Artificial-Noise-Aided Secure Multi-User Multi-Antenna Transmission With Quantized CSIT: A Comprehensive Design and Analysis

We consider a low-complexity transceiver design for secure communications of a multiuser multi-antenna system with an external multi-antenna eavesdropper. We propose to employ Tomlinson–Harashima precoder (THP) to simultaneously transmit message-bearing signals and artificial noise (AN) according to the quantized channel state information (CSI). Based on random vector quantization of the channel vectors, we obtain analytical approximations of the ergodic secrecy rate (ESR) of each legitimate receiver (LR) and the ergodic secrecy sum rate of the system with arbitrary system parameters. Based on the obtained analytical results, the near-optimal power allocation to the information signals and AN can be obtained using a numerical method. We show using an information-theoretical method that, besides the advantage in the ESR over the linear precoding scheme, THP can reduce the supported rate of the eavesdropper’s channel by preventing the eavesdropper from obtaining the legitimate channels’ (quantized) CSI. The ESR loss of each LR compared with the perfect CSI case will increase without bound for a fixed number of feedback bits. We also derive a feedback bit scaling law to solve this problem. Finally, numerical results are provided to verify our analytical results and also the advantage of the proposed secure nonlinear transceiver over the corresponding linear scheme.

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.

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.

In this work we investigate the degrees of freedom (DoF) performance of the multiple-input multiple-output (MIMO) interference channel (IC) with limited channel state information (CSI) feedback. We generalise two space-time interference alignment (STIA) algorithms to the K user MIMO IC with a transmit power constraint and show how these schemes exploit both current and outdated CSI to achieve an improved DoF performance. We show that by combining the STIA schemes with traditional methods major DoF gain can be achieved for a variety of limited CSI feedback scenarios in comparison to what would be obtained via the use of the traditional techniques on their own. In particular we prove that optimal DoF can still be achieved in situations where current CSI is unavailable for a derived fraction of the time. Finally we validate the promised DoF results via system simulation and show how these DoF gains reflect in terms of sum rate achievable.

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.

We consider a transmit beamforming for an OFDM channel with multiple transmit antennas and single receive antenna. With channel information, a receiver selects and quantizes transmit beamforming vector for each subcarrier. The quantized beamformers are then relayed to the transmitter via a rate-limited feedback channel. We propose to reduce the required number of feedback bits by applying a common transmit beamformer for a cluster of adjacent subcarriers. The sum capacity over all subcarriers depends on a cluster size, the number of feedback bits, and the number of channel taps. Approximation of the optimal cluster size that maximizes the sum rates is derived and is shown to predict simulation results very well. Numerical results show that operating with the optimal cluster size can achieve significant performance gain.

This paper studies the capacity issue of adaptive multiple-input-multiple-output (MIMO) transmissions with channel state information (CSI) feedback over a time-varying channel which is modeled as time-correlated blocks. The CSI is estimated at the receiver and fed back periodically to the transmitter to enable adaptive transmissions. With the objective to maximize the ergodic capacity, a CSI-feedback strategy is proposed based on the optimization of following two parameters. (1) The bit number for the quantization of each CSI and (2) the time interval to refresh the CSI. The first parameter determines the accuracy of the quantization and the latter one deal with the time variation of the channel. The optimization is conducted under a given feedback-capacity constraint i.e., the maximum number of feedback bits per block is fixed in average. A theoretical result is derived and numerical results are presented to show the effectiveness of the proposed strategy.

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.

We consider a downlink multiuser MISO system with bounded errors in the Channel State Information at the Transmitter (CSIT). We first look at the robust design problem of achieving max-min fairness amongst users (in the worst-case sense). Contrary to the conventional approach adopted in literature, we propose a rather unorthodox design based on a Rate-Splitting (RS) strategy. Each user's message is split into two parts, a common part and a private part. All common parts are packed into one super common message encoded using a public codebook, while private parts are independently encoded. The resulting symbol streams are linearly precoded and simultaneously transmitted, and each receiver retrieves its intended message by decoding both the common stream and its corresponding private stream. For CSIT uncertainty regions that scale with SNR (e.g. by scaling the number of feedback bits), we prove that a RS-based design achieves higher max-min (symmetric) Degrees of Freedom (DoF) compared to conventional designs (NoRS). For the special case of non-scaling CSIT (e.g. fixed number of feedback bits), and contrary to NoRS, RS can achieve a non-saturating max-min rate. We propose a robust algorithm based on the cutting-set method coupled with the Weighted Minimum Mean Square Error (WMMSE) approach, and we demonstrate its performance gains over state-of-the art designs. Finally, we extend the RS strategy to address the Quality of Service (QoS) constrained power minimization problem, and we demonstrate significant gains over NoRS-based designs.

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.

This paper investigates a precoding method in downlink multiuser multiple-input multiple-output (MIMO) transmission with multiple base station (BS) cooperation, where each user device basically feeds back the instantaneous channel state information (CSI) to only the nearest BS, but the users near the cell edge additionally feedback the instantaneous CSI to the second nearest BS among the cooperating BSs. Our precoding method is categorized as a form of multi-cell processing (MCP) [5], in which the transmission information to a user is shared by the cooperating BSs in order to utilize fully the degrees of freedom of the spatial channel, and is based on block diagonalization of the channel matrix. However, since some elements of the channel matrix are unknown, we allow partially non-orthogonal transmission. More specifically, we allow inter-user interference to users with limited instantaneous CSI feedback from the channel where the instantaneous CSIs of those users are not obtained at the BSs. The other sources of inter-user interference are set to zero based on the block diagonalization of the channel matrix. The proposed method more efficiently utilizes the degrees of freedom of the spatial channel compared to the case with full orthogonal transmission at the cost of increased inter-user interference. Simulation results show the effectiveness of the proposed method compared to the conventional approaches, which can accommodate the partial CSI feedback scenario, from the viewpoints of the required transmission power and achievable throughput.

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.