Limited Feedback Diversity Techniques for Correlated Channels

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.

This work proposes a new limited feedback channel estimation framework. The proposed approach exploits a sparse representation of the double directional wireless channel model involving an over complete dictionary that accounts for the antenna directivity patterns at both base station (BS) and user equipment (UE). Under this sparse representation, a computationally efficient limited feedback algorithm that is based on single-bit compressive sensing is proposed to effectively estimate the downlink channel. The algorithm is lightweight in terms of computation, and suitable for real-time implementation in practical systems. More importantly, under our design, using a small number of feedback bits, very satisfactory channel estimation accuracy is achieved even when the number of BS antennas is very large, which makes the proposed scheme ideal for massive MIMO 5G cellular networks. Judiciously designed simulations reveal that the proposed algorithm outperforms a number of popular feedback schemes in terms of beam forming gain for subsequent downlink transmission, and reduces feedback overhead substantially when the BS has a large number of antennas.

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 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.

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 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.

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.

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.

In this article, we analyze the selective multiple-input multiple-output broadcast channel, where links are assumed to be selective in both time and frequency. The assumption of full channel knowledge at the transmitter side requires a large amount of feedback, and it is therefore not practical to be implemented in real systems. A more feasible solution with finite rate feedback originally proposed by Jindal in IEEE Trans. Inf. Theory is applied here to the selective fading case, where the minimal number of feedback bits required to achieve the full multiplexing is derived. We show that the correlation between time frequency channels can be used in order to minimize the number of feedback bits to the transmitter side while conserving the maximal multiplexing gain. Finally, the practical implementation of a time-frequency channel quantization scheme is addressed, and a low-complexity scheme that also achieves the multiplexing gain is proposed.

We present a fast sub-optimal searching algorithm for the closed-loop transmit diversity scheme used in wireless systems. Under the low mobility condition and with perfect channel knowledge at the receiving end, our proposed searching algorithm can use a limited number of feedback bits to provide a sub-optimal solution that can achieve SNR values close to the optimal solution with a greatly reduced complexity and outperform other sub-optimal schemes. The scheme also works well under the presence of feedback errors.

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 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.

Reconfigurable intelligent surfaces (RISs) represent a pioneering technology to realize smart electromagnetic environments by reshaping the wireless channel. Jointly designing the transceiver and RIS relies on the channel state information (CSI), whose feedback has not been investigated in multi-RIS-assisted frequency division duplexing systems. In this study, the limited feedback of the RIS-assisted wireless channel is examined by capitalizing on the ability of the RIS in channel customization. By configuring the phase shifters of the surfaces using statistical CSI, we customize a sparse channel in rich-scattering environments, which significantly reduces the feedback overhead in designing the transceiver and RISs. Since the channel is customized in terms of singular value decomposition (SVD) with full-rank, the optimal SVD transceiver can be approached without a matrix decomposition and feeding back the complete channel parameters. The theoretical spectral efficiency (SE) loss of the proposed transceiver and RIS design is derived by considering the limited CSI quantization. To minimize the SE loss, a bit partitioning algorithm that splits the limited number of bits to quantize the CSI is developed. Extensive numerical results show that the channel customization-based transceiver with reduced CSI can achieve satisfactory performance compared with the optimal transceiver with full CSI. Given the limited number of feedback bits, the bit partitioning algorithm can minimize the SE loss by adaptively allocating bits to quantize the channel parameters.

To increase the flexibility of network architecture, a mobile X-haul network (MXN) structure has been considered, in which the wireless front-haul, mid-haul, and backhaul links are integrated into a wireless X-haul link. Accordingly, the mobile station can be served by flexible transmission reception point (f-TRP) or remote radio head through the access link and the associated data should be delivered from XDU to the f-TRP through the X-haul link. Accordingly, the system throughput is determined by the minimum value of the access link capacity and the X-haul link capacity. In this paper, when millimeter-wave (mmWave) is exploited in such MXN with in-band full duplex, the optimal beamforming strategy is proposed, in which the receive beamforming for the X-haul link and the transmit beamforming for the access link are jointly designed to maximize the system throughput. Furthermore, we investigate the rate loss due to the quantization error of the channel state information at f-TRP with limited feedback, in which its upper bound is analytically derived and exploited in the determination of the number of feedback bits for a given finite rate loss.