Shannon's upper bound for AWGN channel, but what about Multipath?
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From: Mark on 7 Apr 2010 10:11 My question is about the Shannon bound.. The Shannon bound tells us the upper limit of information capacity for a given AWGN channel bandwidth and and available power. For any given AWGN channel BW there is an optimum modulation order and coding to get the best throughput for a given available power. The Shannon bound tells us this upper limit of capacity for that AWGN channel. What about a dispersive channel with multipath. Does the Shannon bound apply to these channels as well or is there a different fundamental lower limit to the channel capacity due to multipath? If there is a fundamental lower limit, is there an analytical experssion for the new lower limit? (assuming the multipath can be quantified) thanks Mark
From: Rune Allnor on 7 Apr 2010 10:42 On 7 apr, 16:11, Mark <makol...(a)yahoo.com> wrote: > My question is about the Shannon bound.. > > The Shannon bound tells us the upper limit of information capacity for > a given AWGN channel bandwidth and and available power. For any > given AWGN channel BW there is an optimum modulation order and coding > to get the best throughput for a given available power. The Shannon > bound tells us this upper limit of capacity for that AWGN channel. > > What about a dispersive channel with multipath. Does the Shannon > bound apply to these channels as well or is there a different > fundamental lower limit to the channel capacity due to multipath? > > If there is a fundamental lower limit, is there an analytical > experssion for the new lower limit? (assuming the multipath can be > quantified) The multipath will introduce a noise source correlated with the signal of interest, which will not improve transmission. From there on, it will be a question about the exact nature of the multipath scenario, i.e. whether the main parameters are known or not (e.g. Tx/Rx heights above a reflecting plane), and random factors (e.g. terrain features or other surface roughness of the reflecting plane). Similar arguments apply to the dispercive case. So it might be wise to view the Shannon limit as an absolutely best case in the ideal scenario, and then introduce scenario parameters as further limitations to be examined on a case by case basis. Rune
From: Vladimir Vassilevsky on 7 Apr 2010 10:51 Mark wrote: > My question is about the Shannon bound.. > > The Shannon bound tells us the upper limit of information capacity for > a given AWGN channel bandwidth and and available power. For any > given AWGN channel BW there is an optimum modulation order and coding > to get the best throughput for a given available power. The Shannon > bound tells us this upper limit of capacity for that AWGN channel. > > What about a dispersive channel with multipath. Does the Shannon > bound apply to these channels as well or is there a different > fundamental lower limit to the channel capacity due to multipath? Multipath is just a linear filter. If multipath is perfectly accounted for on transmit and receive sides, you calculate the Shannon limit by integration through the bandwidth. However, the estimate of the channel is always imperfect, and you can account for that imperfection as the equvalent reduction in the SNR. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
From: Marco.Pausini on 8 Apr 2010 04:55 Actually the answer is a bit more complicated. The capacity of a time-invariant multipath channel is not given by a single formula, but it depends on what the transmitter and receiver know about the channel. Also, the definition of channel capacity for fading channels is not unique. Finally, capacity of a time-varying multipath channel is unknown in general, although it can be approximated. For an introduction to this topic, refer to "Wireless Communications", A. Goldsmith, Chapter 4. Marco
From: Mark on 12 Apr 2010 12:17
On Apr 8, 4:55 am, "Marco.Pausini" <marco.pausini(a)n_o_s_p_a_m.gmail.com> wrote: > Actually the answer is a bit more complicated. > > The capacity of a time-invariant multipath channel is not given by a single > formula, but it depends on what the transmitter and receiver know about the > channel. Also, the definition of channel capacity for fading channels is > not unique. Finally, capacity of a time-varying multipath channel is > unknown in general, although it can be approximated. > > For an introduction to this topic, refer to "Wireless Communications", A. > Goldsmith, Chapter 4. > > Marco thanks to all for the comments... It seems if the receiver can sort out the mess, the more rays you get the more signal power you get so in theory the channel capacity should improve... of course in practice, it's a mess.. Mark |