Approximate Capacity of Fast Fading Interference Channels With no Instantaneous CSIT

Abstract

We develop a characterization of fading models, which assigns a number called logarithmic Jensen's gap to a given fading model. We show that as a consequence of a finite logarithmic Jensen's gap, approximate capacity region can be obtained for fast fading interference channels (FF-IC) for several scenarios. We illustrate three instances where a constant capacity gap can be obtained as a function of the logarithmic Jensen's gap. Firstly for an FF-IC with neither feedback nor instantaneous channel state information at transmitter (CSIT), if the fading distribution has finite logarithmic Jensen's gap, we show that a rate-splitting scheme based on average interference-to-noise ratio (inr) can achieve its approximate capacity. Secondly we show that a similar scheme can achieve the approximate capacity of FF-IC with feedback and delayed CSIT, if the fading distribution has finite logarithmic Jensen's gap.Thirdly, when this condition holds, we show that point-to-point codes can achieve approximate capacity for a class of FF-IC with feedback. We prove that the logarithmic Jensen's gap is finite for common fading models, including Rayleigh and Nakagami fading, thereby obtaining the approximate capacity region of FF-IC with these fading models.

Generalized Degrees of Freedom of Noncoherent Diamond Networks

“…We now compare our achievable gDoF with that of a standard training-based scheme. The approximate capacity region of coherent fast fading IC with feedback is given in [7]. The gDoF for the case which uses 2 symbols for training can be easily obtained from the gDoF region for the coherent case with a multiplication factor of (1 − 2/T ).…”

“…In [18], a similar result was derived for the IC with feedback, obtaining the capacity region within 2 bits. In [7], the approximate capacity region (within a constant additive gap) for fast fading interference channels (FF-IC), with no instantaneous CSIT but with perfect channel knowledge at the receiver, was derived. There, the authors used a rate-splitting scheme based on the average interference-to-noise ratio, extending the existing rate-splitting schemes for IC [8], [18], and proved that this was approximately optimal for FF-IC.…”

“…The proof follows by analyzing a Han-Kobayashi scheme similar to [7] with ratesplitting based on the average interference-to-noise ratio and noncoherent joint decoding at the receivers. The details are in Section III-B.…”

“…The rest of the symbols are used for communication using a rate-splitting scheme for the coherent fading IC. (See [7] for the coherent fast fading IC scheme.) We also consider the noncoherent IC with channel state and output feedback.…”

“…Afterwards, the behavior is dominated by the decrease in the private information. 4 our results can demonstrate improvement in the rates compared to the natural training-based scheme at finite SNRs, the rate-SNR points are given in Table II on page 10. For the feedback case, we again propose a noncoherent scheme that performs rate-splitting based on the INR similar to [7]. We evaluate the gDoF region and compare it with a standard training-based scheme and prove that the noncoherent scheme outperforms the standard trainingbased scheme (see Section IV on page 16…”