math>y</math> is recovered. The signal <math>y</math> is what would be received if <math>x</math> were transmitted through the digital [[baseband]] equivalent of the channel plus [[Noise (electronics)|noise]]. The signal is then [[Equalizer (communications)|equalized]]. The equalizer attempts to unravel the [[Intersymbol interference|ISI]] in the received signal to recover the transmitted symbols. It then outputs the bits <math>\hat{c}</math> associated with those symbols. The vector <math>\hat{c}</math> may represent hard decisions on the bits or soft decisions. If the equalizer makes soft decisions, it outputs information relating to the probability of the bit being a 0 or a 1. If the equalizer makes hard decisions on the bits, it quantizes the soft bit decisions and outputs either a 0 or a 1. Next, the signal is deinterleaved which is a simple permutation transformation that undoes the transformation the interleaver executed. Finally, the bits are decoded by the decoder. The [[decoder]] estimates <math>\hat{a}</math> from <math>\hat{b}</math>. | |||
A diagram of the communication system is shown below. In this diagram, the channel is the equivalent baseband channel, meaning that it encompasses the D/A, the up converter, the channel, the down converter, and the A/D. | |||
[[Image:COMMblockdiagram.png|none]] | |||
===Turbo Equalizer Overview=== | |||
The block diagram of a communication system employing a turbo equalizer is shown below. The turbo equalizer encompasses the equalizer, the decoder, and the blocks in between. | |||
[[Image:TEQUdiagram.png|none]] | |||
The difference between a turbo equalizer and a standard equalizer is the feedback loop from the decoder to the equalizer. Due to the structure of the code, the decoder not only estimates the information bits <math>a</math>, but it also discovers new information about the coded bits <math>b</math>. The decoder is therefore able to output extrinsic information, <math>\tilde{b}</math> about the likelihood that a certain code bit stream was transmitted. Extrinsic information is new information that is not derived from information input to the block. This extrinsic information is then mapped back into information about the transmitted symbols <math>x</math> for use in the equalizer. These extrinsic symbol likelihoods, <math>\tilde{x}</math>, are fed into the equalizer as ''a priori'' symbol probabilities. The equalizer uses this ''a priori'' information as well as the input signal <math>y</math> to estimate extrinsic probability information about the transmitted symbols. The ''a priori'' information fed to the equalizer is initialized to 0, meaning that the initial estimate <math>\hat{a}</math> made by the turbo equalizer is identical to the estimate made by the standard receiver. The information <math>\hat{x}</math> is then mapped back into information about <math>b</math> for use by the decoder. The turbo equalizer repeats this iterative process until a stopping criterion is reached. | |||
===Turbo Equalization in Practical Systems=== | |||
In practical turbo equalization implementations, an additional issue need to be considered. The ''[[channel state information]] (CSI)'' that the equalizer operates on comes from some channel estimation technique, and hence un-reliable. Firstly, in order to improve the reliability of the CSI, it is desirable to include the channel estimation block also into the turbo equalization loop, and parse soft or hard decision directed channel estimation within each turbo equalization iteration.<ref>M. Sandell, C. Luschi, P. Strauch, and R.Yan, “Iterative Data Detection | |||
and Channel Estimation for Advanced TDMA Systems,” IEEE GLOBECOM, Australia, pp. 3728–3733, Nov 1998.</ref><ref>S. Y. Park and C. G. Kang, “Complexity-Reduced Iterative MAP Receiver for Interference Suppression in OFDM-Based Spatial Multiplexing Systems,” IEEE Transactions on Vehicular Technology, vol. 53, pp. 1316–1326, Sep 2004.</ref> Secondly, incorporating the presence of CSI uncertainty into the turbo equalizer design leads to a more robust approach with significant performance gains in practical scenarios.<ref>M. Danish Nisar and Wolfgang Utschick. [http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5672616 "Minimax Robust A-priori Information Aware Channel Equalization"], in IEEE Transactions on Signal Processing, Volume 59, pp 1734 - 1745, April 2011.</ref><ref>N. Kalantarova, S. S. Kozat, and A. T. Erdogan, “Robust Turbo Equalization Under Channel Uncertainties,” IEEE | |||
Transactions on Signal Processing, 2012.</ref> | |||
== References == | |||
<references /> | |||
== External links == | |||
* [http://www.turboequalization.net/ Turbo Equalization Resources] includes an annotated bibliography, interactive block diagram, and turbo equalization simulation code. | |||
* [http://www.ifp.illinois.edu/~singer/journalpapers/koetter_2004.pdf Turbo Equalization] a Signal Processing Magazine primer on turbo equalization. Since it was written for the signal processing community in general, it is relatively accessible. | |||
* [http://www.ifp.illinois.edu/~singer/journalpapers/tuchler_2002a.pdf Turbo Equalization: Principles and New Results] an IEEE Transactions on Communications journal article that offers a detailed, clear explanation of turbo equalization. | |||
==See also== | |||
*[[Equalizer (communications)]] | |||
{{DEFAULTSORT:Turbo Equalizer}} | |||
[[Category:Telecommunication theory]] | |||
[[Category:Signal processing]] | |||
Revision as of 07:56, 4 February 2014
In digital communications, a turbo equalizer is a type of receiver used to receive a message corrupted by a communication channel with intersymbol interference (ISI). It approaches the performance of a maximum a posteriori (MAP) receiver via iterative message passing between a soft-in soft-out (SISO) equalizer and a SISO decoder.[1] It is closely related to turbo codes, as a turbo equalizer may be considered a turbo decoder if the channel is viewed as a convolutional code.
History
In 1993, turbo codes were introduced by Berrou, Glavieux, and Thitimajshima.[2] In 1995, the turbo principle, which was developed for turbo codes, was applied to an equalizer by Douillard, Jézéquel, and Berrou.[3] They formulated the ISI receiver problem as a turbo code decoding problem, where the channel is thought of as a rate 1 convolutional code and the error correction coding is the second code. In 1997, Glavieux, Laot, and Labat demonstrated that a linear equalizer could be used in a turbo equalizer framework.[4] This discovery made turbo equalization computationally efficient enough to be applied to a wide range of applications.[5]
Overview
Standard Communication System Overview
Before discussing turbo equalizers, it is necessary to understand the basic receiver in the context of a communication system. This is the topic of this section.
At the transmitter, information bits are encoded. Encoding adds redundancy by mapping the information bits to a longer bit vector – the code bit vector . The encoded bits are then interleaved. Interleaving permutes the order of the code bits resulting in bits . The main reason for doing this is to insulate the information bits from bursty noise. Next, the symbol mapper maps the bits into complex symbols . These digital symbols are then converted into analog symbols with an D/A converter. Typically the signal is then up-converted to pass band frequencies by mixing it with a carrier signal. This is a necessary step for complex symbols. The signal is then ready to be transmitted through the channel.
At the receiver, the operations performed by the transmitter are reversed to recover , an estimate of the information bits. The down-converter mixes the signal back down to baseband. The A/D converter then samples the analog signal, making it digital. At this point, is recovered. The signal is what would be received if were transmitted through the digital baseband equivalent of the channel plus noise. The signal is then equalized. The equalizer attempts to unravel the ISI in the received signal to recover the transmitted symbols. It then outputs the bits associated with those symbols. The vector may represent hard decisions on the bits or soft decisions. If the equalizer makes soft decisions, it outputs information relating to the probability of the bit being a 0 or a 1. If the equalizer makes hard decisions on the bits, it quantizes the soft bit decisions and outputs either a 0 or a 1. Next, the signal is deinterleaved which is a simple permutation transformation that undoes the transformation the interleaver executed. Finally, the bits are decoded by the decoder. The decoder estimates from .
A diagram of the communication system is shown below. In this diagram, the channel is the equivalent baseband channel, meaning that it encompasses the D/A, the up converter, the channel, the down converter, and the A/D.
Turbo Equalizer Overview
The block diagram of a communication system employing a turbo equalizer is shown below. The turbo equalizer encompasses the equalizer, the decoder, and the blocks in between.
The difference between a turbo equalizer and a standard equalizer is the feedback loop from the decoder to the equalizer. Due to the structure of the code, the decoder not only estimates the information bits , but it also discovers new information about the coded bits . The decoder is therefore able to output extrinsic information, about the likelihood that a certain code bit stream was transmitted. Extrinsic information is new information that is not derived from information input to the block. This extrinsic information is then mapped back into information about the transmitted symbols for use in the equalizer. These extrinsic symbol likelihoods, , are fed into the equalizer as a priori symbol probabilities. The equalizer uses this a priori information as well as the input signal to estimate extrinsic probability information about the transmitted symbols. The a priori information fed to the equalizer is initialized to 0, meaning that the initial estimate made by the turbo equalizer is identical to the estimate made by the standard receiver. The information is then mapped back into information about for use by the decoder. The turbo equalizer repeats this iterative process until a stopping criterion is reached.
Turbo Equalization in Practical Systems
In practical turbo equalization implementations, an additional issue need to be considered. The channel state information (CSI) that the equalizer operates on comes from some channel estimation technique, and hence un-reliable. Firstly, in order to improve the reliability of the CSI, it is desirable to include the channel estimation block also into the turbo equalization loop, and parse soft or hard decision directed channel estimation within each turbo equalization iteration.[6][7] Secondly, incorporating the presence of CSI uncertainty into the turbo equalizer design leads to a more robust approach with significant performance gains in practical scenarios.[8][9]
References
- ↑ R. Koetter, A.C. Singer, and M. Tüchler Turbo Equalization IEEE Signal Processing Mag., vol. 21, no. 1, pp. 67–80, Jan. 2004.
- ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010 International Conference on Communications, 1993. - ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010 European Transactions on Telecommunications, vol. 6, no. 5, pp. 507-511, September–October 1995. - ↑ A. Glavieux, C. Laot, and J. Labat, “Turbo equalization over a frequency selective channel,” in Proc. Int. Symp. Turbo Codes, Brest, France, Sept. 1997, pp. 96–102.
- ↑ M. Tüchler, R. Koetter, and A.C. Singer, “Turbo Equalization: Principles and New Results,” IEEE Transactions on Communications, vol. 50, no. 5, pp. 754-767, May 2002.
- ↑ M. Sandell, C. Luschi, P. Strauch, and R.Yan, “Iterative Data Detection and Channel Estimation for Advanced TDMA Systems,” IEEE GLOBECOM, Australia, pp. 3728–3733, Nov 1998.
- ↑ S. Y. Park and C. G. Kang, “Complexity-Reduced Iterative MAP Receiver for Interference Suppression in OFDM-Based Spatial Multiplexing Systems,” IEEE Transactions on Vehicular Technology, vol. 53, pp. 1316–1326, Sep 2004.
- ↑ M. Danish Nisar and Wolfgang Utschick. "Minimax Robust A-priori Information Aware Channel Equalization", in IEEE Transactions on Signal Processing, Volume 59, pp 1734 - 1745, April 2011.
- ↑ N. Kalantarova, S. S. Kozat, and A. T. Erdogan, “Robust Turbo Equalization Under Channel Uncertainties,” IEEE Transactions on Signal Processing, 2012.
External links
- Turbo Equalization Resources includes an annotated bibliography, interactive block diagram, and turbo equalization simulation code.
- Turbo Equalization a Signal Processing Magazine primer on turbo equalization. Since it was written for the signal processing community in general, it is relatively accessible.
- Turbo Equalization: Principles and New Results an IEEE Transactions on Communications journal article that offers a detailed, clear explanation of turbo equalization.