Power Scaling of Uplink Massive MIMO Systems with Arbitrary-Rank Channel Means

This paper investigates the uplink achievable rates of massive multiple-input multiple-output (MIMO) antenna systems in Ricean fading channels, using maximal-ratio combining (MRC) and zero-forcing (ZF) receivers, assuming perfect and imperfect channel state information (CSI). In contrast to previous relevant works, the fast fading MIMO channel matrix is assumed to have an arbitrary-rank deterministic component as well as a Rayleigh-distributed random component. We derive tractable expressions for the achievable uplink rate in the large-antenna limit, along with approximating results that hold for any finite number of antennas. Based on these analytical results, we obtain the scaling law that the users' transmit power should satisfy, while maintaining a desirable quality of service. In particular, it is found that regardless of the Ricean $K$-factor, in the case of perfect CSI, the approximations converge to the same constant value as the exact results, as the number of base station antennas, $M$, grows large, while the transmit power of each user can be scaled down proportionally to $1/M$. If CSI is estimated with uncertainty, the same result holds true but only when the Ricean $K$-factor is non-zero. Otherwise, if the channel experiences Rayleigh fading, we can only cut the transmit power of each user proportionally to $1/\sqrt M$. In addition, we show that with an increasing Ricean $K$-factor, the uplink rates will converge to fixed values for both MRC and ZF receivers

Power Allocation Schemes for Multicell Massive MIMO Systems

This paper investigates the sum-rate gains brought by power allocation strategies in multicell massive multipleinput multiple-output systems, assuming time-division duplex transmission. For both uplink and downlink, we derive tractable expressions for the achievable rate with zero-forcing receivers and precoders respectively. To avoid high complexity joint optimization across the network, we propose a scheduling mechanism for power allocation, where in a single time slot, only cells that do not interfere with each other adjust their transmit powers. Based on this, corresponding transmit power allocation strategies are derived, aimed at maximizing the sum rate per-cell. These schemes are shown to bring considerable gains over equal power allocation for practical antenna configurations (e.g., up to a few hundred). However, with fixed number of users (N), these gains diminish as M turns to infinity, and equal power allocation becomes optimal. A different conclusion is drawn for the case where both M and N grow large together, in which case: (i) improved rates are achieved as M grows with fixed M/N ratio, and (ii) the relative gains over the equal power allocation diminish as M/N grows. Moreover, we also provide applicable values of M/N under an acceptable power allocation gain threshold, which can be used as to determine when the proposed power allocation schemes yield appreciable gains, and when they do not. From the network point of view, the proposed scheduling approach can achieve almost the same performance as the joint power allocation after one scheduling round, with much reduced complexity

Existence of solutions for fourth order differential equation with four-point boundary conditions

AbstractIn this paper we investigate the existence of solutions of a class of four-point boundary value problems for a fourth order ordinary differential equation. Our analysis relies on a nonlinear alternative of Leray–Schauder type

One-shot ultraspectral imaging with reconfigurable metasurfaces

One-shot spectral imaging that can obtain spectral information from thousands of different points in space at one time has always been difficult to achieve. Its realization makes it possible to get spatial real-time dynamic spectral information, which is extremely important for both fundamental scientific research and various practical applications. In this study, a one-shot ultraspectral imaging device fitting thousands of micro-spectrometers (6336 pixels) on a chip no larger than 0.5 cm$^2$, is proposed and demonstrated. Exotic light modulation is achieved by using a unique reconfigurable metasurface supercell with 158400 metasurface units, which enables 6336 micro-spectrometers with dynamic image-adaptive performances to simultaneously guarantee the density of spectral pixels and the quality of spectral reconstruction. Additionally, by constructing a new algorithm based on compressive sensing, the snapshot device can reconstruct ultraspectral imaging information ($\Delta\lambda$/$\lambda$~0.001) covering a broad (300-nm-wide) visible spectrum with an ultra-high center-wavelength accuracy of 0.04-nm standard deviation and spectral resolution of 0.8 nm. This scheme of reconfigurable metasurfaces makes the device can be directly extended to almost any commercial camera with different spectral bands to seamlessly switch the information between image and spectral image, and will open up a new space for the application of spectral analysis combining with image recognition and intellisense