In this paper, we propose to exploit the richly scattered multi-path nature of a frequency selective channel to provide additional degrees of freedom for desigining effective precoding schemes for multi-user communications. We design the precoding matrix for multi-user communications based on the Generalized Multi-Unitary Decomposition (GMUD), where the channel matrix H is transformed into P_i*R_r*Q_i^H. An advantage of GMUD is that multiple pairs of unitary matrices P_i and Q_i can be obtained with one single R_r. Since the column of Q_i can be used as the transmission beam of a particular user, multiple solutions of Q_i provide a large selection of transmission beams, which can be exploited to achieve high degrees of orthogonality between the multipaths, as well as between the interfering users. Hence the proposed precoding technique based on GMUD achieves better performance than precoding based on singular value decomposition.
A frequency domain (FD) time-reversal (TR) precoder is proposed to perform physical layer security (PLS) in single-input single-output (SISO) systems using orthogonal frequency-division multiplexing (OFDM) and artificial noise (AN) signal injection. The AN signal does not corrupt the data transmission to the legitimate receiver but degrades the decoding performance of the eavesdropper. This scheme guarantees the secrecy of a communication towards a legitimate user when the transmitter knows the instantaneous channel state information (CSI) of the legitimate link thanks to the channel reciproci…
We consider downlink precoding in a frequency-selective multi-user Massive MIMO system with highly efficient but non-linear power amplifiers at the base station (BS). A low-complexity precoding algorithm is proposed, which generates constant-envelope (CE) signals at each BS antenna. To achieve a desired per-user information rate, the extra total transmit power required under the per-antenna CE constraint when compared to the commonly used less stringent total average transmit power constraint, is small.
Hybrid analog/digital precoding allows millimeter wave MIMO systems to leverage large antenna array gains while permitting low cost and power consumption hardware. Most prior work has focused on hybrid precoding for narrow-band mmWave systems. MmWave systems, however, will likely operate on wideband channels with frequency selectivity. Therefore, this paper considers frequency selective hybrid precoding with RF beamforming vectors taken from a quantized codebook. For this system, a low-complexity yet near-optimal greedy algorithm is developed for the design of the hybrid analog/digital precode…
Hybrid analog/digital precoding offers a compromise between hardware complexity and system performance in millimeter wave (mmWave) systems. This type of precoding allows mmWave systems to leverage large antenna array gains that are necessary for sufficient link margin, while permitting low cost and power consumption hardware. Most prior work has focused on hybrid precoding for narrowband mmWave systems, with perfect or estimated channel knowledge at the transmitter. MmWave systems, however, will likely operate on wideband channels with frequency selectivity. Therefore, this paper considers wid…
We consider zero-forcing equalization of frequency selective MIMO channels by causal and linear time-invariant precoders in the presence of intersymbol interference. Our motivation is twofold. First, we are concerned with the optimal performance of causal precoders from a worst case point of view. Therefore we construct an optimal causal precoder, whereas contrary to other works our construction is not limited to finite or rational impulse responses. Moreover we derive a novel numerical approach to computation of the optimal perfomance index achievable by causal precoders for given channels. T…
In this paper, we study the frequency-selective broadcast channel with confidential messages (BCC) in which the transmitter sends a confidential message to receiver 1 and a common message to receivers 1 and 2. In the case of a block transmission of N symbols followed by a guard interval of L symbols, the frequency-selective channel can be modeled as a N * (N+L) Toeplitz matrix. For this special type of multiple-input multiple-output (MIMO) channels, we propose a practical Vandermonde precoding that consists of projecting the confidential messages in the null space of the channel seen by receiv…
Convolutional precoding in polarization-adjusted convolutional (PAC) codes can reduce the number of minimum weight codewords (a.k.a error coefficient) of polar codes. This can result in improving the error correction performance of (near) maximum likelihood (ML) decoders such as sequential decoders and sphere decoders. However, PAC codes cannot be decoded by sphere decoding. The reason is twofold: 1) Sphere decoding of polar codes is performed from the last bit - due to the lower rectangular shape of the polar transform. Whereas the shape of PAC codes generator matrix is no longer triangular. …
Ultra-reliable wireless communication links require the utilization of all diversity sources of a wireless communication channel. Hadani et al. propose a two dimensional discrete symplectic Fourier transform (DSFT) as orthogonal pre-coder for a time-frequency modulation scheme. In this paper we explore \emph{general} orthogonal precoding (OP) and its performance in time- and frequency-selective channels. We show that iterative parallel interference cancellation (PIC) and iterative channel estimation methods can be used for the detection of OP. A scalar signal model for OP transmission is obtai…
Millimeter wave (mmWave) is a practical solution to provide high data rate for the vehicle-to-everything (V2X) communications. This enables the future autonomous vehicles to exchange big data with the base stations (BSs) such as the velocity and the location to improve the awareness of the advanced driving assistance system (ADAS). In this context, we consider a single-cell multiuser doubly-selective system wherein the BS simultaneously serves multiple vehicles. To accomplish this requirement, the BS is implemented in hybrid architecture to support multiple spatial streams while the vehicles h…
Discrete-time Rayleigh fading single-input single-output (SISO) and multiple-input multiple-output (MIMO) channels are considered, with no channel state information at the transmitter or the receiver. The fading is assumed to be stationary and correlated in time, but independent from antenna to antenna. Peak-power and average-power constraints are imposed on the transmit antennas. For MIMO channels, these constraints are either imposed on the sum over antennas, or on each individual antenna. For SISO channels and MIMO channels with sum power constraints, the asymptotic capacity as the peak sig…
A channel delay spread larger than the cyclic prefix (CP) creates inter-carrier/symbol interference (ISI/ICI) in orthogonal frequency-division multiplexing (OFDM). Recent interests in low-latency applications have motivated the usage of shorter OFDM symbols where one can either downscale the CP at the cost of interference, or maintain it but with larger overhead. Alternatively, this paper studies channel shortening methods exploiting the properties of large multi-antenna precoding in order to steer the transmitted signal energy toward channel paths inside an insufficient CP. It is shown that I…
With the increase of physical antenna and subcarrier numbers in MIMO-OFDM systems, channel side information feedback amount and signal precoding complexity overburden will consume much more system resource, even become intolerable. To solve this problem, previous works mainly focused on fixed subcarrier grouping size and precoded MIMO signals in the same group with unitary channel state information (CSI). It could reduce the system overburden, but such a process would lead to system capacity loss due to the channel mismatch in precoding procedure. In this paper, we consider a MIMOOFDM system o…
Hybrid precoding design can be challenging for broadband millimeter-wave (mmWave) massive MIMO due to the frequency-flat analog precoder in radio frequency (RF). Prior broadband hybrid precoding work usually focuses on fully-connected array (FCA), while seldom considers the energy-efficient partially-connected subarray (PCS) including the fixed subarray (FS) and dynamic subarray (DS). Against this background, this paper proposes a machine learning based broadband hybrid precoding for mmWave massive MIMO with DS. Specifically, we first propose an optimal hybrid precoder based on principal compo…
Multiple-input multiple-output (MIMO) or multi-antenna communication is a key technique to achieve high spectral efficiency in wireless systems. For the point-to-point MIMO channel, it is a well-known result that the channel singular value decomposition (SVD) based linear precoding and decoding achieves the channel capacity, which also diagonalizes the MIMO channel into parallel single-input single-output (SISO) sub-channels for independent encoding and decoding. However, in multi-user MIMO systems, the optimal transmit covariance of each MIMO link is generally not its channel SVD based as a r…
We propose a nonlinear phase-quantized constant-envelope precoding algorithm for the massive multi-user (MU) multiple-input multiple-output (MIMO) downlink. Specifically, we adapt the squared-infinity norm Douglas-Rachford splitting (SQUID) precoder to systems that use oversampling digital-to-analog converters (DACs) at the base station (BS) and orthogonal frequency-division multiplexing (OFDM) to communicate over frequency-selective channels. We demonstrate that the proposed SQUID-OFDM precoder is able to generate transmit signals that are constrained to constant envelope, which enables the u…
We consider downlink precoding in a frequency-selective multi-user massive MIMO system with highly efficient but non-linear power amplifiers at the base station (BS). A low-complexity precoding algorithm is proposed, which generates constant-envelope (CE) transmit signals for each BS antenna. To avoid large variations in the phase angle transmitted from each antenna, the difference of the phase angles transmitted in consecutive channel uses is limited to $[-απ\,,\, απ]$ for a fixed $0 < α\leq 1$. To achieve a desired per-user information rate, the extra total transmit power required under the …
Hybrid analog/digital precoding architectures can address the trade-off between achievable spectral efficiency and power consumption in large-scale MIMO systems. This makes it a promising candidate for millimeter wave systems, which require deploying large antenna arrays at both the transmitter and receiver to guarantee sufficient received signal power. Most prior work on hybrid precoding focused on narrowband channels and assumed fully-connected hybrid architectures. MmWave systems, though, are expected to be wideband with frequency selectivity. In this paper, a closed-form solution for fully…
The rate maximization for the $K$-user interference channels (ICs) has been investigated extensively in the literature. However, the dual problem of minimizing the error probability with given signal modulations and/or data rates of the users is less exploited. In this paper, by utilizing the additional degrees of freedom attained from the improper signaling (versus the conventional proper signaling), we optimize the precoding matrices for the $K$-user single-input single-output (SISO) ICs to achieve minimal pair-wise error probability (PEP) and symbol error rate (SER) with two proposed algori…
In this paper, we consider the uplink and downlink precoder design for two-user power-domain multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) systems. We propose novel uplink and downlink precoding and decoding schemes that lower the decoding complexity at the receiver by decomposing the MIMO-NOMA channels of the users into multiple single-input single-output (SISO)-NOMA channels via simultaneous triangularization (ST) of the MIMO channels of the users and a low-complexity self-interference cancellation at the receiver. The proposed ST MIMO-NOMA schemes avoid channel…
The degrees of freedom (DoF) of the $K$-user multiple-input multiple-output (MIMO) interference channel are studied when perfect, but delayed channel state information is available at the transmitter side (delayed CSIT). Recent works have proposed schemes that achieve increasing DoF values, but at the cost of long communication delays. This work proposes three linear precoding strategies, formulated in such a way that the achievable DoF can be derived as a function of the transmission delay, thus elucidating its achievable DoF-delay trade-off. All strategies are based on the concept of interfe…
Given the high throughput requirement for 5G, merging millimeter wave technologies and multi-user MIMO seems a very promising strategy. As hardware limitations impede to realize a full digital architecture, hybrid MIMO architectures, using digital precoding and phased antenna arrays, are considered a feasible solution to implement multi-user MIMO at millimeter wave. However, real channel propagation and hardware non-idealities can significantly degrade the performance of such systems. Experimenting the new architecture is thus crucial to confirm and to support system design. Nevertheless, hybr…
Given a multiple-input multiple-output (MIMO) channel, feedback from the receiver can be used to specify a transmit precoding matrix, which selectively activates the strongest channel modes. Here we analyze the performance of Random Vector Quantization (RVQ), in which the precoding matrix is selected from a random codebook containing independent, isotropically distributed entries. We assume that channel elements are i.i.d. and known to the receiver, which relays the optimal (rate-maximizing) precoder codebook index to the transmitter using B bits. We first derive the large system capacity of b…
In this paper, the problem of designing a forward link linear precoder for Massive Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, we employ a novel and efficient methodology that allows for a sparse representation of multiple users and groups in a fashion similar to Joint Spatial Division and Multiplexing. Then, the method is generalized to include Orthogonal Frequency Division Multiplexing (OFDM) for frequency selective channels, resulting in Combined Frequency and Spatial Division and Multiplexing, a configuration …
Multi-Input Multi-Output (MIMO) techniques have been incorporated with Orthogonal Frequency Division Multiplexing (OFDM) for broadband wireless communication systems. Bit-Interleaved Coded Multiple Beamforming (BICMB) can achieve both spatial diversity and spatial multiplexing for flat fading MIMO channels. For frequency selective fading MIMO channels, BICMB with OFDM (BICMB-OFDM) can be employed to provide both spatial diversity and multipath diversity, making it an important technique. In our previous work, the subcarrier grouping technique was applied to combat the negative effect of subcar…
Hybrid analog-digital precoding is challenging for broadband millimeter-wave (mmWave) massive MIMO systems, since the analog precoder is frequency-flat but the mmWave channels are frequency-selective. In this paper, we propose a principal component analysis (PCA)-based broadband hybrid precoder/combiner design, where both the fully-connected array and partially-connected subarray (including the fixed and adaptive subarrays) are investigated. Specifically, we first design the hybrid precoder/combiner for fully-connected array and fixed subarray based on PCA, whereby a low-dimensional frequency-…
Faster-than-Nyquist (FTN) signaling is a non-orthogonal transmission technique, which has the potential to provide significant spectral efficiency improvement. This paper studies the capacity of FTN signaling for both frequency-flat and for frequency-selective multiple-input multiple-output (MIMO) channels. We show that precoding in time and waterfilling in space is capacity achieving for frequency-flat MIMO FTN. For frequency-selective fading, joint waterfilling in time, space and frequency is required.
We analyze out-of-band (OOB) emissions in the massive multi-user (MU) multiple-input multiple-output (MIMO) downlink. We focus on systems in which the base station (BS) is equipped with low-resolution digital-to-analog converters (DACs) and orthogonal frequency-division multiplexing (OFDM) is used to communicate to the user equipments (UEs) over frequency-selective channels. We demonstrate that analog filtering in combination with simple frequency-domain digital predistortion (DPD) at the BS enables a significant reduction of OOB emissions, but degrades the signal-to-interference-noise-and-dis…
We consider high-dimensional MIMO transmissions in frequency division duplexing (FDD) systems. For precoding, the frequency selective channel has to be measured, quantized and fed back to the base station by the users. When the number of antennas is very high this typically leads to prohibitively high quantization complexity and large feedback. In 5G New Radio (NR), a modular quantization approach has been applied for this, where first a low-dimensional subspace is identified for the whole frequency selective channel, and then subband channels are linearly mapped to this subspace and quantized…
The use of orthogonal signaling schemes such as time-, frequency-, or code-division multiplexing (T-, F-, CDM) in multi-user systems allows for power-efficient simple receivers. It is shown in this paper that by using orthogonal signaling on frequency selective fading channels, the cooperative Nash bargaining (NB)-based precoding games for multi-user systems, which aim at maximizing the information rates of all users, are simplified to the corresponding cooperative resource allocation games. The latter provides additional practically desired simplifications to transmitter design and significan…
Millimeter wave (mm-wave) and massive MIMO have been proposed for next generation wireless systems. However, there are many open problems for the implementation of those technologies. In particular, beamforming is necessary in mm-wave systems in order to counter high propagation losses. However, conventional beamsteering is not always appropriate in rich scattering multipath channels with frequency selective fading, such as those found in indoor environments. In this context, time-reversal (TR) is considered a promising beamforming technique for such mm-wave massive MIMO systems. In this paper…
In the $K$-user single-input single-output (SISO) frequency-selective fading interference channel, it is shown that the maximal achievable multiplexing gain is almost surely $K/2$ by using interference alignment (IA). However, when the signaling dimensions are limited, allocating all the resources to all users simultaneously is not optimal. So, a group based interference alignment (GIA) scheme is proposed, and it is formulated as an unbounded knapsack problem. Optimal and greedy search algorithms are proposed to obtain group patterns. Analysis and numerical results show that the GIA scheme can…
The most relevant linear precoding method for frequency-flat MIMO broadcast channels is block diagonalization (BD) which, under certain conditions, attains the same nonlinear dirty paper coding channel capacity. However, BD is not easily translated to frequency-selective channels, since space-time information is required for transceiver design. In this paper, we demonstrate that BD is feasible in frequency-selective MIMO broadcast channels to eliminate inter-user interference (IUI) if the transmit block length is sufficiently large, and if the number of transmit antennas is greater than the nu…
A Universal Random Precoding Framework for MIMO Systems
College of Information Science and Electronic Engineering, Zhejiang University（浙江大学信息科学与工程学院）；State Key Laboratory of Integrated Services Networks, Xidian University（西安电子科技大学综合业务网国家重点实验室）；National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China（电子科技大学无线通信国家重点实验室）
Most methodologies for modeling Transmission Line (TL) based channels define the input-output relationship in the frequency domain (FD) and handle the TL resorting to a two-port network (2PN) formalism. These techniques have not yet been formally mapped into a discrete-time (DT) block model, which is useful to simulate and estimate the channel response as well as to design optimal precoding strategies. TL methods also fall short when they are applied to Time Varying (TV) systems, such as the power line channel. The objective of this paper is to establish if and how one can introduce a DT block…
Due to limited backhaul/feedback link capacity and channel state information (CSI) feedback delay, obtaining global and instantaneous channel state information at the transmitter (CSIT) is a main obstacle in practice. In this paper, novel transmission schemes are proposed for a class of interference networks that can achieve new trade-off regions between the sum of degrees of freedom (sum-DoF) and CSI feedback delay with distributed and temperately-delayed CSIT. More specifically, a distributed space-time interference alignment (STIA) scheme is proposed for the two-user multiple-input multiple…
A novel architecture for MIMO transmission and reception of filterbank multicarrier (FBMC) modulated signals under strong frequency selectivity is presented. The proposed system seeks to approximate an ideal frequency-selective precoder and linear receiver by Taylor expansion, exploiting the structure of the analysis and synthesis filterbanks. The resulting architecture is implemented by linearly combining conventional MIMO linear transceivers, which are applied to sequential derivatives of the original filterbank. The classical per-subcarrier precoding/linear receiver configuration is obtaine…
In this paper, we study the waveform design problem for a single-input single-output (SISO) radio-frequency (RF) wireless power transfer (WPT) system in frequency-selective channels. First, based on the actual non-linear current-voltage model of the diode at the energy receiver, we derive a semi-closed-form expression for the deliverable DC voltage in terms of the incident RF signal and hence obtain the average harvested power. Next, by adopting a multisine waveform structure for the transmit signal of the energy transmitter, we jointly design the multisine signal amplitudes and phases overall…
Given the critical dependence of broadcast channels by the accuracy of channel state information at the transmitter (CSIT), we develop a general downlink model with zero-forcing (ZF) precoding, applied in realistic heterogeneous cellular systems with multiple antenna base stations (BSs). Specifically, we take into consideration imperfect CSIT due to pilot contamination, channel aging due to users relative movement, and unavoidable residual additive transceiver hardware impairments (RATHIs). Assuming that the BSs are Poisson distributed, the main contributions focus on the derivations of the up…
Hybrid analog and digital precoding allows millimeter wave (mmWave) systems to achieve both array and multiplexing gain. The design of the hybrid precoders and combiners, though, is usually based on knowledge of the channel. Prior work on mmWave channel estimation with hybrid architectures focused on narrowband channels. Since mmWave systems will be wideband with frequency selectivity, it is vital to develop channel estimation solutions for hybrid architectures based wideband mmWave systems. In this paper, we develop a sparse formulation and compressed sensing based solutions for the wideband …
In this paper, we propose low complexity algorithms based on Markov chain Monte Carlo (MCMC) technique for signal detection and channel estimation on the uplink in large scale multiuser multiple input multiple output (MIMO) systems with tens to hundreds of antennas at the base station (BS) and similar number of uplink users. A BS receiver that employs a randomized sampling method (which makes a probabilistic choice between Gibbs sampling and random sampling in each iteration) for detection and a Gibbs sampling based method for channel estimation is proposed. The algorithm proposed for detectio…
