BER and Noise Bandwidth
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From: bando on 17 Jun 2010 17:23 Hi, I have a question related to bit error rate and noise bandwidth. In a digital communications link that utilizes a matched filter design, a key factor in the filter design is the choice of an excess bandwidth parameter. This term affects whether or not the filter may be implementable, and also affects the occupied bandwidth of the signal. Larger excess bandwidth means more occupied bandwidth. The occupied bandwidth B is usually given in the form: B = (1+alpha)*Rs where alpha is said to be the excess bandwidth parameter and Rs is the symbol rate. alpha is unitless and both B and Rs have units of Hz. My question is, in computing the noise bandwidth to determine the expected signal to noise ratio, does one use the value Rs or the value B? In simulations with BPSK signals using a root-raised cosine matched filter design with a flat channel and AWGN I have matched the BER vs. Eb/N0 response using a variety of values for alpha and assuming Rs for the noise bandwidth. The simulation is largely insensitive to the choice of alpha. The results match the theoretical error curve nicely. This leads me to think the correct answer is to use Rs, regardless of alpha (and corresponding B). I am puzzled as to why this is the case since increasing alpha (and B) does allow more noise power into the detector. The only answer I can come up with (and I'm not satisfied hence the post) is that the downsampling of the received signal to one ideal sample (at max eye opening) per symbol must perform a filtering function that removes extra noise. Are my answer and justification correct? Is there a good published source I can use for verification/validation? Thanks for your help! ~Bando The actual bandwidth
From: Vladimir Vassilevsky on 17 Jun 2010 21:07 bando wrote: > Hi, > > I have a question related to bit error rate and noise bandwidth. In a > digital communications link that utilizes a matched filter design, a key > factor in the filter design is the choice of an excess bandwidth parameter. Wrong > This term affects whether or not the filter may be implementable, and also > affects the occupied bandwidth of the signal. Larger excess bandwidth > means more occupied bandwidth. The occupied bandwidth B is usually given > in the form: > > B = (1+alpha)*Rs > > where alpha is said to be the excess bandwidth parameter and Rs is the > symbol rate. alpha is unitless and both B and Rs have units of Hz. > > My question is, in computing the noise bandwidth to determine the expected > signal to noise ratio, does one use the value Rs or the value B? Neither. The noise is integrated from 0 to inf through the matched filter. You can convert this into the equvalent flat noise bandwidth. > In simulations with BPSK signals using a root-raised cosine matched filter > design with a flat channel and AWGN I have matched the BER vs. Eb/N0 > response using a variety of values for alpha and assuming Rs for the noise > bandwidth. The simulation is largely insensitive to the choice of alpha. > The results match the theoretical error curve nicely. > > This leads me to think the correct answer is to use Rs, regardless of alpha > (and corresponding B). No. > I am puzzled as to why this is the case since > increasing alpha (and B) does allow more noise power into the detector. No. > The only answer I can come up with (and I'm not satisfied hence the post) > is that the downsampling of the received signal to one ideal sample (at max > eye opening) per symbol must perform a filtering function that removes > extra noise. Matched filter = OPTIMAL filter. Does this ring a bell in your head ? > Are my answer and justification correct? No way. > Is there a good published source > I can use for verification/validation? A textbook on digital commucation such as Sklar or Proakis ? VLV
From: bando on 17 Jun 2010 22:30 VLV, Your post was not very helpful. Could you be more specific? Saying no, and wrong does not help me to learn. ~Bando
From: Jerry Avins on 17 Jun 2010 23:40 On 6/17/2010 10:30 PM, bando wrote: > VLV, > > Your post was not very helpful. Could you be more specific? Saying no, > and wrong does not help me to learn. Be grateful for what you get. Dispelling misconceptions is a valuable service. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
From: dvsarwate on 18 Jun 2010 11:48 On Jun 17, 10:40 pm, Jerry Avins <j...(a)ieee.org> wrote: > > Be grateful for what you get. Dispelling misconceptions is a valuable > service. > When the pulse shape (and corresponding matched filter) is a root-raised-cosine signal, the noise-equivalent bandwidth (or equivalent flat noise bandwidth referred to by VLV) is Rs regardless of the value of alpha, 0 <= alpha <= 1. Increasing the value of alpha does increase B, but the additional noise let in by this increase in bandwidth is offset *exactly* by the decrease in the noise in the central portion of the band, that is, the noise-equivalent bandwidth is the same (Rs) regardless of the value of alpha. From this, the OP jumped to the more general (and incorrect) assumption that the noise equivalent bandwidth is always Rs, regardless of the pulse shape, and to this statement, VLV quite correctly and briefly responded No. Perhaps my more verbose statement will help dispel one or more of the OP's misconceptions, but I can only second VLV's suggestion that the OP consult a good book on digital communications, and VLV also suggested two good books to look at. In other words, the OP's assertion that VLV's post was not very helpful is also incorrect. VLV gave good (and free) advice. --Dilip Sarwate
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