We study the generalized degrees of freedom (gDoF) of the block-fading noncoherent MIMO channel with asymmetric distributions of link strengths, and a coherence time of T symbol durations. We first derive the optimal signaling structure for communication over this channel, which is distinct from that for the i.i.d MIMO setting. We prove that for T = 1, the gDoF is zero for MIMO channels with arbitrary link strength distributions, extending the result for MIMO with i.i.d links. We then show that selecting the statistically best antenna is gDoF-optimal for both Multiple Input Single Output (MISO) and Single Input Multiple Output (SIMO) channels. We also derive the gDoF for the 2 × 2 MIMO channel with different exponents in the direct and cross links. In this setting, we show that it is always necessary to use both antennas to achieve the optimal gDoF, in contrast to the results for 2 × 2 MIMO with identical link distributions.
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.
We study the generalized degrees of freedom (gDoF) of the block-fading noncoherent multiple input multiple output (MIMO) channel with asymmetric distributions of link strengths and a coherence time of T symbol durations. We derive the optimal signaling structure for communication for asymmetric MIMO, which is distinct from that for the MIMO with independent and identically distributed (i.i.d.)links. We extend the existing results for the single input multiple output (SIMO) channel with i.i.d. links to the asymmetric case, proving that selecting the statistically best antenna is gDoF-optimal. Using the gDoF result for SIMO, we prove that for T = 1, the gDoF is zero for MIMO channels with arbitrary link strengths. We show that selecting the statistically best antenna is gDoF-optimal for the multiple input single output (MISO) channel. We also derive the gDoF for the 2 × 2 MIMO channel with different exponents in the direct and cross links. In this setting, we show that it is always necessary to use both the antennas to achieve the optimal gDoF, in contrast to the results for the 2 × 2 MIMO with i.i.d. links. We show that having weaker crosslinks, gives gDoF gain compared to the case with i.i.d. links. For noncoherent MIMO with i.i.d. links, the traditional method of training each transmit antenna independently is degrees of freedom (DoF) optimal, whereas we observe that for the asymmetric 2 × 2 MIMO, the traditional training is not gDoF-optimal. We extend this observation to a larger M × M MIMO by demonstrating a strategy that can achieve larger gDoF than a traditional training-based method.
In this paper, we study the 2-user Gaussian interference-channel with feedback and fading links. We show that for a class of fading models, when no channel state information at transmitter (CSIT) is available, the rate-splitting schemes for static interference channel, when extended to the fading case, yield an approximate capacity region characterized to within a constant gap. We also show a constant-gap capacity result for the case without feedback. Our scheme uses rate-splitting based on average interference-to-noise ratio (inr). This scheme is shown to be optimal to within a constant gap if the fading distributions have the quantity log (E [inr]) − E [log (inr)] uniformly bounded over the entire operating regime. We show that this condition holds in particular for Rayleigh fading and Nakagami fading models. The capacity region for the Rayleigh fading case is obtained within a gap of 2.83 bits for the feedback case, and within 1.83 bits for the non-feedback case.
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