Guys, I need a clarification on shannon capacity equation for QAM systems with coding. Lets assume M-QAM with code rate R Let m = log2(M) My goal is to find at what SNR (Eb/No) we achieve capacity with the shannon equation. C= Wlog2(1+SNR). I am a little confused. can someone please explain with an example value of M and R Thanks H
Capacity for QAM
Started by ●March 19, 2010
Reply by ●March 19, 20102010-03-19
On Mar 19, 8:01�am, "hramcha" <hramcha@n_o_s_p_a_m.gmail.com> wrote:> Guys, > > I need a clarification on shannon capacity equation for QAM systems with > coding. > > Lets assume M-QAM with code rate R > > Let m = log2(M) > > My goal is to find at what SNR (Eb/No) we achieve capacity with the shannon > equation. > > C= Wlog2(1+SNR). > > I am a little confused. can someone please explain with an example value of > M and R > > Thanks > > HThe Shannon equation is also known as the Shannon "BOUND". As such it is the theoretical best capactiy that you can ever get for a given SNR. Any actual combination of modualtion and coding will be worse then the upper bound. So you can make a plot of the Shannon bound as a line and then your specific modulation and coding as a point and see how close your system has approached the upper bound. The Shanoon equation does not tell you the actual capacity of any particualr system, it tells you the theoretical upper limit. Mark
Reply by ●March 19, 20102010-03-19
Mark wrote:> On Mar 19, 8:01 am, "hramcha" <hramcha@n_o_s_p_a_m.gmail.com> wrote: >> Guys, >> >> I need a clarification on shannon capacity equation for QAM systems with >> coding. >> >> Lets assume M-QAM with code rate R >> >> Let m = log2(M) >> >> My goal is to find at what SNR (Eb/No) we achieve capacity with the shannon >> equation. >> >> C= Wlog2(1+SNR). >> >> I am a little confused. can someone please explain with an example value of >> M and R >> >> Thanks >> >> H > > The Shannon equation is also known as the Shannon "BOUND". As such it > is the theoretical best capactiy that you can ever get for a given > SNR. Any actual combination of modualtion and coding will be worse > then the upper bound. So you can make a plot of the Shannon bound as > a line and then your specific modulation and coding as a point and see > how close your system has approached the upper bound. > > The Shanoon equation does not tell you the actual capacity of any > particualr system, it tells you the theoretical upper limit. > > MarkMoreover, the Shannon bound isn't a bound like the wall of a room that you might lean against, or a speed limit on a freeway (that of course none of us ever exceed :-) ). It's more like the speed of light -- one can, with great effort and under special circumstances, reach this bound in this fallen and imperfect world, but it takes a lot of effort and it is fragile. In reality most systems don't approach it all that closely, and the ones that do use more elaborate modulation schemes than simple QAM. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
Reply by ●March 19, 20102010-03-19
On 3/19/2010 9:38 AM, Tim Wescott wrote:> Mark wrote: >> On Mar 19, 8:01 am, "hramcha" <hramcha@n_o_s_p_a_m.gmail.com> wrote: >>> Guys, >>> >>> I need a clarification on shannon capacity equation for QAM systems with >>> coding. >>> >>> Lets assume M-QAM with code rate R >>> >>> Let m = log2(M) >>> >>> My goal is to find at what SNR (Eb/No) we achieve capacity with the >>> shannon >>> equation. >>> >>> C= Wlog2(1+SNR). >>> >>> I am a little confused. can someone please explain with an example >>> value of >>> M and R >>> >>> Thanks >>> >>> H >> >> The Shannon equation is also known as the Shannon "BOUND". As such it >> is the theoretical best capactiy that you can ever get for a given >> SNR. Any actual combination of modualtion and coding will be worse >> then the upper bound. So you can make a plot of the Shannon bound as >> a line and then your specific modulation and coding as a point and see >> how close your system has approached the upper bound. >> >> The Shanoon equation does not tell you the actual capacity of any >> particualr system, it tells you the theoretical upper limit. >> >> Mark > > Moreover, the Shannon bound isn't a bound like the wall of a room that > you might lean against, or a speed limit on a freeway (that of course > none of us ever exceed :-) ). It's more like the speed of light -- one > can, with great effort and under special circumstances, reach this bound > in this fallen and imperfect world, but it takes a lot of effort and it > is fragile. In reality most systems don't approach it all that closely, > and the ones that do use more elaborate modulation schemes than simple QAM. >There've been some BPSK and QPSK systems that have gotten within a dB or so (or even less) of capacity. It's not trivial to maintain synchronization at that low of an SNR, but it has been done. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
Reply by ●March 19, 20102010-03-19
On Mar 19, 11:38�am, Tim Wescott <t...@seemywebsite.now> wrote:> > Moreover, the Shannon bound isn't a bound like the wall of a room that > you might lean against, or a speed limit on a freeway (that of course > none of us ever exceed :-) ). �It's more like the speed of light -- one > can, with great effort and under special circumstances, reach this bound > in this fallen and imperfect world, but it takes a lot of effort and it > is fragile. �In reality most systems don't approach it all that closely, > and the ones that do use more elaborate modulation schemes than simple QAM. >Actually, the Shannon bound *is* like a speed limit on a freeway. It is quite possible for a communication system to transmit at rates above the rate given by Shannon's capacity formula just as it is possible to exceed the speed limit on the freeway. It is just that it is impossible to transmit **reliably** at rates above the capacity. If one wants to continue the analogy, it is not possible to exceed the speed limit and simultaneously achieve good gas mileage. For any given transmit power and bandwidth (and noise spectral density), if 16-QAM gives good error rates at (say) 50% of the Shannon capacity, then using 1024-QAM with the same transmit power, symbol rate (and hence bandwidth) will give a system that will operate at 125% of the Shannon capacity. Of course, the BER will be so close to 50% that nobody will want to use such a system, but hey, it *is* transmitting 10 bits per symbol rather than 4, and *is* operating above capacity as was wanted. Who cares about the BER? Hope this muddies the waters further... --Dilip Sarwate
Reply by ●March 20, 20102010-03-20
dvsarwate wrote:> ... it is not possible to exceed the speed limit and > simultaneously achieve good gas mileage. ...Actually, Dilip, I noticed a different effect with two of my cars. They seemed to use a pretty constant amount of fuel for a given length of time. The faster I went, the further a gallon took me. Go figure! Jerry -- Discovery consists of seeing what everybody has seen, and thinking what nobody has thought. .. Albert Szent-Gyorgi �����������������������������������������������������������������������
Reply by ●March 20, 20102010-03-20
On Mar 19, 10:18�pm, Jerry Avins <j...@ieee.org> wrote:> dvsarwate wrote: > > ... it is not possible to exceed the speed limit and > > simultaneously achieve good gas mileage. �... > > Actually, Dilip, I noticed a different effect with two of my cars. They > seemed to use a pretty constant amount of fuel for a given length of > time. The faster I went, the further a gallon took me. Go figure! > > Jerry > -- > Discovery consists of seeing what everybody has seen, and thinking what > nobody has thought. � �.. Albert Szent-Gyorgi > �����������������������������������������������������������������������75% of car accidents occur within 5 miles of home. So, one should be more careful while driving in the neighborhood? No, one should drive as fast as possible upon leaving home so as to get out of the danger zone as quickly as possible and enter the "safe" zone 5 miles away. --Dilip Sarwate
Reply by ●March 20, 20102010-03-20
>On Mar 19, 10:18=A0pm, Jerry Avins <j...@ieee.org> wrote: >> dvsarwate wrote: >> > ... it is not possible to exceed the speed limit and >> > simultaneously achieve good gas mileage. =A0... >> >> Actually, Dilip, I noticed a different effect with two of my cars. They >> seemed to use a pretty constant amount of fuel for a given length of >> time. The faster I went, the further a gallon took me. Go figure! >> >> Jerry >> -- >> Discovery consists of seeing what everybody has seen, and thinking what >> nobody has thought. =A0 =A0.. Albert Szent-Gyorgi > >75% of car accidents occur within 5 miles of home. >So, one should be more careful while driving in the >neighborhood? No, one should drive as fast as possible >upon leaving home so as to get out of the danger zone >as quickly as possible and enter the "safe" zone 5 miles >away.Why not move 5 miles away, to a safer place? Steve
Reply by ●March 20, 20102010-03-20
On 20 Mar, 02:24, dvsarwate <dvsarw...@gmail.com> wrote:> �Of course, the > BER will be so close to 50% that nobody will want to use such a > system, > but hey, it *is* transmitting 10 bits per symbol rather than 4, and > *is* > operating above capacity as was wanted. �Who cares about the BER?This argument plays straight into the hands of the enviro-mentalists: If the BER is roughly 50% in the first place, why transmit at all? One can just install random bit generator at the reciever, and do away with the transmitter. Doing away with the RF stages in both ends will save tremendeous amounts of power, extending battery life with who know how many times. And of course, this scheme will be robust with respect to just about any external influence, be it intereference, multipath or anything else. Rune
Reply by ●March 20, 20102010-03-20
dvsarwate wrote:>On Mar 19, 10:18=A0pm, Jerry Avins <j...@ieee.org> wrote: >> dvsarwate wrote: >> > ... it is not possible to exceed the speed limit and >> > simultaneously achieve good gas mileage. =A0... >> >> Actually, Dilip, I noticed a different effect with two of my cars. They >> seemed to use a pretty constant amount of fuel for a given length of >> time. The faster I went, the further a gallon took me. Go figure! >> > > >75% of car accidents occur within 5 miles of home. >So, one should be more careful while driving in the >neighborhood? No, one should drive as fast as possible >upon leaving home so as to get out of the danger zone >as quickly as possible and enter the "safe" zone 5 miles >away.How is that related to gas mileage, your original argument? Anyway, there are any number of factors why that might happen, including the pdf of your car's position/time having its strongest amplitude near home. Plus, for whatever reason, people like to roll through stop signs in neighborhoods, but are more careful with other stop signs. To throw a wrench in things, there is also an accident factor if you're driving at a significantly different speed than the rest of traffic. When the envirowackos pressured Houston to drop its freeway speed limits to 55mph about a decade ago, just about everybody ignored the change (and even the police chief was unhappy with it), and it was fairly dangerous for the twerps who actually did drop their speed (particularly since so many idiots here feel entitled to drive slowly in the left lane, but that's another story). Fortunately, it got changed back.
