A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses imperfect channel-state information derived from transmitted pilots to extract the individual data streams. The power radiated by the terminals can be made inversely proportional to the square-root of the number of base station antennas with no reduction in performance. In contrast if perfect channel-state information were available the power could be made inversely proportional to the number of antennas. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) detection are derived. An MRC receiver normally performs worse than ZF and MMSE. However as power levels are reduced, the cross-talk introduced by the inferior maximum-ratio receiver eventually falls below the noise level and this simple receiver becomes a viable option. The tradeoff between the energy efficiency (as measured in bits/J) and spectral efficiency (as measured in bits/channel use/terminal) is quantified for a channel model that includes small-scale fading but not large-scale fading. It is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single-antenna system.

/pdf/energy-and-spectral-efficiency-of-very-large-multiuser-mimo-4ksk4lv9wl.pdf

Energy and Spectral Efficiency of Very Large Multiuser MIMO Systems

A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses imperfect channel-state information derived from transmitted pilots to extract the individual data streams. The power radiated by the terminals can be made inversely proportional to the square-root of the number of base station antennas with no reduction in performance. In contrast if perfect channel-state information were available the power could be made inversely proportional to the number of antennas. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) detection are derived. A MRC receiver normally performs worse than ZF and MMSE. However as power levels are reduced, the cross-talk introduced by the inferior maximum-ratio receiver eventually falls below the noise level and this simple receiver becomes a viable option. The tradeoff between the energy efficiency (as measured in bits/J) and spectral efficiency (as measured in bits/channel use/terminal) is quantified. It is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single-antenna system.

This paper presents an overview of the theory and currently known techniques for multi-cell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacity-limiting factor, multi-cell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit inter-cell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multi-cell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental information-theoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and system-level integration. A few promising and quite fundamental research avenues are also suggested.

/pdf/multi-cell-mimo-cooperative-networks-a-new-look-at-1e6uuxtyow.pdf

Multi-Cell MIMO Cooperative Networks: A New Look at Interference

Tables of integrals

(1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.

https://link.springer.com/content/pdf/10.1057%2Fjors.1987.184.pdf

Applied Probability and Queues

This correspondence studies the statistical distribution of the signal-to-interference-plus-noise ratio (SINR) for the minimum mean-square error (MMSE) receiver in multiple-input multiple-output (MIMO) wireless communications. The channel model is assumed to be (transmit) correlated Rayleigh flat-fading with unequal powers. The SINR can be decomposed into two independent random variables: SINR=SINR/sup ZF/+T, where SINR/sup ZF/ corresponds to the SINR for a zero-forcing (ZF) receiver and has an exact Gamma distribution. This correspondence focuses on characterizing the statistical properties of T using the results from random matrix theory. First three asymptotic moments of T are derived for uncorrelated channels and channels with equicorrelations. For general correlated channels, some limiting upper bounds for the first three moments are also provided. For uncorrelated channels and correlated channels satisfying certain conditions, it is proved that T converges to a Normal random variable. A Gamma distribution and a generalized Gamma distribution are proposed as approximations to the finite sample distribution of T. Simulations suggest that these approximate distributions can be used to estimate accurately the probability of errors even for very small dimensions (e.g., two transmit antennas).

/pdf/on-the-distribution-of-sinr-for-the-mmse-mimo-receiver-and-5g9bzw028d.pdf

On the distribution of SINR for the MMSE MIMO receiver and performance analysis

A nonasymptotic framework is presented to analyze the diversity-multiplexing tradeoff of a multiple-input-multiple-output (MIMO) wireless system at finite signal-to-noise ratios (SNRs). The target data rate at each SNR is proportional to the capacity of an additive white Gaussian noise (AWGN) channel with an array gain. The proportionality constant, which can be interpreted as a finite-SNR spatial multiplexing gain, dictates the sensitivity of the rate adaptation policy to SNR. The diversity gain as a function of SNR for a fixed multiplexing gain is defined by the negative slope of the outage probability versus SNR curve on a log-log scale. The finite-SNR diversity gain provides an estimate of the additional power required to decrease the outage probability by a target amount. For general MIMO systems, lower bounds on the outage probabilities in correlated Rayleigh fading and Rician fading are used to estimate the diversity gain as a function of multiplexing gain and SNR. In addition, exact diversity gain expressions are determined for orthogonal space-time block codes (OSTBC). Spatial correlation significantly lowers the achievable diversity gain at finite SNR when compared to high-SNR asymptotic values. The presence of line-of-sight (LOS) components in Rician fading yields diversity gains higher than high-SNR asymptotic values at some SNRs and multiplexing gains while resulting in diversity gains near zero for multiplexing gains larger than unity. Furthermore, as the multiplexing gain approaches zero, the normalized limiting diversity gain, which can be interpreted in terms of the wideband slope and the high-SNR slope of spectral efficiency, exhibits slow convergence with SNR to the high-SNR asymptotic value. This finite-SNR framework for the diversity-multiplexing tradeoff is useful in MIMO system design for realistic SNRs and propagation environments

Finite-SNR Diversity&#8211;Multiplexing Tradeoff for Correlated Rayleigh and Rician MIMO Channels

We consider spatial multiplexing systems in correlated multiple-input multiple-output (MIMO) fading channels with equal power allocated to each transmit antenna. Under this constraint, the number and subset of transmit antennas together with the transmit symbol constellations are determined assuming knowledge of the channel correlation matrices. We first consider a fixed data rate system and vary the number of transmit antennas and constellation such that the minimum margin in the signal-to-noise ratio (SNR) is maximized for linear and Vertical Bell Laboratories Layered Space-Time (V-BLAST) receivers. We also derive transmit antenna and constellation selection criteria for a successive interference cancellation receiver (SCR) with a fixed detection order and a variable number of bits transmitted on each substream. Compared with a system using all available antennas, performance results show significant gains using a subset of transmit antennas, even for independent fading channels. Finally, we select a subset of transmit antennas to maximize data rate given a minimum SNR margin. A lower bound on the maximum outage data rate is derived. The maximum outage data rate of the SCR receiver is seen to be close to the outage channel capacity.

Spatial multiplexing with transmit antenna and constellation selection for correlated MIMO fading channels

Unobtrusive continuous monitoring of important vital signs and activity metrics has the potential to provide remote health monitoring, at-home screening, and rapid notification of critical events such as heart attacks, falls, or respiratory distress. This paper contains validation results of a wireless Bluetooth Low Energy (BLE) patch sensor consisting of two electrocardiography (ECG) electrodes, a microcontroller, a tri-axial accelerometer, and a BLE transceiver. The sensor measures heart rate, heart rate variability (HRV), respiratory rate, posture, steps, and falls and was evaluated on a total of 25 adult participants who performed breathing exercises, activities of daily living (ADLs), various stretches, stationary cycling, walking/running, and simulated falls. Compared to reference devices, the heart rate measurement had a mean absolute error (MAE) of less than 2 bpm, time-domain HRV measurements had an RMS error of less than 15 ms, respiratory rate had an MAE of 1.1 breaths per minute during metronome breathing, posture detection had an accuracy of over 95% in two of the three patch locations, steps were counted with an absolute error of less than 5%, and falls were detected with a sensitivity of 95.2% and specificity of 100%.

Wireless patch sensor for remote monitoring of heart rate, respiration, activity, and falls

In this paper, outage regions are computed for the quasi-static fading multiple access channel (MAC) with constraints on the individual user outage probabilities and no channel state information at the transmitters (CSIT) An outage rate region is defined as the set of rate vectors for which the user outage probability constraints are satisfied simultaneously Outage probability is typically defined in terms of a common outage event, defined as the event that a target user rate vector lies outside the achievable region of the MAC, conditioned on the fading state In contrast, rate regions without CSIT are computed in this paper based on individual outage events and individual probability constraints that are satisfied simultaneously An individual outage event for a given user occurs if the user's message is not correctly decoded, irrespective of the decoding success of the messages for other users Individual outage rate regions are useful for the MAC with heterogeneous user channels and quality-of-service (QoS) requirements Explicit outage rate regions and total throughputs are computed for the two-user fading MAC It is shown that rate regions and throughputs are significantly larger using individual outage probabilities than using the common outage probability

Ravi Narasimhan

Papers

On the distribution of SINR for the MMSE MIMO receiver and performance analysis

Finite-SNR Diversity–Multiplexing Tradeoff for Correlated Rayleigh and Rician MIMO Channels

Spatial multiplexing with transmit antenna and constellation selection for correlated MIMO fading channels

Wireless patch sensor for remote monitoring of heart rate, respiration, activity, and falls

Individual Outage Rate Regions for Fading Multiple Access Channels

Ravi Narasimhan

Papers

On the distribution of SINR for the MMSE MIMO receiver and performance analysis

Finite-SNR Diversity&#8211;Multiplexing Tradeoff for Correlated Rayleigh and Rician MIMO Channels

Spatial multiplexing with transmit antenna and constellation selection for correlated MIMO fading channels

Wireless patch sensor for remote monitoring of heart rate, respiration, activity, and falls

Individual Outage Rate Regions for Fading Multiple Access Channels

Finite-SNR Diversity–Multiplexing Tradeoff for Correlated Rayleigh and Rician MIMO Channels