Reduced feedback for selective fading MIMO broadcast channels

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 study a MIMO fading broadcast channel where each receiver has perfect channel state information while the channel state information at the transmitter is acquired by explicit channel feedback from each receiver through capacity-constrained feedback links. Two feedback schemes are considered, i.e., the analog and digital feedback. We analyze the achievable ergodic rates of zero-forcing dirty-paper coding (ZF-DPC), which is a nonlinear precoding scheme inherently superior to linear ZF beamforming. Closed-form lower and upper bounds on the achievable ergodic rates of ZF-DPC with Gaussian inputs and uniform power allocation are derived. Based on the closed-form rate bounds, sufficient and necessary conditions on the feedback channels to ensure nonzero and full downlink multiplexing gain are obtained. Specifically, for analog feedback in both AWGN and Rayleigh fading feedback channels, it is sufficient and necessary to scale the average feedback link SNR linearly with the downlink SNR in order to achieve the full multiplexing gain. While for the random vector quantization-based digital feedback with angle distortion measure in an error-free feedback link, it is sufficient and necessary to scale the number of feedback bits B per user as where M is the number of transmit antennas and is the average downlink SNR.

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 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.

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.

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.

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.

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.

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.

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.

For MIMO beamforming, the Eigen Beamforming (EB) technique provides the best performance with the expense of knowing full channel information. To reduce such an expense, the Quantized Beamforming (QB) has been presented by using only some feedback bits to calculate the suitable beamforming vectors. However, QB has a drawback in the complexity of finding the beamforming vectors and it is more difficult for a lot of feedback bits. In this paper, the new technique named as Angular Beamforming (AB) has been presented to overcome such a drawback of QB. The investigations are undertaken by sending multiple data streams into 4x4 MIMO system. The effect of different data streams and number of feedback bits are studied. The simulation results indicate that AB technique performs very well and its performance is as good as QB.

In a wireless multi-user system using multiple antennas, full multiplexing gain can be achieved through perfect channel state information (CSI) at the base station (BS). However, because of the limitations on the feedback rate and of standard requirements, such as the 3GPP, it is difficult to obtain perfect CSI, or even partial CSI with the extremely large number of feedback bits needed at the region of high signal-to-noise ratios (SNR) in practical systems. Instead of a feedback channel resource, this paper considers another resource for the system, a cooperation channel, which can be used by users to participate in cooperation in a broadcast fading channel. The cooperation among users in a multi-user system has the effect of transforming it into a cooperative point-to-point MIMO system. This paper analyzes the cooperation channel gain and the mobile power used in a cooperation channel to maintain a constant rate gap against the zero-forcing beamforming scheme with full CSI at the BS. In addition, the performance results of this proposed cooperation strategy are provided by computer simulations.

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.

Spatial interference avoidance is a simple and effective way of mitigating interference in multi-antenna wireless networks. The deployment of this technique requires channel-state-information (CSI) feedback from each receiver to all interferers, resulting in substantial network overhead. This paper proposes the method of distributive feedback control that intelligently allocates feedback bits over multiple feedback links and adapts feedback to channel dynamics. Using tools from stochastic optimization, the structure of the optimal control policy is characterized. Specifically, the optimal numbers of feedback bits are proved to increase with corresponding interference-channel gains and feedback is performed only when such gains are large or the transmit-CSI errors are significant. Simulation demonstrates that the proposed feedback-control design yields significant throughput gain over the conventional fixed-feedback approach especially at low mobility.

In this paper, we propose a full rate space-time block code selection technique, which achieves full diversity when more than two transmit antennas are used for transmission. Only one or few feedback bits are needed at the transmitter, representing relative state information of the channels. Moreover, the proposed scheme allows separate decoding of transmitted symbols at the receiver. It is shown by computer simulations that, the new approach provides SNR improvement, especially when feedback errors occur, compared to the transmit antenna selection technique associated with Alamouti's scheme, for the same number of feedback bits