I have read a lot about the cyclic prefix used in OFDM, to combat ISI due to multipath. I think I somewhat understand this. You make your guard interval longer that the delay spread, so 1 symbol leaks energy into the next only within that guard interval. However, doesnt intra-symbol interference still exist, that is the same symbol interefering with itself due to being received within that delay spread period and so those phase shifts may add up destructively.How is this taken care of? Does this make sense, or am I missing some key concept in understanding ISi and guard intervals.
OFDM and ISI
Started by ●March 15, 2007
Reply by ●March 15, 20072007-03-15
On Mar 16, 12:18 am, "Zeph80" <surabhi_tal...@hotmail.com> wrote:> I have read a lot about the cyclic prefix used in OFDM, to combat ISI due > to multipath. I think I somewhat understand this. You make your guard > interval longer that the delay spread, so 1 symbol leaks energy into the > next only within that guard interval. However, doesnt intra-symbol > interference still exist, that is the same symbol interefering with itself > due to being received within that delay spread period and so those phase > shifts may add up destructively.How is this taken care of? Does this make > sense, or am I missing some key concept in understanding ISi and guard > intervals.Let me try to give you a slightly different picture. Sinusoidal signals are eigen-functions of LTI systems. So, in OFDM, we take IFFT and send "sinusoids" over the channel. Now, assuming that the channel is an LTI system, take a cyclic prefix of more than the channel length. Now, the OFDM symbol is of the form: (x[N - L], x[N - L + 1], ... x[N - 1], x[0], x[1], ..., x[N - 1]) if I use L-1 length cyclic prefix. Again, after convolving with the channel, what would happen is that in the OFDM symbol, zoom in t the region where x[0], x[1] etc. are present. There, you would get y[n]'s which are linear combinations of x[n], x[n - 1] .. x[n-M-1] if the channel has length M. For example, y[0] = h[0]x[0] + h[1]x[N - 1] + ... + h[M - 1]x[N - M - 1] Notice that this is due to the cyclic prefix coming in. So, the above form of convolution is nothing but circular convoution, at least within the symbols of interest. Using the fact that for periodic (or periodically extended sequences), DFT(y) = DFT(x) * DFT(h), all you do is estimate h (or DFT(h)) using some means, such as a pilot. Then, just the reciprocal of DFT(h) becomes a simple equalizer, though there are better methods which I am not aware of as of now. HTH. Kumar
Reply by ●March 16, 20072007-03-16
>On Mar 16, 12:18 am, "Zeph80" <surabhi_tal...@hotmail.com> wrote: >> I have read a lot about the cyclic prefix used in OFDM, to combat ISIdue>> to multipath. I think I somewhat understand this. You make your guard >> interval longer that the delay spread, so 1 symbol leaks energy intothe>> next only within that guard interval. However, doesnt intra-symbol >> interference still exist, that is the same symbol interefering withitself>> due to being received within that delay spread period and so thosephase>> shifts may add up destructively.How is this taken care of? Does thismake>> sense, or am I missing some key concept in understanding ISi and guard >> intervals. > >Let me try to give you a slightly different picture. Sinusoidal >signals are eigen-functions of LTI systems. So, in OFDM, we take IFFT >and send "sinusoids" over the channel. Now, assuming that the channel >is an LTI system, take a cyclic prefix of more than the channel >length. Now, the OFDM symbol is of the form: > >(x[N - L], x[N - L + 1], ... x[N - 1], x[0], x[1], ..., x[N - 1]) > >if I use L-1 length cyclic prefix. Again, after convolving with the >channel, what would happen is that in the OFDM symbol, zoom in t the >region where x[0], x[1] etc. are present. There, you would get y[n]'s >which are linear combinations of x[n], x[n - 1] .. x[n-M-1] if the >channel has length M. For example, > >y[0] = h[0]x[0] + h[1]x[N - 1] + ... + h[M - 1]x[N - M - 1] > >Notice that this is due to the cyclic prefix coming in. So, the above >form of convolution is nothing but circular convoution, at least >within the symbols of interest. Using the fact that for periodic (or >periodically extended sequences), > >DFT(y) = DFT(x) * DFT(h), > >all you do is estimate h (or DFT(h)) using some means, such as a >pilot. Then, just the reciprocal of DFT(h) becomes a simple equalizer, >though there are better methods which I am not aware of as of now. > >HTH. > >Kumar > >I know that the contents of the cyclic prefix, are relevant. But just that fact that it exists as a guard interval also has a significance in terms of the multipath. Are you saying that assuming we didnt have to have the last contents copied into the cyclic prefix portion ( so just some random guard time), the answer to my question is that we still need some form of equalization to prevent intra-symbol interference. And does inducing circular convolution ( by using those specific cyclic pefix contents) make channel estimation and hence equalization easier?
Reply by ●March 16, 20072007-03-16
>>On Mar 16, 12:18 am, "Zeph80" <surabhi_tal...@hotmail.com> wrote: >>> I have read a lot about the cyclic prefix used in OFDM, to combat ISI >due >>> to multipath. I think I somewhat understand this. You make your guard >>> interval longer that the delay spread, so 1 symbol leaks energy into >the >>> next only within that guard interval. However, doesnt intra-symbol >>> interference still exist, that is the same symbol interefering with >itself >>> due to being received within that delay spread period and so those >phase >>> shifts may add up destructively.How is this taken care of? Does this >make >>> sense, or am I missing some key concept in understanding ISi andguard>>> intervals. >> >>Let me try to give you a slightly different picture. Sinusoidal >>signals are eigen-functions of LTI systems. So, in OFDM, we take IFFT >>and send "sinusoids" over the channel. Now, assuming that the channel >>is an LTI system, take a cyclic prefix of more than the channel >>length. Now, the OFDM symbol is of the form: >> >>(x[N - L], x[N - L + 1], ... x[N - 1], x[0], x[1], ..., x[N - 1]) >> >>if I use L-1 length cyclic prefix. Again, after convolving with the >>channel, what would happen is that in the OFDM symbol, zoom in t the >>region where x[0], x[1] etc. are present. There, you would get y[n]'s >>which are linear combinations of x[n], x[n - 1] .. x[n-M-1] if the >>channel has length M. For example, >> >>y[0] = h[0]x[0] + h[1]x[N - 1] + ... + h[M - 1]x[N - M - 1] >> >>Notice that this is due to the cyclic prefix coming in. So, the above >>form of convolution is nothing but circular convoution, at least >>within the symbols of interest. Using the fact that for periodic (or >>periodically extended sequences), >> >>DFT(y) = DFT(x) * DFT(h), >> >>all you do is estimate h (or DFT(h)) using some means, such as a >>pilot. Then, just the reciprocal of DFT(h) becomes a simple equalizer, >>though there are better methods which I am not aware of as of now. >> >>HTH. >> >>Kumar >> >> > >I know that the contents of the cyclic prefix, are relevant. But justthat>fact that it exists as a guard interval also has a significance in termsof>the multipath. Are you saying that assuming we didnt have to have thelast>contents copied into the cyclic prefix portion ( so just some randomguard>time), the answer to my question is that we still need some form of >equalization to prevent intra-symbol interference. >And does inducing circular convolution ( by using those specific cyclic >pefix contents) make channel estimation and hence equalization easier? > > >Yes, because the equalizer will be single tap, just dividing by DFT(h).
Reply by ●March 16, 20072007-03-16
Zeph80 wrote:> I have read a lot about the cyclic prefix used in OFDM, to combat ISI due > to multipath. I think I somewhat understand this. You make your guard > interval longer that the delay spread, so 1 symbol leaks energy into the > next only within that guard interval. However, doesnt intra-symbol > interference still exist, that is the same symbol interefering with itself > due to being received within that delay spread period and so those phase > shifts may add up destructively.How is this taken care of? Does this make > sense, or am I missing some key concept in understanding ISi and guard > intervals.The same symbol interfering with itself due to being received at different delays so that phase shifts may add up destructively is /fading/, not /ISI/ don't confuse the two. jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●March 16, 20072007-03-16
>Zeph80 wrote: >> I have read a lot about the cyclic prefix used in OFDM, to combat ISIdue>> to multipath. I think I somewhat understand this. You make your guard >> interval longer that the delay spread, so 1 symbol leaks energy intothe>> next only within that guard interval. However, doesnt intra-symbol >> interference still exist, that is the same symbol interefering withitself>> due to being received within that delay spread period and so thosephase>> shifts may add up destructively.How is this taken care of? Does thismake>> sense, or am I missing some key concept in understanding ISi and guard >> intervals. > >The same symbol interfering with itself due to being received at >different delays so that phase shifts may add up destructively is >/fading/, not /ISI/ don't confuse the two. > >jerry >-- >Engineering is the art of making what you want from things you can get. >¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ >And would you just remedy that by adding a fading margin? Or if you had a good know sequence estimate(some pilot code), could that help in better training your equalizers to even deal with this(if u had afairly static channel, you would know your multipath componnents are causing the same symbols echoes to add destructively and factor that phase change /compensate for it?. Or is that equlaizers just deal with ISI.
Reply by ●March 16, 20072007-03-16
>Zeph80 wrote: >> I have read a lot about the cyclic prefix used in OFDM, to combat ISIdue>> to multipath. I think I somewhat understand this. You make your guard >> interval longer that the delay spread, so 1 symbol leaks energy intothe>> next only within that guard interval. However, doesnt intra-symbol >> interference still exist, that is the same symbol interefering withitself>> due to being received within that delay spread period and so thosephase>> shifts may add up destructively.How is this taken care of? Does thismake>> sense, or am I missing some key concept in understanding ISi and guard >> intervals. > >The same symbol interfering with itself due to being received at >different delays so that phase shifts may add up destructively is >/fading/, not /ISI/ don't confuse the two. > >jerry >-- >Engineering is the art of making what you want from things you can get. >¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ >And would you just remedy that by adding a fading margin? Or if you had a good know sequence estimate(some pilot code), could that help in better training your equalizers to even deal with this(if u had afairly static channel, you would know your multipath componnents are causing the same symbols echoes to add destructively and factor that phase change /compensate for it?. Or is that equlaizers just deal with ISI.
Reply by ●March 16, 20072007-03-16
Zeph80 wrote:>> Zeph80 wrote: >>> I have read a lot about the cyclic prefix used in OFDM, to combat ISI > due >>> to multipath. I think I somewhat understand this. You make your guard >>> interval longer that the delay spread, so 1 symbol leaks energy into > the >>> next only within that guard interval. However, doesnt intra-symbol >>> interference still exist, that is the same symbol interefering with > itself >>> due to being received within that delay spread period and so those > phase >>> shifts may add up destructively.How is this taken care of? Does this > make >>> sense, or am I missing some key concept in understanding ISi and guard >>> intervals. >> The same symbol interfering with itself due to being received at >> different delays so that phase shifts may add up destructively is >> /fading/, not /ISI/ don't confuse the two. >> >> jerry >> -- >> Engineering is the art of making what you want from things you can get. >> ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ >> > > > And would you just remedy that by adding a fading margin? Or if you had a > good know sequence estimate(some pilot code), could that help in better > training your equalizers to even deal with this(if u had afairly static > channel, you would know your multipath componnents are causing the same > symbols echoes to add destructively and factor that phase change > /compensate for it?. Or is that equlaizers just deal with ISI.The delays that cause fading are comparable to a carrier period. Symbol times are much longer than that. The same structure is unlikely to be effective with both. When interference makes the signal vanish, no amount of compensation will restore it. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
