ANALYSIS OF HIGH-SNR PERFORMANCE OF MIMO MULTI-CHANNEL BEAM FORMING IN DOUBLE-SCATTERING CHANNELS

ABSTRACT This Work investigates the symbol error rate (SER) performance of the multiple-input multiple-output (MIMO) multi-channel beam forming (MB) in the general double scattering channel. We derive an asymptotic expansion on the marginal eigen value distribution of the MIMO channel matrix, and apply the result to get an approximate expression on the average SER at high signal-tonoise ratio (SNR). Two parameters pertaining to the SER, i.e., the diversity gain and the array gain, are analyzed. Our results show that it suffices for the double scattering channel to have only limited scatterers, if the same diversity gain as the Rayleigh channel is desired; however, once the number of scatterers is below a certain level, the array gain in the double-scattering channel will vary with the SNR logarithmically

Smooth eigenvalue correction

Second-order statistics play an important role in data modeling. Nowadays, there is a tendency toward measuring more signals with higher resolution (e.g., high-resolution video), causing a rapid increase of dimensionality of the measured samples, while the number of samples remains more or less the same. As a result the eigenvalue estimates are significantly biased as described by the Marčenko Pastur equation for the limit of both the number of samples and their dimensionality going to infinity. By introducing a smoothness factor, we show that the Marčenko Pastur equation can be used in practical situations where both the number of samples and their dimensionality remain finite.\ud \ud Based on this result we derive methods, one already known and one new to our knowledge, to estimate the sample eigenvalues when the population eigenvalues are known. However, usually the sample eigenvalues are known and the population eigenvalues are required. We therefore applied one of the these methods in a feedback loop, resulting in an eigenvalue bias correction method.\ud \ud We compare this eigenvalue correction method with the state-of-the-art methods and show that our method outperforms other methods particularly in real-life situations often encountered in biometrics: underdetermined configurations, high-dimensional configurations, and configurations where the eigenvalues are exponentially distributed

Low-Complexity Near-Optimal Detection Algorithms for MIMO Systems

As the number of subscribers in wireless networks and their demanding data rate are exponentially increasing, multiple-input multiple-output (MIMO) systems have been scaled up in the 5G where tens to hundreds of antennas are deployed at base stations (BSs). However, by scaling up the MIMO systems, designing detectors with low computational complexity and close to the optimal error performance becomes challenging. In this dissertation, we study the problem of efficient detector designs for MIMO systems. In Chapter 2, we propose efficient detection algorithms for small and moderate MIMO systems by using lattice reduction and subspace (or conditional) detection techniques. The proposed algorithms exhibit full receive diversity and approach the bit error rate (BER) of the optimal maximum likelihood (ML) solution. For quasi-static channels, the complexity of the proposed schemes is cubic in the system dimension and is only linear in the size of the QAM modulation used. However, the computational complexity of lattice reduction algorithms imposes a large burden on the proposed detectors for large MIMO systems or fast fading channels. In Chapter 3, we propose detectors for large MIMO systems based on the combination of minimum mean square error decision feedback equalization (MMSE-DFE) and subspace detection tailored to an appropriate channel ordering. Although the achieved diversity order of the proposed detectors does not necessarily equal the full receive diversity for some MIMO systems, the coding gain allows for close to ML error performance at practical values of signal-to-noise ratio (SNR) at the cost of a small computational complexity increase over the classical MMSE- DFE detection. The receive diversity deficiency is addressed by proposing another algorithm in which a partial lattice reduction (PLR) technique is deployed to improve the diversity order. Massive multiuser MIMO (MU-MIMO) is another technology where the BS is equipped with hundreds of antennas and serves tens of single-antenna user terminals (UTs). For the uplink of massive MIMO systems, linear detectors, such as zero-forcing (ZF) and minimum mean square error (MMSE), approach the error performances of sophisticated nonlinear detectors. However, the exact solutions of ZF and MMSE involve matrix-matrix multiplication and matrix inversion operations which are expensive for massive MIMO systems. In Chapter 4, we propose efficient truncated polynomial expansion (TPE)-based detectors that achieve the error performance of the exact solutions with a computational complexity proportional to the system dimensions. The millimeter wave (mmWave) massive MIMO is another key technology for 5G cellular networks. By using hybrid beamforming techniques in which a few numbers of radio frequency (RF) chains are deployed at the BSs and the UTs, the fully-digital precoder (combiner) is approximated as a product of analog and digital precoders (combiners). In Chapter 5, we consider a signal detection scheme using the equivalent channel consisting of the precoder, mmWave channel, and combiner. The available structure in the equivalent channel enables us to achieve the BER of the optimal ML solution with a significant reduction in the computational complexity