Precoding Design for Multi-Antenna Multicast Broadcast Services With Limited Feedback

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.

In this paper, a comprehensive comparison analysis in terms of outage probability and average symbol error ratio (SER) is presented for cooperative cognitive multiple-input and multiple-output (CC-MIMO) multiuser systems with amplify-and-forward (AF) protocol. Specially, we consider two scenarios where the CC-MIMO multiuser systems have the perfect and imperfect channel state information (CSI). The CC-MIMO multiuser systems consist of one multi-antenna source, one single-antenna relay, and multiple multi-antenna destinations. At the secondary source and destinations, the maximal ratio transmission (MRT) and maximal ratio combining (MRC) are employed, respectively. For such CC-MIMO multiuser systems, we first obtain the exact closed-form expressions of outage probability under the two cases where the CC-MIMO multiuser systems have the perfect and imperfect CSI. Then, to reduce the implementation complexity, the tight lower bounds of outage probability and average SER are derived. Finally, to obtain insight, by using the high signal-to-noise ratio (SNR) approximation, the asymptotic estimations of outage probability are achieved. The numerical results show that the derivations are agreed with the simulations, which validate our derivations. At the same time, the results show that, for the systems without perfect CSI, the achievable diversity order reduces to one, regardless of the number of antennas at the cognitive source and destinations as well as the number of the cognitive destinations. Nevertheless, these key parameters affect the coding gain of the CC-MIMO multiuser systems. When the systems have the perfect CSI (or without feedback delay), the achievable diversity gain is determined by the minimum between the number of source’s antennas and the product of the number of destinations and the number of destination’s antennas. For the effect of PU’s parameters, our results indicate that primary systems only affect the coding gain but not the diversity gain.

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.

Multiple input multiple output (MIMO) processing techniques are of interest for the next generation wireless communication systems due to their potential ability to dramatically improve the system capacity. There have been existed several multi-user MIMO (MU-MIMO) transmit schemes such as zero-forcing dirty paper coding (ZF-DPC), and zero-forcing beamforming (ZFBF). In this paper, we analysis and compare the dynamic transmission schemes based on TDMA and SDMA under perfect and imperfect channel state information (CSI). The system throughput (sum data rate), the optimal user number that can be supported are evaluated under perfect CSI by computer simulations. The effect of imperfect CSI on the throughput of TDMA and SDMA is also investigated. The results show that under perfect channel state information at both transmitter and receiver, the SDMA schemes can achieve a larger throughput than the TDMA scheme because SDMA can fully explore the multiuser diversity by transmitting to the optimal set of users. In contrast, the results show that the system performance of SDMA scheme is sensitive to the channel error.

In this paper, with the aid of new analytical method, we present a new closed-form expression for the ergodic capacity of full-duplex relaying (FDR) systems, with multiple antenna amplify-and-forward (AF) cooperative networks and imperfect channel state information (CSI). At the relay, the loopback self-interfernce (LI) is mitigated by using receive zero-forcing (ZF) precoding scheme, then steering the signal to the destination by using the maximum-ratio transmission (MRT) technique. To facilitate comparison, a closed-form expression for the ergodic capacity of half-duplex relaying (HDR) systems with multiple antenna AF cooperative networks is also addressed, when maximum-ratio combining (MRC)/MRT precoding schemes are performed at the relay input/output, respectively. Therefore, since perfect CSI is not available in practice, this paper investigates the impact of channel estimation errors on the performance of receive ZF/MRT and MRC/MRT schemes. These expressions are exact in the case of perfect CSI and form a very tight indistinguishable lower-bound in the case of imperfect CSI. Numerical results sustained by Monte-Carlo simulations show the exactness of the proposed analytical expressions in perfect CSI and the tightness of the lower-bounds in imperfect CSI. In addition, it is seen here that the FDR AF cooperative systems outperforms the HDR AF cooperative systems in terms of capacity. Furthermore, in contrast to perfect CSI, in the presence of imperfect CSI, an ergodic capacity ceiling is seen as SNR increases. Besides, it is seen that the ergodic capacity degradation due to imperfect CSI is higher in the FDR case because of the extra LI estimation errors.

This paper investigates a multiuser MIMO relay downlink system with imperfect channel estimation and limited feedback. Compared with the system using perfect channel state information (CSI), we analyze the achievable rate loss due to CSI mismatch arising from both channel estimation and CSI quantization feedback. An upper bound to the rate loss is firstly derived to characterize the effect of imperfect CSI. Given the rate loss bound, we then present a limited feedback strategy for both two-hop channels in the relay system to guarantee a bounded rate loss for growing SNRs. This newly presented strategy reveals the relationship between CSI quantization level and other system parameters, including the transmit power and the pilots for channel estimation, on the entire two-hop system. Finally, computer simulations are carried out for verifying the correctness of our derived results.

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.

The potential gains of multiple antennas in wireless systems can be limited by channel state information imperfections. In this context, this paper tackles the limited feedback in multiuser correlated multiple input single output (MU-MISO). We propose a framework to feedback the minimum number of bits with limited performance degradation. This framework is based on decor relating the channel state information by compression and then quantize the compressed (CSI) and feedback it to the base station (BS). We characterize the rate loIEEss resulting from the proposed framework. An upper bound on the rate loss is derived in terms of the amount of feedback and the statistics of the channel. Based on this characterization, we propose an adaptive bit allocation algorithm that takes into the account the channel statistics to reduce the rate loss induced by the quantization. Moreover, in order to maintain a constant rate loss with respect to perfect CSI, it is shown that the number of feedback bits should scale linearly with the SNR (in dB) and to the rank of the user transmit correlation matrix. We validate the proposed framework by Monte-carlo simulations.

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 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.

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 traditional limited feedback scheme can use imperfect channel state information to achieve interference alignment (IA) in a fully connected situation. But these solutions could no longer be used directly in heterogeneous networks where partial connectivity is considered. To solve this problem, this article proposes an IA scheme based on limited feedback with differentiation for the two‐tiered heterogeneous network. First, users who are affected by different types and numbers of interference and corresponding base stations are divided into different units according to the partial connectivity of heterogeneous networks. Then, we design interference alignment algorithm for each unit separately. Next, considering the imperfect channel state information, we derive the leakage of interference caused by the limited feedback, and give expressions for the upper bound of sum rate loss in various units. Finally, dynamic feedback bit allocation is carried out to each unit with the goal of minimizing the throughput loss in the limited feedback system. The simulation results show that the proposed IA scheme can eliminate interference well and efficiency of limited feedback can be improved through dynamic feedback bit allocation, so that system can obtain higher sum rate than other schemes.

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 wireless communication systems, the intended receiver is able to obtain the perfect channel state information (CSI) as long as the training sequence is sufficiently long, and then through a quantized feedback channel (QFC), the transmitter gets imperfect CSI caused by the quantized noise. In general, the design of efficient coding schemes for wireless channels with imperfect CSI at the transmitter (I-CSIT) is difficult and challenging, and one possible method is to construct such a scheme by using channel feedback. In the literature, it has already been shown that the classical Schalkwijk-Kailath (SK) scheme for the additive white Gaussian noise (AWGN) channel with noiseless feedback is a highly efficient coding scheme since its coding complexity is extremely low and the decoding error doubly exponentially decays as the coding blocklength tends to infinity. Existing SK-type schemes mainly focus on the case that perfect CSI is known at the transceiver, and adopt modulo lattice function to eliminate the impact of feedback channel noise (often considered as AWGN) on the performance of SK-type schemes. However, for channels with I-CSIT and QFC, this does not work since the distribution of quantized noise is unknown and I-CSIT brings additional non-convergence estimation error to the transceiver, leading to the application of SK-type schemes to practical wireless scenarios becomes challenging. In this paper, first, for the quasi-static fading channel with I-CSIT and QFC, we design a modulo lattice based SK-type scheme where the receiver adopts an auxiliary signal to decode the message, and numerical results show that the rate of our scheme almost approaches that of the same model with perfect CSI at the transceiver and noise-free feedback for some cases. Next, we further extend the above scheme to the two-path fading scenario, which is modeled as the two-ray channel with I-CSIT and QFC. Treating the signal of the second path as a relay, our extended scheme combines the amplify-and-forward relay strategy and the previously proposed scheme for the same model without ISI. However, this extended scheme cannot be applied to multi-path fading scenario, to this end, we propose a new SK-type scheme for the multi-path fading case. The intuition behind this scheme is to transform the multi-path fading channel into a fading MIMO channel by discrete fourier transform (DFT), and then apply the SK-type scheme to the MIMO channel in frequency domain and use inverse DFT to obtain the codeword in time domain. The study of this paper may provide a way to design efficient coding scheme for fading channels in the presence of imperfect CSI and quantized feedback.

The advantages envisioned from using large antenna arrays have made massive multiple- input multiple-output systems (also known as massive MIMO) a promising technology for future wireless standards. Despite the advantages that massive MIMO systems provide, increasing the number of antennas introduces new technical challenges that need to be resolved. In particular, symbol detection is one of the key challenges in massive MIMO. Obtaining accurate channel state information (CSI) for the extremely large number of chan- nels involved is a difficult task and consumes significant resources. Therefore for Massive MIMO systems coherent detectors must be able to cope with highly imperfect CSI. More importantly, non-coherent schemes which do not rely on CSI for symbol detection become very attractive. Expectation propagation (EP) has been recently proposed as a low complexity algo- rithm for symbol detection in massive MIMO systems , where its performance is evaluated on the premise that perfect channel state information (CSI) is available at the receiver. However, in practical systems, exact CSI is not available due to a variety of reasons in- cluding channel estimation errors, quantization errors and aging. In this work we study the performance of EP in the presence of imperfect CSI due to channel estimation er- rors and show that in this case the EP detector experiences significant performance loss. Moreover, the EP detector shows a higher sensitivity to channel estimation errors in the high signal-to-noise ratio (SNR) regions where the rate of its performance improvement decreases. We investigate this behavior of the EP detector and propose a Modified EP detector for colored noise which utilizes the correlation matrix of the channel estimation error. Simulation results verify that the modified algorithm is robust against imperfect CSI and its performance is significantly improved over the EP algorithm, particularly in the higher SNR regions, and that for the modified detector, the slope of the symbol error rate (SER) vs. SNR plots are similar to the case of perfect CSI. Next, an algorithm based on expectation propagation is proposed for noncoherent symbol detection in large-scale SIMO systems. It is verified through simulation that in terms of SER, the proposed detector outperforms the pilotbased coherent MMSE detector for blocks as small as two symbols. This makes the proposed detector suitable for fast fading channels with very short coherence times. In addition, the SER performance of this detec- tor converges to that of the optimum ML receiver when the size