Adaptive Modulation Based on Finite-Rate Feedback in Multiuser Diversity Systems

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 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.

In multiuser massive MIMO systems, it is not clear whether users should feed back the channel or the precoder when they can exchange the channel state information (CSI). This paper compares the precoder feedback scheme with the channel feedback scheme. It is found that when there are sufficient number of bits for CSI exchange, the precoder feedback scheme can reduce the interference leakage to 1 /(K − 1) of the channel feedback scheme, where K is the number of users. Moreover, the interference leakage under the precoder feedback scheme decreases faster than the channel feedback scheme when the number of feedback bits increases.

In this paper, we consider the problem of channel feedback in massive multiple-input-multiple-output (MIMO) systems. For the downlink scenario, we present a detailed comparison between the performance of the quantized and the analog channel feedback schemes for the case of having multiple antenna users. Both schemes’ performance is evaluated by deriving an upper bound on the rate gap between the rate of the system with perfect channel state information (CSI) and with imperfect CSI for both feedback schemes. We compare the two schemes, namely, quantized channel feedback and analog channel feedback, under the same resources allocated for channel feedback for a fair comparison. Moreover, we consider two different downlink transmission schemes; the first one does not consider power allocation across the streams and the second one does power allocation (water-filling) across the streams. Our results show that the analog feedback scheme performs better in the low signal to noise (SNR) region when performing power allocation across the multiple data streams. However, the quantized channel feedback scheme performs better at the high SNR region, where the quantized CSI can provide a better approximation of the actual CSI. Finally, simulation results are presented to verify our theoretical analysis and demonstrate our conclusions.

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.

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.

In the presence of perfect channel state information (CSI), the achievable degrees of freedom (DoF) in wireless interference networks can be linearly scaled up with the number of users. Achievability is based on the idea of interference alignment (IA). However, in the presence of imperfect CSI, the sum rate becomes degraded, and full DoF may no longer be achievable. In this paper, the authors propose novel least squares (LS)- and minimum mean square error (MMSE)-based IA schemes that adaptively design beamformers by relying on the availability of imperfect CSI and knowledge of the channel estimation error variance in advance. Interestingly and unlike the other robust algorithms, the proposed adaptive schemes do not impose extra computational complexity compared to their nonadaptive counterparts. It is shown that the LS-based IA is able to outperform interference leakage minimization algorithms under both perfect and imperfect CSI. Furthermore, the authors compare the performance of the proposed MMSE-based IA with maximum signal-to-interference-plus-noise ratio (Max-SINR) algorithm. The authors show that while under perfect CSI, the MMSE-based IA achieves the same performance as that of Max-SINR, the former outperforms the latter under CSI mismatch. Meanwhile, it is shown that the proposed MMSE-based IA needs less CSI to be available and has less computational complexity compared to Max-SINR.

This paper proposes an efficient two-stage beamforming and scheduling algorithm for the limited-feedback cooperative multi-point (CoMP) systems. The system includes multiple base-stations cooperatively transmitting data to a pool of users, which share a rate-limited feedback channel for sending back the channel state information (CSI). The feedback mechanism is divided into two stages that are used separately for scheduling and beamforming. In the first stage, the users report their best channel gain from all the base-station antennas and the basestations schedule the best user for each of their antennas. The scheduled users are then polled in the second stage to feedback their quantized channel vectors. The paper proposes an analytical framework to derive the bit allocation between the two feedback stages and the bit allocation for quantizing each user's CSI. For a total number of feedback bits B, it is shown that the number of bits assigned to the second feedback stage should scale as log B. Furthermore, in quantizing channel vectors from different base-stations, each user should allocate its feedback budget in proportion to the logarithm of the corresponding channel gains. These bit allocation are then used to show that the overall system performance scales double-logarithmically with B and logarithmically with the transmit SNR. The paper further presents several numerical results to show that, in comparison with other beamforming-scheduling algorithms in the literature, the proposed scheme provides a consistent improvement in downlink sum rate and network utility. Such improvements, in particular, are achieved in spite of a significant reduction in the beamforming-scheduling computational complexity, which makes the proposed scheme an attractive solution for practical system implementations.

In wireless communications, the assumption that the transmitter has perfect channel state information (CSI) is often unreasonable, due to feedback delays, estimation errors, and quantization errors. In order to accurately assess system performance, a more careful analysis with imperfect CSI is needed. In this paper, the impact of partial CSI due to feedback delays in a multiuser Orthogonal Frequency Division Multiplexing (MU-OFDM) cognitive radio (CR) system is investigated. The effect of partial CSI on the bit error rate (BER) is analyzed. A relationship between the transmit power and the number of bits loaded on a subcarrier is derived which takes into account the target BER requirement. With this relationship, existing resource allocation schemes which are based on perfect CSI being available can be applied when only partial CSI is available. Simulation results are provided to illustrate how the system performance degrades with increasingly poor CSI.

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.

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.

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.

Considering that wireless unidirectional full-duplex (FD) transmission is one of the FD transmissions over 5G mobile wireless networks, this paper proposes a joint receive and transmit relay beamformer design for systems consisting of a source, a FD relay, an intended destination, and an eavesdropper. The source and destination are single-antenna nodes, whereas the FD relay is a multi-antenna node. Assuming that full channel state information (CSI) is available and the eavesdropper processes two blocks of received data at a time, the joint optimization problem is reformulated as a semidefinite relaxation (SDR) problem (in terms of relay transmit beamformer), which is tight in the sense that the rank-one beamformer can always be recovered from the SDR solution. In order to significantly minimize the computational cost of the SDR implementation, a novel semi-analytical approach based on dual optimization is proposed to obtain the optimum transmit beamformer. When the number of data blocks is arbitrary, we propose a successive convex approximation approach for solving the original non-convex optimization problem and show that a stationary solution can be efficiently obtained. We then propose a distributionally robust beamformer design for the case of an arbitrary number of blocks, assuming that the means and covariance matrices of the eavesdropper's channels are known. Computer simulations show that the proposed semi-analytical solution matches with that obtained from numerical optimization of the SDR problem, the FD scheme significantly outperforms its half-duplex counterpart, and the proposed robust design provides robustness against CSI uncertainty.

Consider a parallel channel with M independent flat-fading subchannels. There exists a smart jammer which has possession of a copy of perfect channel state information (CSI) measured and sent back by a receiver to its transmitter. Under this model, a class of two-person zero-sum games is investigated where either achievable mutual information rate or Chernoff bound is taken as the underlying pay-off function with the strategy space of each player determined by respective power control and hopping functions. More specifically, we have tackled and answered the following three fundamental questions. The first one is about whether the transmitter and jammer should hop or fully use all degrees of freedom over the entire parallel channels given the full CSI available to both of them, i.e. to hop or not to hop. The second question is about the impact of sending back CSI on system performance considering that the smart jammer can exploit CSI to further enhance its interference effects, i.e. to feedback or not to feedback. The last question is about whether the amount of feedback information can be reduced given the mutual restrictions between transmitter and jammer, i.e. when to feedback and when not to.

We study the throughput capacity region of the Gaussian multi-access (MAC) fading channel with perfect channel state information (CSI) at the receiver and at the transmitters (CSI-TR), at low power regime. We show that it has a multidimensional rectangle structure and thus is simply characterized by single user capacity points. More specifically, we show that at low power regime, the boundary surface of the capacity region shrinks to a single point corresponding to the sum-rate maximizer and that the coordinates of this point coincide with single user capacity bounds. Using the duality of Gaussian MAC and broadcast channels (BC), we provide a simple characterization of the BC capacity region at low power regime.