Análise de desempenho de receptores baseados em reticulados para MIMO e fastICA em sistemas MIMO cego massivos

Orientador: Gustavo FraidenraichTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Estatísticas da taxa-soma dos decodificadores Integer Forcing (IF) e outros decodificadores baseados em reticulados para sistemas de Múltipla Entrada e Múltipla Saída (MIMO) são analisadas. Duas aproximações para a taxa-soma de decodificadores lineares são derivadas. A primeira aproximação é baseada no algoritimo Gauss-Lagrange para sistemas com duas antenas no transmissor e receptor (arranjo 2x2) e canais descorrelacionados. A segunda aproximação considera um sistema com um arranjo nxn de antenas, para o caso correlacionado e descorrelacionado e é baseado no segundo teorema de Minkowiski O desempenho de decodificadores IF e Compute and Forward Transform (CFT) são analisados na presença de erro de estimação de canal. Uma aproximação para a taxa-soma média na presença de erros de estimação de canal e canais com realização fixa é derivada. Uma aproximação para a taxa-soma ergódica dos decodificadores IF na presença de canais correlacionados e descorrelacionados também é derivada. Decodificadores lineares IF atraíram atenção significativa devido ao seu potencial de atingir melhor desempenho do que outros decodificadores lineares, especialmente quando as matrizes de canal são aproximadamente singulares. No entanto, uma análise mais profunda de seu desempenho na presença de canais não determinísticos é necessária para que se possa quantificar sua vantagem em relação a decodificadores lineares clássicos e para que se possa corretamente projetar sistemas baseados nestes decodificadoresAbstract: The statistics of the sum-rate of Integer Forcing (IF) and other lattice-based Multiple Input Multiple Output (MIMO) systems are analyzed. Two approximations to the achievable sum-rate of the IF linear receiver and their respective analytical probability density functions (PDF) are derived. The first approximation is based on the Gauss-Lagrange algorithm for systems with two antennas at the transmitter and receiver (2x2 arrays) and uncorrelated channels. The second approximation considers an nxn array for both correlated and uncorrelated channels and its derivation is based on Minkowiski's second theorem. The performance of IF and Compute and Forward Transform (CFT) receivers is also analyzed under the presence of channel estimation errors. An approximation to their average sum-rate in the presence of these errors for fixed channel realizations is derived. An approximation to the Ergodic IF sum-rate for correlated and uncorrelated channels is also derived. IF linear receiver has attracted significant attention recently due to their potential to perform better than other linear receivers, especially in the presence of channel matrices that are close to singular. However, a more in-depth analysis of its performance in the presence of non-deterministic channels is necessary in order to quantify its advantage over classical linear receivers and to correctly design systems that rely on these decoders. Another contribution of this work involves blind decoding in Massive MIMO systems. We propose a variation to the fast Independent Component Analysis (fastICA) which takes into consideration the shape of the constellations to obtain better performanceDoutoradoTelecomunicações e TelemáticaDoutor em Engenharia ElétricaCAPE

Massive MIMO has Unlimited Capacity

The capacity of cellular networks can be improved by the unprecedented array gain and spatial multiplexing offered by Massive MIMO. Since its inception, the coherent interference caused by pilot contamination has been believed to create a finite capacity limit, as the number of antennas goes to infinity. In this paper, we prove that this is incorrect and an artifact from using simplistic channel models and suboptimal precoding/combining schemes. We show that with multicell MMSE precoding/combining and a tiny amount of spatial channel correlation or large-scale fading variations over the array, the capacity increases without bound as the number of antennas increases, even under pilot contamination. More precisely, the result holds when the channel covariance matrices of the contaminating users are asymptotically linearly independent, which is generally the case. If also the diagonals of the covariance matrices are linearly independent, it is sufficient to know these diagonals (and not the full covariance matrices) to achieve an unlimited asymptotic capacity.Comment: To appear in IEEE Transactions on Wireless Communications, 17 pages, 7 figure

Asymptotic Analysis of the Downlink in Cooperative Massive MIMO Systems

We consider the downlink of a cooperative cellular communications system, where several base-stations around each mobile cooperate and perform zero-forcing to reduce the received interference at the mobile. We derive closed-form expressions for the asymptotic performance of the network as the number of antennas per base station grows large. These expressions capture the trade off between various system parameters, and characterize the joint effect of noise and interference (where either noise or interference is asymptotically dominant and where both are asymptotically relevant). The asymptotic results are verified using Monte Carlo simulations, which indicate that they are useful even when the number of antennas per base station is only moderately large. Additionally, we show that when the number of antennas per base station grows large, power allocation can be optimized locally at each base station. We hence present a power allocation algorithm that achieves near optimal performance while significantly reducing the coordination overhead between base stations. The presented analysis is significantly more challenging than the uplink analysis, due to the dependence between beamforming vectors of nearby base stations. This statistical dependence is handled by introducing novel bounds on marked shot-noise point processes with dependent marks, which are also useful in other contexts

Receive Combining vs. Multi-Stream Multiplexing in Downlink Systems with Multi-Antenna Users

In downlink multi-antenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas $N$ and the use of these antennas. Assuming that the total number of receive antennas at the multi-antenna users is much larger than $N$, the maximal multiplexing gain can be achieved with many different transmission/reception strategies. For example, the excess number of receive antennas can be utilized to schedule users with effective channels that are near-orthogonal, for multi-stream multiplexing to users with well-conditioned channels, and/or to enable interference-aware receive combining. In this paper, we try to answer the question if the $N$ data streams should be divided among few users (many streams per user) or many users (few streams per user, enabling receive combining). Analytic results are derived to show how user selection, spatial correlation, heterogeneous user conditions, and imperfect channel acquisition (quantization or estimation errors) affect the performance when sending the maximal number of streams or one stream per scheduled user---the two extremes in data stream allocation. While contradicting observations on this topic have been reported in prior works, we show that selecting many users and allocating one stream per user (i.e., exploiting receive combining) is the best candidate under realistic conditions. This is explained by the provably stronger resilience towards spatial correlation and the larger benefit from multi-user diversity. This fundamental result has positive implications for the design of downlink systems as it reduces the hardware requirements at the user devices and simplifies the throughput optimization.Comment: Published in IEEE Transactions on Signal Processing, 16 pages, 11 figures. The results can be reproduced using the following Matlab code: https://github.com/emilbjornson/one-or-multiple-stream

Hardware-Conscious Wireless Communication System Design

The work at hand is a selection of topics in efficient wireless communication system design, with topics logically divided into two groups.One group can be described as hardware designs conscious of their possibilities and limitations. In other words, it is about hardware that chooses its configuration and properties depending on the performance that needs to be delivered and the influence of external factors, with the goal of keeping the energy consumption as low as possible. Design parameters that trade off power with complexity are identified for analog, mixed signal and digital circuits, and implications of these tradeoffs are analyzed in detail. An analog front end and an LDPC channel decoder that adapt their parameters to the environment (e.g. fluctuating power level due to fading) are proposed, and it is analyzed how much power/energy these environment-adaptive structures save compared to non-adaptive designs made for the worst-case scenario. Additionally, the impact of ADC bit resolution on the energy efficiency of a massive MIMO system is examined in detail, with the goal of finding bit resolutions that maximize the energy efficiency under various system setups.In another group of themes, one can recognize systems where the system architect was conscious of fundamental limitations stemming from hardware.Put in another way, in these designs there is no attempt of tweaking or tuning the hardware. On the contrary, system design is performed so as to work around an existing and unchangeable hardware limitation. As a workaround for the problematic centralized topology, a massive MIMO base station based on the daisy chain topology is proposed and a method for signal processing tailored to the daisy chain setup is designed. In another example, a large group of cooperating relays is split into several smaller groups, each cooperatively performing relaying independently of the others. As cooperation consumes resources (such as bandwidth), splitting the system into smaller, independent cooperative parts helps save resources and is again an example of a workaround for an inherent limitation.From the analyses performed in this thesis, promising observations about hardware consciousness can be made. Adapting the structure of a hardware block to the environment can bring massive savings in energy, and simple workarounds prove to perform almost as good as the inherently limited designs, but with the limitation being successfully bypassed. As a general observation, it can be concluded that hardware consciousness pays off

Performance of Multi-antenna Wireless Systems with Channel Estimation Error

Wireless services and applications have become extremely popular and widely employed over the past decades. This, in turn, has led to a dramatic increase in the number of wireless users who demand reliable services with high data rates. But such services are very challenging to provide due to radio channel impairments including multipath fading and co-channel interference. In this regard, the use of multiple antennas in wireless systems was proposed recently which has rapidly received great attention. Multi-antenna technology is shown to have powerful capabilities to improve reliability via spatial diversity and to increase data rates via spatial multiplexing as compared with traditional single-antenna systems. Furthermore, by exploiting additional spatial dimensions, transmit beamforming techniques can be used to manage co-channel interference in such systems. In a rich scattering environment, multiple antennas that are located sufficiently far apart at a transmitter experience independent fading with high probability. Therefore, the transmitter can send redundant versions of the same data stream over these independent channels to improve reliability. In particular, if the transmitter has access to perfect channel state information (CSI), it can set the beamforming weights such that the received signals from different transmit antennas combine constructively at some intended receiver(s) and destructively at some unintended receiver(s) so that no co-channel interference is generated. Spatial multiplexing is another powerful multi-antenna transmission technique which aids in enhancing data rates without increasing bandwidth or transmit power. Multiple parallel and independent channels can be established between a transmitter and a receiver that both use multiple antennas in a rich scattering environment. Therefore, multiple independent streams of data can be simultaneously sent over these channels within the bandwidth of operation. This, in turn, enhances the data rate by a multiplicative factor equal to the number of the independent streams. Water-filling is a strategy that achieves the maximum data rate in such multiple-input multiple-output (MIMO) systems when perfect CSI is available at both the transmitter and the receiver. In practice, CSI can be obtained at the receiver by the use of training sequences and its accuracy can be increased by carefully selecting sequences with good auto-correlation properties. The transmitter can acquire CSI by using the channel reciprocity principle in wireless systems or by relying on a feedback path to convey the CSI from the receiver. Due to practical limitations such as rate-limited feedback links and the delay involved in such procedures, perfect CSI can be very challenging to obtain at the transmitter side. This motivates the need to evaluate the effect of imperfect CSI at the transmitter (CSIT) on the performance of transmit diversity and beamforming in multiple-input single-output (MISO) systems and water-filling power allocation in MIMO systems. In this thesis, transmit diversity and beamforming are studied in a MISO system with an n-antenna transmitter, an intended single-antenna receiver, and some unintended single- antenna receivers. Two scenarios are considered, namely, null-steering beamforming and ε-threshold beamforming in which the allowable interference threshold at the unintended receivers is zero and ε > 0, respectively. With perfect CSIT, null-steering beamforming can successfully nullify interference at m unintended receivers, where m < n, and achieve a nonzero received power at the intended receiver with a mean value that grows linearly with n − m and is directly proportional to the power of the line-of-sight component between the transmitter and the intended receiver. With imperfect CSIT, null-steering beamforming based on erroneous channel estimates results in a nonzero interference at the unintended receivers with a mean value that is interestingly independent of n. Also, it is shown that a moderate line-of-sight component can significantly reduce the effect of estimation error on the performance of the intended link. Intuitively, the allowance of a small nonzero interference at the unintended receivers, as in ε-threshold beamforming, should improve the received power at the intended receiver. The analysis in this thesis shows that this enhancement is marginal and not worthwhile, notably in the case of imperfect CSIT. Therefore, there is no significant loss in the perfor- mance of the intended link if the transmitter performs null-steering beamforming instead. In fact, the transmitter can employ additional antennas to improve the performance of the intended link without generating significant extra interference on the unintended receivers. Furthermore, in this thesis, the effect of channel estimation error on the performance of water-filling power allocation in a MIMO system is explored when the transmitter and the receiver both have n antennas. At low signal to noise ratios (SNR), the gap be- tween water-filling throughput with perfect CSIT and the throughput corresponding to equal-power allocation with no CSIT is large asymptotically. It is thus interesting and worthwhile to evaluate how water-filling based on erroneous channel estimates may result in a throughput that falls between these two extremes. In this regard, it is first shown that, at low SNR, the normalized (by 1/n) water-filling throughput with imperfect CSIT converges to a non-random value denoted by R, almost surely as n increases. Denoting CP as the asymptotic normalized water-filling throughput with perfect CSIT and using it as a baseline for comparison, we then compare R with CP and find that for moderate channel estimation errors, water-filling can still achieve significant normalized throughputs that are close to CP. Furthermore, when the quality of channel estimation is very low, water-filling is shown asymptotically to achieve the same throughput as equal power allocation in the low SNR regime