Reciprocity Calibration for Massive MIMO: Proposal, Modeling and Validation

This paper presents a mutual coupling based calibration method for time-division-duplex massive MIMO systems, which enables downlink precoding based on uplink channel estimates. The entire calibration procedure is carried out solely at the base station (BS) side by sounding all BS antenna pairs. An Expectation-Maximization (EM) algorithm is derived, which processes the measured channels in order to estimate calibration coefficients. The EM algorithm outperforms current state-of-the-art narrow-band calibration schemes in a mean squared error (MSE) and sum-rate capacity sense. Like its predecessors, the EM algorithm is general in the sense that it is not only suitable to calibrate a co-located massive MIMO BS, but also very suitable for calibrating multiple BSs in distributed MIMO systems. The proposed method is validated with experimental evidence obtained from a massive MIMO testbed. In addition, we address the estimated narrow-band calibration coefficients as a stochastic process across frequency, and study the subspace of this process based on measurement data. With the insights of this study, we propose an estimator which exploits the structure of the process in order to reduce the calibration error across frequency. A model for the calibration error is also proposed based on the asymptotic properties of the estimator, and is validated with measurement results.Comment: Submitted to IEEE Transactions on Wireless Communications, 21/Feb/201

ON THE SOLVABILITY OF CERTAIN (SSIE) WITH OPERATORS OF THE FORM B(r, s)

Given any sequence z = (zn)n≥1 of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y = (yn)n≥1 such that y/z = (yn/zn)n≥1 ∈ E; in particular, sz(c) denotes the set of all sequences y such that y/z converges. In this paper we deal with sequence spaces inclusion equations (SSIE), which are determined by an inclusion each term of which is a sum or a sum of products of sets of sequences of the form Xa(T) and Xx(T) where a is a given sequence, the sequence x is the unknown, T is a given triangle, and Xa(T) and Xx(T) are the matrix domains of T in the set X . Here we determine the set of all positive sequences x for which the (SSIE) sx(c) (B(r, s)) sx(c)⊂ (B(r', s')) holds, where r, r', s' and s are real numbers, and B(r, s) is the generalized operator of the first difference defined by (B(r, s)y)n = ryn+syn−1 for all n ≥ 2 and (B(r, s)y)1 = ry1. We also determine the set of all positive sequences x for which ryn + syn−1 /xn → l implies r'yn + s'yn−1 /xn → l (n → ∞) for all y and for some scalar l. Finally, for a given sequence a, we consider the a–Tauberian problem which consists of determining the set of all x such that sx(c) (B(r, s)) ⊂ sa(c)

Achievable Rates and Training Overheads for a Measured LOS Massive MIMO Channel

This paper presents achievable uplink (UL) sumrate predictions for a measured line-of-sight (LOS) massive multiple-input, multiple-output (MIMO) (MMIMO) scenario and illustrates the trade-off between spatial multiplexing performance and channel de-coherence rate for an increasing number of base station (BS) antennas. In addition, an orthogonal frequency division multiplexing (OFDM) case study is formed which considers the 90% coherence time to evaluate the impact of MMIMO channel training overheads in high-speed LOS scenarios. It is shown that whilst 25% of the achievable zero-forcing (ZF) sumrate is lost when the resounding interval is increased by a factor of 4, the OFDM training overheads for a 100-antenna MMIMO BS using an LTE-like physical layer could be as low as 2% for a terminal speed of 90m/s.Comment: 4 pages, 5 figure

Temporal Analysis of Measured LOS Massive MIMO Channels with Mobility

The first measured results for massive multiple-input, multiple-output (MIMO) performance in a line-of-sight (LOS) scenario with moderate mobility are presented, with 8 users served by a 100 antenna base Station (BS) at 3.7 GHz. When such a large number of channels dynamically change, the inherent propagation and processing delay has a critical relationship with the rate of change, as the use of outdated channel information can result in severe detection and precoding inaccuracies. For the downlink (DL) in particular, a time division duplex (TDD) configuration synonymous with massive MIMO deployments could mean only the uplink (UL) is usable in extreme cases. Therefore, it is of great interest to investigate the impact of mobility on massive MIMO performance and consider ways to combat the potential limitations. In a mobile scenario with moving cars and pedestrians, the correlation of the MIMO channel vector over time is inspected for vehicles moving up to 29 km/h. For a 100 antenna system, it is found that the channel state information (CSI) update rate requirement may increase by 7 times when compared to an 8 antenna system, whilst the power control update rate could be decreased by at least 5 times relative to a single antenna system.Comment: Accepted for presentation at the 85th IEEE Vehicular Technology Conference in Sydney. 5 Pages. arXiv admin note: substantial text overlap with arXiv:1701.0881

Bounded linear and compact operators between the Hahn space and spaces of strongly summable and bounded sequences

We establish the characterisations of the classes of bounded linear operators from the generalised Hahn sequence space hd, where d is an unbounded monotone increasing sequence of positive real numbers, into the spaces wp0, wp and wp∞ of sequences that are strongly summable to zero, strongly summable and strongly bounded by the Cesaro method of order one and index p for 1 ≤ p < ∞. Furthermore, we prove estimates for the Hausdorff measure of noncompactness of bounded linear operators from hd into wp, and identities for the Hausdorff measure of noncompactness of bounded linear operators from hd to wp0. We use these results to characterise the classes of compact operators from hd to wp and wp0. Finally, we provide an example for some applications of our results and visualisations in crystallography.Bulletin t. 153 de l'Académie serbe des sciences et des arts. Classe des sciences mathématiques et naturelles. Sciences mathematiques no 45

On the New Generalized Hahn Sequence Space hpd

In this article, we define the new generalized Hahn sequence space h p d, where d = ðdkÞ ∞ k=1 is monotonically increasing sequence with dk ≠ 0 for all k ∈ ℕ, and 1 < p < ∞. Then, we prove some topological properties and calculate the α − , β − , and γ − duals of h p d. Furthermore, we characterize the new matrix classes ðhd, λÞ, where λ = fbv, bvp, bv∞, bs, cs,g, and ðμ, hdÞ, where μ = fbv, bv0, bs, cs0, csg. In the last section, we prove the necessary and sufficient conditions of the matrix transformations from h p d into λ = fℓ∞, c, c0, ℓ1, hd, bv, bs, csg, and from μ = fℓ1, bv0, bs, cs0g into h p d

Indoor Localization Using Radio, Vision and Audio Sensors: Real-Life Data Validation and Discussion

This paper investigates indoor localization methods using radio, vision, and audio sensors, respectively, in the same environment. The evaluation is based on state-of-the-art algorithms and uses a real-life dataset. More specifically, we evaluate a machine learning algorithm for radio-based localization with massive MIMO technology, an ORB-SLAM3 algorithm for vision-based localization with an RGB-D camera, and an SFS2 algorithm for audio-based localization with microphone arrays. Aspects including localization accuracy, reliability, calibration requirements, and potential system complexity are discussed to analyze the advantages and limitations of using different sensors for indoor localization tasks. The results can serve as a guideline and basis for further development of robust and high-precision multi-sensory localization systems, e.g., through sensor fusion and context and environment-aware adaptation.Comment: 6 pages, 6 figure