56895304
Trainable Projected Gradient Detector for Massive Overloaded MIMO Channels: Data-Driven Tuning Approach
This paper presents a deep learning-aided iterative detection algorithm for massive overloaded multiple-input multiple-output (MIMO) systems where the number of transmit antennas <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is larger than that of receive antennas <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula>. Since the proposed algorithm is based on the projected gradient descent method with trainable parameters, it is named the trainable projected gradient-detector (TPG-detector). The trainable internal parameters, such as the step-size parameter, can be optimized with standard deep learning techniques, i.e., the back propagation and stochastic gradient descent algorithms. This approach is referred to as data-driven tuning and ensures fast convergence during parameter estimation in the proposed scheme. The TPG-detector mainly consists of matrix-vector product operations whose computational cost is proportional to <inline-formula> <tex-math notation="LaTeX">$m n$ </tex-math></inline-formula> for each iteration. In addition, the number of trainable parameters in the TPG-detector is independent of the number of antennas. These features of the TPG-detector result in a fast and stable training process and reasonable scalability for large systems. The numerical simulations show that the proposed detector achieves a comparable detection performance to those of the existing algorithms for the massively overloaded MIMO channels, e.g., the state-of-the-art IW-SOAV detector, with a lower computation cost.
109962045
A generalized nyquist criterion and an optimum linear receiver for a pulse modulation system
A pulse modulation system is modeled with M waveforms {s m (t)}M 1 , each of which is amplitude scaled and simultaneously transmitted over a single physical channel. An infinite pulse train is assumed with signal interval T, which is determined by bandwidth consideration of the channel. We restrict the receiver to be linear with M outputs, one for each signal waveform. At a high signal-to-noise ratio the main sources of interference at the input to the receiver are the intersymbol interference and crosstalk; by crosstalk we mean the interference between the different waveforms. It is desirable, therefore, for the receiver to eliminate both types of interference and to minimize the remaining error due to additive noise in the channel. This constraint on the intersymbol interference and crosstalk is defined as the generalized Nyquist criterion. The receiver which accomplishes the above is determined for a mean square error criterion. Finally, some examples are presented which demonstrate the ease with which the generalized Nyquist criterion can be used to design waveforms without intersymbol interference or crosstalk.
1192503
Efficient High-Performance Decoding for Overloaded MIMO Antenna Systems
The practical challenge of capacity-achieving forward error-correcting codes (e.g., space-time turbo codes) is overcoming the tremendous complexity associated by their optimal joint maximum-likelihood (ML) decoding. For this reason, iterative soft decoding has been studied to approach the optimal ML decoding performance at affordable complexity. In multiple-input multiple-output (MIMO) channels, a judicious decoding strategy consists of two stages: 1) estimate the soft bits using list version of sphere decoding or its variants, and 2) update the soft bits through iterative soft decoding. A promising MIMO decoder is required to produce reliable soft-bit estimates at the first stage before iterative soft decoding is performed. In this paper, we focus on the overloaded (or fat) MIMO antenna systems where the number of receive antennas is less than the number of signals multiplexed in the spatial domain. In this scenario, the original form of sphere decoding is inherently not applicable and our aim is to generalize sphere decoding geometrically to cope with overloaded detection. The so-called slab-sphere decoding (SSD) proposed guarantees to obtain exact-ML hard detection while reducing complexity greatly. With the list-version of SSD, (his paper proposes an efficient MIMO soft decoder, which can generate reliable soft-bit estimates at affordable complexity as inputs for iterative soft decoding for promising performance. A case study in the IEEE 802.16 settings is carried out for performance evaluation
11786443
Low-complexity near-optimal signal detection in underdetermined large-MIMO systems
In this paper, we consider signal detection in n<sub>t</sub> × n<sub>r</sub> underdetermined MIMO (UD-MIMO) systems, where i) n<sub>t</sub> >; n<sub>r</sub> with a overload factor α = n<sub>t</sub> over n<sub>r</sub> >; 1, ii) n<sub>t</sub> symbols are transmitted per channel use through spatial multiplexing, and iii) n<sub>t</sub>, n<sub>r</sub> are large (in the range of tens). A low-complexity detection algorithm based on reactive tabu search is considered. A variable threshold based stopping criterion is proposed which offers near-optimal performance in large UD-MIMO systems at low complexities. A lower bound on the maximum likelihood (ML) bit error performance of large UD-MIMO systems is also obtained for comparison. The proposed algorithm is shown to achieve BER performance close to the ML lower bound within 0.6 dB at an uncoded BER of 10<sup>-2</sup> in 16 × 8 V-BLAST UD-MIMO system with 4-QAM (32 bps/Hz). Similar near-ML performance results are shown for 32 × 16, 32 × 24 V-BLAST UD-MIMO with 4-QAM/16-QAM as well. A performance and complexity comparison between the proposed algorithm and the λ-generalized sphere decoder (λ-GSD) algorithm for UD-MIMO shows that the proposed algorithm achieves almost the same performance of λ-GSD but at a significantly lesser complexity.
6745484
New decoding strategy for underdetermined MIMO transmission using sparse decomposition
In this paper we address the problem of large dimension decoding in MIMO systems. The complexity of the optimal maximum likelihood detection makes it unfeasible in practice when the number of antennas, the channel impulse response length or the source constellation size become too high. We consider a MIMO system with finite constellation and model it as a system with sparse signal sources. We formulate the decoding problem as an underdetermined sparse source recovering problem and apply the ℓ1-minimization to solve it. The resulting decoding scheme is applied to large MIMO systems and to frequency selective channel. We also review the computational cost of some ℓ1-minimization algorithms. Simulation results show significant improvement compared to other existing receivers.
16441960
Massive overloaded MIMO signal detection via convex optimization with proximal splitting
In this paper, we propose signal detection schemes for massive overloaded multiple-input multiple-output (MIMO) systems, where the number of receive antennas is less than that of transmitted streams. Using the idea of the sum-of-absolute-value (SOAV) optimization, we formulate the signal detection as a convex optimization problem, which can be solved via a fast algorithm based on Douglas-Rachford splitting. To improve the performance, we also propose an iterative approach to solve the optimization problem with weighting parameters update in a cost function. Simulation results show that the proposed scheme can achieve much better bit error rate (BER) performance than conventional schemes, especially in large-scale overloaded MIMO systems.
9811644
Convex Optimization-Based Signal Detection for Massive Overloaded MIMO Systems
This paper proposes signal detection schemes for massive multiple-input multiple-output (MIMO) systems, where the number of receive antennas is less than that of transmitted streams. Assuming practical baseband digital modulation and taking advantage of the discreteness of transmitted symbols, we formulate the signal detection problem as a convex optimization problem, called sum-of-absolute-value (SOAV) optimization. Moreover, we extend the SOAV optimization into the weighted-SOAV (W-SOAV) optimization and propose an iterative approach to solve the W-SOAV optimization with updating the weights in the objective function. Furthermore, for coded MIMO systems, we also propose a joint detection and decoding scheme, where log likelihood ratios of transmitted symbols are iteratively updated between the MIMO detector and the channel decoder. In addition, a theoretical performance analysis is provided in terms of the upper bound of the size of the estimation error obtained with the W-SOAV optimization. Simulation results show that the bit error rate performance of the proposed scheme is better than that of conventional schemes, especially in large-scale overloaded MIMO systems.
13333501
Learning Fast Approximations of Sparse Coding
In Sparse Coding (SC), input vectors are reconstructed using a sparse linear combination of basis vectors. SC has become a popular method for extracting features from data. For a given input, SC minimizes a quadratic reconstruction error with an L1 penalty term on the code. The process is often too slow for applications such as real-time pattern recognition. We proposed two versions of a very fast algorithm that produces approximate estimates of the sparse code that can be used to compute good visual features, or to initialize exact iterative algorithms. The main idea is to train a non-linear, feed-forward predictor with a specific architecture and a fixed depth to produce the best possible approximation of the sparse code. A version of the method, which can be seen as a trainable version of Li and Osher's coordinate descent method, is shown to produce approximate solutions with 10 times less computation than Li and Os-her's for the same approximation error. Unlike previous proposals for sparse code predictors, the system allows a kind of approximate "explaining away" to take place during inference. The resulting predictor is differentiable and can be included into globally-trained recognition systems.
4924456
Trainable ISTA for Sparse Signal Recovery
In this paper, we propose a novel sparse signal recovery algorithm called Trainable ISTA (TISTA). The proposed algorithm consists of two estimation units such as a linear estimation unit and a minimum mean squared error (MMSE) estimator-based shrinkage unit. The estimated error variance required in the MMSE shrinkage unit is precisely estimated from a tentative estimate of the original signal. The remarkable feature of the proposed scheme is that TISTA includes adjustable variables controlling a step size and the error variance for the MMSE shrinkage. The variables are adjusted by standard deep learning techniques. The number of trainable variables of TISTA is equal to the number of iteration rounds and it is much smaller than those of known learnable sparse signal recovery algorithms. This feature leads to highly stable and fast training processes of TISTA. Computer experiments show that TISTA is applicable to various classes of sensing matrices such as Gaussian matrices, binary matrices and matrices with large condition numbers. Numerical results also demonstrate that TISTA shows significantly faster convergence than those of AMP and LISTA in many cases.
4924456
Trainable ISTA for Sparse Signal Recovery
In this paper, we propose a novel sparse signal recovery algorithm called Trainable ISTA (TISTA). The proposed algorithm consists of two estimation units such as a linear estimation unit and a minimum mean squared error (MMSE) estimator-based shrinkage unit. The estimated error variance required in the MMSE shrinkage unit is precisely estimated from a tentative estimate of the original signal. The remarkable feature of the proposed scheme is that TISTA includes adjustable variables controlling a step size and the error variance for the MMSE shrinkage. The variables are adjusted by standard deep learning techniques. The number of trainable variables of TISTA is equal to the number of iteration rounds and it is much smaller than those of known learnable sparse signal recovery algorithms. This feature leads to highly stable and fast training processes of TISTA. Computer experiments show that TISTA is applicable to various classes of sensing matrices such as Gaussian matrices, binary matrices and matrices with large condition numbers. Numerical results also demonstrate that TISTA shows significantly faster convergence than those of AMP and LISTA in many cases.
58006644
Deep Learning-Aided Trainable Projected Gradient Decoding for LDPC Codes
We present a novel optimization-based decoding algorithm for LDPC codes that is suitable for hardware architectures specialized to feed-forward neural networks. The algorithm is based on the projected gradient descent algorithm with a penalty function for solving a non-convex minimization problem. The proposed algorithm has several internal parameters such as step size parameters, a softness parameter, and the penalty coefficients. We use a standard tool set of deep learning, i.e., back propagation and stochastic gradient descent type algorithms, to optimize these parameters. Several numerical experiments show that the proposed algorithm outperforms the belief propagation decoding in some cases.
52822294
A Model-Driven Deep Learning Network for MIMO Detection
In this paper, we propose a model-driven deep learning network for multiple-input multiple-output (MIMO) detection. The structure of the network is specially designed by unfolding the iterative algorithm. Some trainable parameters are optimized through deep learning techniques to improve the detection performance. Since the number of trainable variables of the network is equal to that of the layers, the network can be easily trained within a very short time. Furthermore, the network can handle time-varying channel with only a single training. Numerical results show that the proposed approach can improve the performance of the iterative algorithm significantly under Rayleigh and correlated MIMO channels.
145882181
Deep Learning Based on Orthogonal Approximate Message Passing for CP-Free OFDM
Channel estimation and signal detection are very challenging for an orthogonal frequency division multiplexing (OFDM) system without cyclic prefix (CP). In this article, deep learning based on orthogonal approximate message passing (DL-OAMP) is used to address these problems. The DL-OAMP receiver includes a channel estimation neural network (CE-Net) and a signal detection neural network based on OAM-P, called OAMP-Net. The CE-Net is initialized by the least square channel estimation algorithm and refined by minimum mean-squared error (MMSE) neural network. The OAMP-Net is established by unfolding the iterative OAMP algorithm and adding some trainable parameters to improve the detection performance. The DL-OAMP receiver is with low complexity and can estimate time-varying channels with only a single training. Simulation results demonstrate that the bit-error rate (BER) of the proposed scheme is lower than those of competitive algorithms for high-order modulation.
75134989
Artificial Intelligence-Aided Receiver for a CP-Free OFDM System: Design, Simulation, and Experimental Test
Orthogonal frequency division multiplexing (OFDM), usually with sufficient cyclic prefix (CP), has been widely applied in various communication systems. The CP in OFDM consumes additional resource and reduces spectrum and energy efficiency. However, channel estimation and signal detection are very challenging for CP-free OFDM systems. In this paper, we propose a novel artificial intelligence (AI)-aided receiver (AI receiver) for a CP-free OFDM system. The AI receiver includes a channel estimation neural network (CE-NET) and a signal detection neural network based on orthogonal approximate message passing (OAMP), called OAMP-NET. The CE-NET is initialized by the least-square channel estimation algorithm and refined by a linear minimum mean-squared error neural network. The OAMP-NET is established by unfolding the iterative OAMP algorithm and adding several trainable parameters to improve the detection performance. We first investigate their performance under different channel models through extensive simulation and then establish a real transmission system using a 5G rapid prototyping system for an over-the-air (OTA) test. Based on our study, the AI receiver can estimate time-varying channels with a single training phase. It also has great robustness to various imperfections and has better performance than those competitive algorithms, especially for high-order modulation. The OTA test further verifies its feasibility to real environments and indicates its potential for future communications systems.
145886103
SURE-TISTA: A Signal Recovery Network for Compressed Sensing
Deep neural network (DNN) has a wide range of applications in various fields, including solving sparse inverse problems. In this paper, we propose a novel network called the Stein’s unbiased risk estimate based-trainable iterative thresholding algorithm (SURE-TISTA) for sparse signal recovery problems. Without prior information, SURE-TISTA outperforms TISTA, an algorithm based on the minimum mean squared error (MMSE) estimator. SURE-TISTA also shows a great robustness in many cases including large-scale and large-variance problems. Meanwhile, SURE-TISTA uses fewer learnable variables to achieve similar performance as learned approximate message passing (LAMP), which has more learnable parameters. Without any error measure estimator, SURE-TISTA achieves a near MMSE-based performance. Our numerical results indicate that SURE-TISTA is superior to TISTA and other traditional algorithms in many aspects, which can be promising in image denoising.
454839
Deep MIMO detection
In this paper, we consider the use of deep neural networks in the context of Multiple-Input-Multiple-Output (MIMO) detection. We give a brief introduction to deep learning and propose a modern neural network architecture suitable for this detection task. First, we consider the case in which the MIMO channel is constant, and we learn a detector for a specific system. Next, we consider the harder case in which the parameters are known yet changing and a single detector must be learned for all multiple varying channels. We demonstrate the performance of our deep MIMO detector using numerical simulations in comparison to competing methods including approximate message passing and semidefinite relaxation. The results show that deep networks can achieve state of the art accuracy with significantly lower complexity while providing robustness against ill conditioned channels and mis-specified noise variance.
29157140
Learning to Detect
In this paper, we consider multiple-input-multiple-output detection using deep neural networks. We introduce two different deep architectures: a standard fully connected multi-layer network, and a detection network (DetNet), which is specifically designed for the task. The structure of DetNet is obtained by unfolding the iterations of a projected gradient descent algorithm into a network. We compare the accuracy and runtime complexity of the proposed approaches and achieve state-of-the-art performance while maintaining low computational requirements. Furthermore, we manage to train a single network to detect over an entire distribution of channels. Finally, we consider detection with soft outputs and show that the networks can easily be modified to produce soft decisions.
25736421
Deep Learning Based MIMO Communications
We introduce a novel physical layer scheme for single user Multiple-Input Multiple-Output (MIMO) communications based on unsupervised deep learning using an autoencoder. This method extends prior work on the joint optimization of physical layer representation and encoding and decoding processes as a single end-to-end task by expanding transmitter and receivers to the multi-antenna case. We introduce a widely used domain appropriate wireless channel impairment model (Rayleigh fading channel), into the autoencoder optimization problem in order to directly learn a system which optimizes for it. We considered both spatial diversity and spatial multiplexing techniques in our implementation. Our deep learning-based approach demonstrates significant potential for learning schemes which approach and exceed the performance of the methods which are widely used in existing wireless MIMO systems. We discuss how the proposed scheme can be easily adapted for open-loop and closed-loop operation in spatial diversity and multiplexing modes and extended use with only compact binary channel state information (CSI) as feedback.
24390528
Deep learning for wireless physical layer: Opportunities and challenges
Machine learning (ML) has been widely applied to the upper layers of wireless communication systems for various purposes, such as deployment of cognitive radio and communication network. However, its application to the physical layer is hampered by sophisticated channel environments and limited learning ability of conventional ML algorithms. Deep learning (DL) has been recently applied for many fields, such as computer vision and natural language processing, given its expressive capacity and convenient optimization capability. The potential application of DL to the physical layer has also been increasingly recognized because of the new features for future communications, such as complex scenarios with unknown channel models, high speed and accurate processing requirements; these features challenge conventional communication theories. This paper presents a comprehensive overview of the emerging studies on DL-based physical layer processing, including leveraging DL to redesign a module of the conventional communication system (for modulation recognition, channel decoding, and detection) and replace the communication system with a radically new architecture based on an autoencoder. These DL-based methods show promising performance improvements but have certain limitations, such as lack of solid analytical tools and use of architectures that are specifically designed for communication and implementation research, thereby motivating future research in this field.
3677231
Deep Learning for Massive MIMO CSI Feedback
In frequency division duplex mode, the downlink channel state information (CSI) should be sent to the base station through feedback links so that the potential gains of a massive multiple-input multiple-output can be exhibited. However, such a transmission is hindered by excessive feedback overhead. In this letter, we use deep learning technology to develop CsiNet, a novel CSI sensing and recovery mechanism that learns to effectively use channel structure from training samples. CsiNet learns a transformation from CSI to a near-optimal number of representations (or codewords) and an inverse transformation from codewords to CSI. We perform experiments to demonstrate that CsiNet can recover CSI with significantly improved reconstruction quality compared with existing compressive sensing (CS)-based methods. Even at excessively low compression regions where CS-based methods cannot work, CsiNet retains effective beamforming gain.
56895329
Deep Learning-Aided Projected Gradient Detector for Massive Overloaded MIMO Channels
The paper presents a deep learning-aided iterative detection algorithm for massive overloaded MIMO systems. Since the proposed algorithm is based on the projected gradient descent method with trainable parameters, it is named as trainable projected descent-detector (TPG-detector). The trainable internal parameters can be optimized with standard deep learning techniques such as back propagation and stochastic gradient descent algorithms. This approach referred to as data-driven tuning brings notable advantages of the proposed scheme such as fast convergence. The numerical experiments show that TPG-detector achieves comparable detection performance to those of the known algorithms for massive overloaded MIMO channels with lower computation cost.
7997436
Improved parallel interference cancellation for CDMA
This paper introduces an improved nonlinear parallel interference cancellation scheme for code-division multiple access (CDMA) that significantly reduces the degrading effect on the desired user of interference from the other users that share the channel. The implementation complexity of the scheme is linear in the number of users and operates on the fact that parallel processing simultaneously removes from each user a part of the interference produced by the remaining users accessing the channel the amount being proportional to their reliability. The parallel processing can be done in multiple stages. The proposed scheme uses tentative decision devices at the multiple stages to produce the most reliably estimated received data for generation and cancellation of user interference. Simulation results are given for a multitude of different situations, in particular, those cases for which the analysis is too complex.
6628106
Adam: A Method for Stochastic Optimization
We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.
7335556
Optimality of large MIMO detection via approximate message passing
Optimal data detection in multiple-input multiple-output (MIMO) communication systems with a large number of antennas at both ends of the wireless link entails prohibitive computational complexity. In order to reduce the computational complexity, a variety of sub-optimal detection algorithms have been proposed in the literature. In this paper, we analyze the optimality of a novel data-detection method for large MIMO systems that relies on approximate message passing (AMP). We show that our algorithm, referred to as individually-optimal (IO) large-MIMO AMP (short IO-LAMA), is able to perform IO data detection given certain conditions on the MIMO system and the constellation set (e.g., QAM or PSK) are met.
54438136
Reconstruction of Complex Discrete-Valued Vector via Convex Optimization With Sparse Regularizers
In this paper, we propose a method for the reconstruction of a complex discrete-valued vector from its linear measurements. In particular, we mainly focus on the underdetermined cases, where the number of measurements is less than that of the unknown complex discrete variables, and propose a reconstruction approach of solving an optimization problem called sum of complex sparse regularizers (SCSR) optimization. The sum of sparse regularizers in the objective function can directly utilize the discrete nature of the unknown vector in the complex domain. We also propose an algorithm for the SCSR optimization problem on the basis of alternating direction method of multipliers. For the proposed convex regularizers, we analytically prove that the sequence obtained by the proposed algorithm converges to the optimal solution of the problem. To obtain better reconstruction performance, we further propose an iterative approach named iterative weighted SCSR (IW-SCSR), where we update the parameters in the objective function in each iteration by using the tentative estimate in the previous iteration. Simulation results show that IW-SCSR can reconstruct the complex discrete-valued vector from its underdetermined linear measurements and achieve good performance in the applications of overloaded multiple-input multiple-output signal detection and channel equalization.
119189866
Complex Trainable Ista for Linear and Nonlinear Inverse Problems
Complex-field signal recovery problems from noisy linear/nonlinear measurements appear in many areas of signal processing and wireless communications. In this paper, we propose a trainable iterative signal recovery algorithm named complex-field TISTA (C-TISTA) which treats complex-field nonlinear inverse problems. C-TISTA is based on the concept of deep unfolding and consists of a gradient descent step with the Wirtinger derivatives followed by a shrinkage step with a trainable complex-valued shrinkage function. Importantly, it contains a small number of trainable parameters so that its training process can be executed efficiently. Numerical results indicate that C-TISTA shows remarkable signal recovery performance compared with existing algorithms.