Abstract

The degrees of freedom (DoF) region is characterized for the 2-user multiple input multiple output (MIMO) broadcast channel (BC), where the transmitter is equipped with M antennas, the two receivers are equipped with N 1 and N 2 antennas, and the levels of channel state information at the transmitter (CSIT) for the two users are parameterized by β 1 , β 2 , respectively. The achievability of the DoF region was established by Hao, Rassouli and Clerckx, but no proof of optimality was heretofore available. The proof of optimality is provided in this work with the aid of sum-set inequalities based on the aligned image sets (AIS) approach.

Highlights

  • The availability of channel state information at the transmitter(s) (CSIT) greatly affects the capacity of wireless networks, so much so that even the coarse degrees of freedom (DoF) metric is significantly impacted

  • The setting of interest is a 2-user multiple input multiple output (MIMO) broadcast channel (BC) where the transmitter is equipped with M antennas, the two receivers are equipped with N1 and N2 antennas, and the levels of CSIT for the two users are parameterized by β1, β2 ∈ [0, 1], respectively, such that βi = 0 represents no CSIT, βi = 1 represents perfect CSIT, and the intermediate values represent corresponding levels of partial CSIT

  • From the achievability side, note that the DoF innerbound shown in [6] remains unaffected if the number of transmit antennas is reduced to N1 + N2

Read more

Summary

Introduction

The availability of channel state information at the transmitter(s) (CSIT) greatly affects the capacity of wireless networks, so much so that even the coarse degrees of freedom (DoF) metric is significantly impacted. The setting of interest is a 2-user MIMO BC where the transmitter is equipped with M antennas, the two receivers are equipped with N1 and N2 antennas, and the levels of CSIT for the two users are parameterized by β1, β2 ∈ [0, 1], respectively, such that βi = 0 represents no CSIT, βi = 1 represents perfect CSIT, and the intermediate values represent corresponding levels of partial CSIT Existing results for this channel focus primarily on the two extremes of perfect CSIT and no CSIT. For arbitrary antenna configurations and arbitrary levels of partial CSIT, an achievable DoF region is established by Hao, Rassouli and Clerckx in [6] The optimality of this achievable region has been shown in [6] for certain parameter regimes (mainly N1 ≤ N2, M ≤ N2), based on existing bounds, as well as AIS arguments. The proof makes use of the sumset inequalities recently developed in [5]

Notation and Definitions
Sum-set Inequalities
System Model
The Channel
Main Result
Deterministic Model
A Key Lemma
Deterministic Channel Model
Useful Lemma
Conclusion
B Proof of Lemma 2
C Proof of Lemma 4
D Proof of Lemma 5
Main idea of the proof
Bounding the Probability of Image Alignment
Bounding the Average Size of Aligned Image Sets
Aligned Image Sets
F Proof of Lemma 6
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call