In this paper, we explore the theoretical properties of subspace recovery using Winsorized Principal Component Analysis (WPCA), utilizing a common data transformation technique that caps extreme values to mitigate the impact of outliers. Despite the widespread use of winsorization in various tasks of multivariate analysis, its theoretical properties, particularly for subspace recovery, have received limited attention. We provide a detailed analysis of the accuracy of WPCA, showing that increasing the number of samples while decreasing the proportion of outliers guarantees the consistency of the sample subspaces from WPCA with respect to the true population subspace. Furthermore, we establish perturbation bounds that ensure the WPCA subspace obtained from contaminated data remains close to the subspace recovered from pure data. Additionally, we extend the classical notion of breakdown points to subspace-valued statistics and derive lower bounds for the breakdown points of WPCA. Our analysis demonstrates that WPCA exhibits strong robustness to outliers while maintaining consistency under mild assumptions. A toy example is provided to numerically illustrate the behavior of the upper bounds for perturbation bounds and breakdown points, emphasizing winsorization’s utility in subspace recovery.

The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for robustness or fail in the presence of only a few outliers. This study introduces an efficient algorithm, called Spherically Normalized SVD, for robust SVD approximation that is highly insensitive to outliers, computationally scalable, and provides accurate approximations of singular vectors. The proposed algorithm achieves remarkable speed by utilizing only two applications of a standard reduced-rank SVD algorithm to appropriately scaled data, significantly outperforming competing algorithms in computation times. To assess the robustness of the approximated singular vectors and their subspaces against data contamination, we introduce new notions of breakdown points for matrix-valued input, including row-wise, column-wise, and block-wise breakdown points. Theoretical and empirical analyses demonstrate that our algorithm exhibits higher breakdown points compared to standard SVD and its modifications. We empirically validate the effectiveness of our approach in applications such as robust low-rank approximation and robust principal component analysis of high-dimensional microarray datasets. Overall, our study presents a highly efficient and robust solution for SVD approximation that overcomes the limitations of existing algorithms in the presence of outliers.

A novel interference alignment technique combined with interference cancellation is proposed. A new scenario of single-antenna 2-user X channel with a multiple-antenna relay is considered. The proposed interference alignment and cancellation scheme does not require any wireline links between receivers. In the proposed scheme, interference signals are not decoded. Instead, interference signals are just aligned, and the aligned signal is cancelled out to extract the desired signal. We call the proposed scheme an aligned interference cancellation technique. It is known that DoF of 4/2 is achievable for the two-user X channel using the interference alignment. In the proposed scheme, relay precoding matrices are designed to accomplish two purposes. One is to cancel out the aligned interference signals perfectly, and the other is to enable an equivalent received signal model of the Alamouti's codes. The proposed relay-aided interference alignment and cancellation technique not only makes interference alignment feasible, but also improves performance. The interference signals are aligned at a specific time slot, and the precoding matrices of the relay are designed to cancel the aligned interference. In simulations, it is verified that the diversity gain of 2 is achieved with the degrees-of-freedom (DoF) of 4/3.

The multiuser MIMO (MU-MIMO) systems tend to have inter-user interference in practical systems with limited feedback. Practical MU-MIMO systems with limited feedback can be divided into two classes in general. One is zero-forcing beamforming (ZFBF), and the other is per user unitary rate control (PU2RC) which is an extended version of random beamforming (RBF). To improve performance, ZFBF needs more feedback bits, and PU2RC needs a larger number of users. We propose a new hybrid MU-MISO system which has the advantages of the two MU-MIMO schemes simultaneously, and analyze the sum-rate performance and the quantization error of the hybrid scheme. The analysis shows how the number of feedback bits, the number of users, and the signal power affect the sum-rate. The throughput scaling laws are also derived in the high and the medium SNR regimes. Simulation results show that the proposed hybrid MU-MISO system performs better than either of the two MU-MIMO systems with the same number of feedback bits. Another advantage is that it has lower complexity for codeword search since it has a hierarchical codebook structure.

Multi-antenna downlink system with limited feedback can provide enormous capacity gains. In practical, two systems can be considered. One is zero-forcing beamforming (ZFBF), and the other is per user unitary rate control (PU2RC) which has been proposed for emerging cellular standards. In order to have good performance, ZFBF requires many feedback bits, and PU2RC requires many users. Recently, the authors proposed a hybrid multi-user MISO system which has merits of those two schemes simultaneously. In this paper, we analyze the sum-rate performance and quantization error of the hybrid scheme. The throughput scaling laws are also derived in high and medium SNR regimes.

This paper analyzes the optimal degrees of freedom (DoF) for K-user M × N MIMO interference channels with constant channel coefficients. In this paper, we use the methodology of interpreting the interference alignment problem as a multivariate polynomial system. The properness of the system enables us to determine the feasibility of interference alignment. Using this methodology, we propose an algorithm to obtain the optimal DoF, and compute the closed-form optimal DoF. We show that K min(M,N) is optimal DoF if δ ≥ min(M,N), where δ = ⌊M+N over K+1⌋. If δ < min(M,N), K M+N over K+1 is optimal DoF when M+N over K+1 is an integer, and ⌈K M+N over K+1⌉ − 1 is the optimal DoF when M+N over K+1 is not an integer. A key contribution of this paper is that it provides a closed-form optimal DoF for M × N MIMO interference channels when the DoF of each user can be different.

In this letter, we analyze the post-scheduling SINR mismatch of a multiuser orthogonal random beamforming (ORBF) system. The mismatch probability is derived for a Gaussian broadcast channel with M transmit antennas and K single-antenna users. Numerical results are shown to be identical to theoretical results. The probability analysis enables us to calculate the minimum number of users to satisfy a target mismatch probability. Another way to use the mismatch probability is to control CQI mismatch handling mechanisms.

In this paper, we analyze channel quality indicator (CQI) mismatch probabilities of multiuser orthogonal random beamforming (ORBF) systems. First, we derive the CQI mismatch probability of the ORBF system with M transmit antennas and K users equipped with one receive antenna. Using that result, we also derive the upper and lower bounds of the per user unitary and rate control (PU2RC) system with 2 transmit antennas and K users equipped with one receive antenna, which is being adopted in the IEEE 802.16m standard. Finally, we compare theoretical results with numerical results from simulation.

This paper presents closed-form expressions of the distribution of signal-to-interference-plus-noise ratios (SINRs) and the average bit error rate (BER) for an orthogonal random beamforming system in multiple-antenna Gaussian broadcast channels. First, we derive the statistical distribution of the SINR of the scheduled transmit signals and confirm that the approximate form of the cumulative distribution function (cdf) of the SINR is equivalent to the formula in \cite{sharif} and \cite{letaief}. We then obtain a closed-form expression for the total average BER of the system by using the approximate cdf. Our theoretical results are compared to the Monte Carlo simulation results.

For a single relay channel, we study the average throughput of two different amplify-and-forward (AF) protocols, which are orthogonal-AF (OAF) and nonorthogonal-AF (NAF). The NAF protocol has been proposed to overcome a significant loss of performance of OAF in the high spectral efficiency region, and it was also shown that NAF performs better than OAF in terms of the diversity-multiplexing tradeoff. However, the results have been evaluated at the asymptotically high signal to noise ratio (SNR), and the power allocation problem between the source and the relay was neglected. We examine which protocol has a better performance in a practical system operating at a finite SNR. We also study where a relay should be located with consideration of the power allocation. In this paper, we show that the performance depends on both SNR and power allocation ratio, which indicates OAF may perform better in a certain environment.

This paper presents a new and simple decoding algorithm for layered space time block codes such as the two independent Alamouti's codes which are also called the double space-time transmit diversity (DSTTD) system. By using group interference suppression and successive interference cancellation, we can treat DSTTD as two independent space-time block codes (STBC). We can then decode both of these STBC's through a simple maximum likelihood (ML) detector with null space-based interference cancellation. We also compare the proposed interference cancellation (IC) scheme with the conventional MMSE IC scheme. The performance of the proposed IC scheme is comparable to that of the MMSE IC scheme while the complexity reduction factor of the proposed scheme can be up to 5 compared to the MMSE IC scheme.

This paper presents a new and simple decoding algorithm for layered space time block codes such as the two independent Alamouti's codes which are also called the double space-time transmit diversity (DSTTD) system. By using group interference suppression and successive interference cancellation, we can treat DSTTD as two independent space-time block codes (STBC). We can then decode both of these STBC's through a simple maximum likelihood (ML) detector with null space-based interference cancellation. We also compare the proposed interference cancellation (IC) scheme with the conventional MMSE IC scheme. The performance of the proposed IC scheme is comparable to that of the MMSE IC scheme while the complexity of the proposed scheme is lower than that of the MMSE IC scheme.