Hi, I have a conceptual question for the group, which I have been struggling with. It can be summarized as "what is the difference between sampling offsets and carrier offsets on a received constellation?". In more detail... Suppose there is a demodulated BPSK signal at the output of an ideal bandpass channel and the receiver is perfect. The received constellation will be at +1, -1. Now if there is a carrier phase offset at the receiver, the constellation will be will be rotated, i.e. some of the energy will come in on the quadrature channel. e.g. a 45 degree carrier phase offset will result in received constellation points (1+j)/sqrt(2) and -(1+j)/sqrt(2). If there is a carrier frequency offset then the phase offset will be changing with time, and the rate of change is equal to the carrier frequency offset. i.e. the constellation rotates around the complex-plane. So far so simple... What happens to the constellation if there are no carrier offsets, but there are sampling offsets in the receiver ADC? Lets say that in the case of no offsets, the pulse shaping is all Nyquist, so that sampling at the correct phase perfectly recovers the signal. Now if there is a fixed sampling phase offset, we will be sampling at the wrong point, so there will be "interference", which is related to the pulse shaping e.g. if we use a raised cosine filter, then the roll-off factor will control the amount of interference (picture the eye-diagram) for a given sampling phase offset. I imagine that in the case of BPSK, this will smear the +1 and -1 constellation points along the real line, is that correct? Is there any reason to think that the constellation will be rotated (as is the case with a carrier phase offset), or that some energy will be received on the quadrature arm? I have been having a long running debate with a colleague on this matter. To bring the problem further, suppose it is a sampling frequency offset rather than a sampling phase offset at the ADC. My opinion is that the interference will change over time but will stil be distributed over the real line (in-phase channel) on the complex plain. The interference at any time will depend on the samping point at that time and on the eye-diagram (due to the pulse-shaping). My colleague has a different view, which is that the sampling frequency offset will cause energy to leak into the quadrature arm, and the constellation will "rotate". I have started to converge on a viewpoint that maybe we are both right, depending on the implementation. I think that if the ADC samples a signal at an intermediate frequency, which must be digitally downconverted, then it is possible that sampling phase offsets could mix the in-phase and quadrature channels, effectively causing rotation. But that if the ADC is sampling a signal which has been perfectly converted to base-band in the analogue domain, then there is no way that sampling frequency offsets could rotate the constellation. who is right? are either of us rights? many thanks
carrier phase and frequency offset vs sampling phase and frequency offset
Started by ●May 2, 2008
Reply by ●May 2, 20082008-05-02
On May 2, 1:15�pm, porterboy <porterbo...@yahoo.com> wrote:> Hi, > > I have a conceptual question for the group, which I have been > struggling with. It can be summarized as "what is the difference > between sampling offsets and carrier offsets on a received > constellation?". �In more detail... >This is a question of where the timing mismatch is introduced. If you have a passband-modulated (say BPSK) system and you sample directly at passband, then sampling frequency offset at the ADC will introduce time dilation. Because of this, in baseband, you have both drifting sampling reference AND what is usually called residual carrier frequency offset. This is one of the disadvantages of all-digital (or mostly) passband- sampling receivers. In fact, the effect of sampling frequency offset is multiplied by the ratio between the sampling frequency and the baseband symbol rate. So you solve this by either having BOTH timing compensator and phase compensator, OR by having an interpolator at the output of the ADC. If you do frequency translation, i.e. demixing, after the ADC, then will have residual carrier frequency offset. If you have an analog demixer (which is perfectly matched to the carrier frequency of the transmitter) and you sample at baseband, then sampling frequency offset will not have residual carrier frequency offset. This is quite well-studied in the OFDM area, since no matter what you do, you'll have the sub-carriers at the baseband level, so it is important to take care of residual carrier frequency offsets as well. And of course, to make it more interesting, the mapping from sampling frequency offset to carrier frequency offset is dependent on which subcarrier you are considering. The scaling is linear. Since I am traveling I do not have access to paper references, unfortunately, but Eric Jacobsen will hook you up ;-). Julius
