Non-uniform directional dictionary-based limited feedback for massive MIMO systems

Channel state information (CSI) at the base station (BS) is crucial to achieve beamforming and multiplexing gains in multiple-input multiple-output (MIMO) systems. State-of-the-art limited feedback schemes require feedback overhead that scales linearly with the number of BS antennas, which is prohibitive for 5G massive MIMO. This paper proposes novel limited feedback algorithms that lift this burden by exploiting the inherent sparsity in double-directional MIMO channel representation using overcomplete dictionaries. These dictionaries are associated with angle of arrival and angle of departure that specifically account for antenna directivity patterns at both ends of the link. The proposed algorithms achieve satisfactory channel estimation accuracy using a small number of feedback bits, even when the number of transmit antennas at the BS is large-making them ideal for 5G massive MIMO. Judicious simulations reveal that they outperform a number of popular feedback schemes and underscore the importance of using angle dictionaries matching the given antenna directivity patterns, as opposed to uniform dictionaries. The proposed algorithms are lightweight in terms of computation, especially on the user equipment side, making them ideal for actual deployment in 5G systems.

A multihop regenerative relay system is considered. We explore adaptive power allocation (PA) under a total power constraint to minimize the system error probability when the perfect channel state information (CSI) is known at the transmitters. We propose adaptive PA schemes with limited feedback when the transmitters have no perfect knowledge of CSI. Simulation results demonstrate the good performance of the proposed PA scheme with perfect CSI. When no perfect CSI is available at the transmitters, the proposed PA schemes with a small number of feedback bits are able to achieve very close performance to the adaptive PA with perfect CSI.

Employing multiple antennas at the transmitter is a well-established technique for providing diversity advantage in wireless systems. Transmit beamforming relies on the assumption of current channel knowledge at the transmitter, which is unrealistic when the forward and reverse links are separated in frequency. One solution to this problem is for the receiver to send a small number of feedback bits that convey channel information to the transmitter. Feedback design techniques have been proposed over the past few years, but they were derived using the assumption of spatially uncorrelated Rayleigh fading. This correspondence addresses the design of limited feedback beamformers when the channel is correlated.

To maintain a specific degree of multiplexing gain with limited feedback in multiple-input/multiple-output broadcast channels, the number of feedback bits has been increased linearly with the signal-to-noise ratio (SNR) measured in decibel, and conditions for the slope of this increase have been derived in previous studies. However, previous studies mostly focused on the chordal distance (ChD) for channel quantization, although it is not an optimally designed distance measure. Thus, the possibility exists that the same degree of multiplexing gain can be obtained by using fewer feedback bits than the existing method requires. In this paper, we propose an optimal distance measure that can maximize the multiplexing gain achieved by limited-feedback-based block diagonalization over broadcast channels. Then, we provide a sufficient condition for the number of feedback bits to achieve a specific degree of multiplexing gain with the proposed method. The sufficient number of feedback bits is given by a linear function of the SNR (decibel) as in previous studies, but the slope of the linear increase can be much less than that obtained in previous studies. As a consequence, the proposed method achieves higher multiplexing gain and corresponding throughput than the existing methods with the same number of feedback bits.

In Multi-user MIMO (MU-MIMO) downlink system, suitable user selection schemes can improve spatial diversity gain. In most of previous studies, it is always assumed that the base station (BS) knows full channel state information (CSI) of each user, which does not consider the reality. However, there are only limited feedback bits in real system. Besides, user fairness is often ignored in most of current user selection schemes. To discuss the user fairness and limited feedback, in this paper, the user selection scheme with limited feedback bits is proposed. The BS utilizes codebook precoding transmitting strategy with LTE codebook. Furthermore, this paper analyzes the influence of the number of feedback bits and the number of users on user fairness and system sum capacity. Simulation results show that in order to achieve better user fairness, we can use fewer bits for feedback CSI when the number of user is small, and more feedback bits when the number of users is large.

Downlink multi-user transmission techniques that allow several users to be served simultaneously in frequency and time have been recognized as a promising means to increase system capacity. However they require accurate channel state information (CSI) at the base station (BS) such that appropriate signal processing can be performed to separate multiple users in the space domain. In practice however, CSI cannot be perfectly known to the BS due to the capacity-limited feedback channel in FDD systems for instance. In this letter we investigate multiuser multiple-input single-output (MU-MISO) transmission with limited feedback. In particular we identify the useful information that the BS needs to deal with inter-user interference and a codebook design is derived accordingly. In addition, an adaptive threshold-based feedback approach is proposed, where only users with good feedback quality are allowed to do feedback. It is shown that the adaptive scheme can effectively improve the system performance given a fixed number of feedback bits.

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 (PU <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> RC) which is an extended version of random beamforming (RBF). To improve performance, ZFBF needs more feedback bits, and PU <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> RC 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.

In this paper, we consider the problem of Angle of Departure (AoD) based channel feedback in Frequency Division Duplex (FDD) massive Multiple-Input Multiple-Output (MIMO) systems with multiple antennas at the users. We consider the use of Zero-Forcing Block Diagonalization (BD) as the downlink precoding scheme. We consider two different cases; one in which the number of streams intended for a user equals the number of antennas at that user and the other case in which the number of streams is less than the number of user antennas. BD requires the feedback of the subspace spanned by the channel matrix at the user or a subspace of it in the case of having less number of streams than the number of antennas at a specific user. Based on our channel model, we propose a channel feedback scheme that requires less feedback overhead compared to feeding back the whole channel matrix. Then, we quantify the rate gap between the rate of the system with perfect Channel State Information (CSI) at the massive MIMO Basestation (BS) and our proposed channel feedback scheme for a given number of feedback bits. Finally, we design feedback codebooks based on optimal subspace packing in the Grassmannian manifold. We show that our proposed codes achieve performance that is very close to the performance of the system with perfect CSI at the BS.

In this paper, we investigate limited feedback precoding for two single-user MIMO systems. The first one employs spatial diversity at the transmitter and Maximum Ratio Combining at the receiver. The second one uses spatial multiplexing at the transmitter and V-BLAST signal processing at the receiver. For both systems, the precoder is selected at the receiver among a codebook and its index is conveyed to the transmitter through an error free feedback channel. For the first system, we consider two Grassmannian precoding codebooks and show through simulation results that a small number of feedback bits can reach the theoretical performance. For the case of a single-user system based on spatial multiplexing, we propose a novel criterion for selecting among codebook matrices the optimum precoding matrix at the receiver which maximizes the minimum signal to interference and noise ratio over the transmitted substreams. Simulation results show that our proposed selection criterion outperforms three other criteria introduced in the literature for the spatial muliplexing MIMO system. They also show a significant enhancement over the unprecoded spatial multiplexing system.

Accurate channel state information (CSI) at base station (BS) is the key to achieve full multiplexing and diversity gain in traditional multiple-input multiple-output (MIMO) systems. In frequency-division-duplex (FDD) systems, it is obtained through downlink training and uplink feedback. However, the training and feedback overhead in massive MIMO systems is unacceptable for the large number of antennas equipped at BS. To reduce the CSI feedback overhead and improve CSI quantization accuracy, we propose a limited feedback scheme for spatio-temporal correlated massive MIMO channel. The proposed scheme jointly performs Karhunen-Loève transform (KLT) and polar-cap quantization on CSI. For the compactly deployed antennas at BS, there exists spatial correlation in massive MIMO channel. When the user equipment (UE) moves slowly, adjacent channels feature temporal correlation. The high dimensional and spatial correlated CSI is compressed through KLT. Then the compressed CSI is normalized to be isotropic to perform polar-cap quantization. Simulation results show that the proposed scheme is capable of improving the sum-rate performance with limited feedback bits for massive MIMO systems.

The scalar N t × N r MIMO system can be designed as the Nt independent SISO transmitters, where N t and N r are the number of transmit and receive antennas, respectively. Each of the transmitters has an independent symbol mapper, which rotates the phase according to the phase of the channel from its antenna to the receiver reference antenna. Every symbol mapper assigns a maximum degree of freedom to the signal, which in turn requires the minimum feedback bits. The Nr received signals reform the same transmit constellation after applying the combining vector of the GMRC (Generalized Maximum Ratio Combining) receiver. The Wireless open-Access Research Platform (WARP) is employed for prototyping and testing these transmitters. The empirical results of a frame transmission reflect the theory and validate the codebooks. However, the hardware-based imperfections and the channel estimation errors affect the performance of the frame. The former errors are originated from a non-ideal time synchronization, Automatic Gain Control (AGC), Analogue to Digital Converters (ADCs) and Digital to Analogue Converters (DACs). The channel estimations are done prior to the frame transmission. However, empirically, the estimated channels are not constant during the frame transmission, and there are fluctuations in their phases and magnitudes. These fluctuations are intensive when there is a line of sight (LOS) path between the antennas. It is shown that codebooks with a low number of feedback bits perform better than those with a large number of feedback bits in this situation.

Massive multiple-input–multiple-output (MIMO) systems which include a large number of service antennas have received a great deal of attention as a means to improve both spectral efficiency (SE) and energy efficiency (EE) of wireless communication systems. In this article, we study the feasibility of using Massive MIMO to support a vast amount of underwater Industrial Internet of Things (IIoT) devices. By using a large number of antennas as compensation entities for the low bandwidth in the underwater channel, we show that underwater Massive MIMO can simultaneously support a massive amount of underwater IIoT devices. Electromagnetic radio frequency (RF) and acoustic waves are used to present the performance with respect to SE, throughput (TP) per user equipment (UE), and coverage. Additionally, we show that both Massive MIMO with RF and acoustic waves have the same closed-form upper bounds which can be used as an important design tool of underwater IIoT networks. Numerical results verify the theoretical analysis.

We present a secure multi-user multi-antenna transmission framework based on artificial-noise-aided linear zero-forcing beamforming, with limited channel state information feedback from multiple distributed legitimate users (LUs). The secrecy performance of the proposed scheme is analytically investigated and optimized. We develop a new accurate closed-form expression of a lower bound on the ergodic secrecy rate (ESR) of each LU without assuming asymptotes for any system parameter. To make system design tractable, we develop another lower bound on ESR which is so analytically amenable that it enables one to not only extend the results of the previous related works but also explore some untouched aspects of the well known artificial-noise-aided scheme. We derive the optimized power allocation coefficient to message-bearing signals which maximizes the latter ESR lower bound. Furthermore, we theoretically study respectively the impacts of the two main parameters, i.e., transmit power $P$ and the number of feedback bits of each LU $B$ , on the power allocation coefficient, and show the asymptotic results for the high-power and high-quantization-resolution systems. We also develop a sufficient condition on $P$ and $B$ under which a positive ESR of each LU can be achieved. We study some important parameters called the minimum required transmit power (MRTP) and the minimum required number of feedback bits (MRFBs) for each LU to achieve a positive ESR or to achieve a target ESR, which have rarely been touched before. Besides, we propose the algorithms to obtain the MRTP and MRFBs. Numerical results are also provided to verify our theoretical results.

The provision for spectrally efficient multicast broadcast services (MBS) is one of the key functional requirements for next generation wireless communication systems. The challenge inherent to MBS is to ensure that all MBS users can be served, and one effective solution to this problem is to employ MIMO multicast transmit precoding. In previous works on MIMO multicast transmit precoding design, the authors either assumed (1) perfect transmitter-side channel state information (CSIT) or (2) special channel conditions that facilitate precoder design with imperfect CSIT. In this paper, we focus on transmit precoding design for MBS where the CSIT is obtained via limited feedback. In addition, we analyze the average minimum receive signal-noise-ratio (RxSNR) among the MBS users and study the order of growth with respect to the number of MBS users, the number of feedback bits, and the number of transmit antennas. Finally, we propose a threshold based feedback reduction scheme and study the tradeoff between feedback cost and performance loss.

Channel state information (CSI) acquisition is one of the major challenges for massive MIMO systems to enable high efficiency MIMO transmissions. Limited feedback schemes, which quantize CSI into limited number of bits and feed these bits back to the base station (BS), are widely used in real-life mobile networks for BSs to obtain downlink CSI. Practical limited feedback schemes usually have large feedback granularity and introduce severe nonlinear quantization error due to the constraint on feedback overhead. It is hard for legacy signal processing technologies to reconstruct CSI accurately for high efficiency downlink transmissions. Different from the legacy signal processing technologies, deep neural networks trained with big data have strong abilities to fit any nonlinear functions and learn the complex signal model behind the big data, which is a useful tool to solve problems that are nonlinear or hard to be described mathematically. Motivated by these observations, we consider a deep learning based approach for BS receivers to reconstruct CSI based on the limited feedback bits from user equipment (UE). The CSI reconstruction is similar with the image super-resolution which reconstructs a high resolution image from a low resolution one based on the structure information learned by the neural network itself. Performance evaluations demonstrate that the proposed method outperforms the legacy algorithms. The improvement on spectrum efficiency is about 25%. It can also reconstruct the CSI with lower density reference signal (RS) than that in current specification, e.g., the RS density can be 1/32 of current one. Therefore, the reference signal and feedback overhead can be reduced with our method. These results show the potential gain of applying deep learning to physical layer signal processing at the receiver side only, which has little air-interface impact and does not require much effort on enhancing network specifications. Therefore, it is feasible to be deployed in current 5th generation mobile networks with the pace of network evolutions, and opens the gate of intelligent physical layer design for future generations of mobile networks.