Limited Channel State Information Research Articles

Ergodic Secrecy Sum-Rate for Downlink Multiuser MIMO Systems With Limited CSI Feedback

This paper investigates the ergodic secrecy sum-rate for the downlink multiuser MIMO system with independent confidential messages, each of which is intended for one of the users and should keep secret from others. We adopt zero-forcing beamforming with limited channel state information (CSI) feedback at the transmitter, and derive the closed-form expression for the ergodic secrecy sum-rate. Moreover, we analyze some of its asymptotic characteristics, which provide guidance on secure transmission design. Finally, all theoretical results are validated by numerical simulations.

Performance Analysis and Optimization for Interference Alignment Over MIMO Interference Channels With Limited Feedback

In this paper, we address the problem of interference alignment (IA) over MIMO interference channels with limited channel state information (CSI) feedback based on quantization codebooks. Due to limited feedback and hence imperfect IA, there are residual interferences across different links and different data streams. As a result, the performance of IA is greatly related to the CSI accuracy (namely number of feedback bits) and the number of data streams (namely transmission mode). In order to improve the performance of IA, it makes sense to optimize the system parameters according to the channel conditions. Motivated by this, we first give a quantitative performance analysis for IA under limited feedback, and derive a closed-form expression for the average transmission rate in terms of feedback bits and transmission mode. By maximizing the average transmission rate, we obtain an adaptive feedback allocation scheme, as well as a dynamic mode selection scheme. Furthermore, through asymptotic analysis, we obtain several clear insights on the system performance, and provide some guidelines on the system design. Finally, simulation results validate our theoretical claims, and show that obvious performance gain can be obtained by adjusting feedback bits dynamically or selecting transmission mode adaptively.

Adaptive orthogonal frequency division multiplexing underwater acoustic communications with limited feedback

In orthogonal frequency division multiplexing (OFDM) underwater acoustic (UWA) communications, some subcarriers may be subject to deep fading. If the channel state information (CSI) is available at the transmitter side, adaptive transmission techniques (e.g., power allocation) can be applied to mitigate the selective fading effect and increase the overall performance. Therefore, it is more valuable to analyze the UWA channel with limited CSI feedback. In this paper, we adopt two time-varying shallow water acoustic channels (slow-varying environment and fast-varying environment) as examples. Lloyd algorithm is employed to quantize the CSI at the receiver and construct the codebook, which is also known to the transmitter. Simulation results compare the performance between two different channels, and the performance between a few bits of feedback, perfect feedback, and non-feedback, respectively.

Pre-processing filter design at transmitters for IBI mitigation in an OFDM system

In order to meet the demands for high transmission rates and high service quality in broadband wireless communication systems, orthogonal frequency division multiplexing (OFDM) has been adopted in some standards. However, the inter-block interference (IBI) and inter-carrier interference (ICI) in an OFDM system affect the performance. To mitigate IBI and ICI, some pre-processing approaches have been proposed based on full channel state information (CSI), which improved the system performance. A pre-processing filter based on partial CSI at the transmitter is designed and investigated. The filter coefficient is given by the optimization processing, the symbol error rate (SER) is tested, and the computation complexity of the proposed scheme is analyzed. Computer simulation results show that the proposed pre-processing filter can effectively mitigate IBI and ICI and the performance can be improved. Compared with pre-processing approaches at the transmitter based on full CSI, the proposed scheme has high spectral efficiency, limited CSI feedback and low computation complexity.

On the Energy Efficiency of AMC and HARQ-IR With QoS Constraints

In this paper, we compare the energy efficiencies of two well-known transmission schemes that can adapt to fading channels for reliable transmissions, namely, adaptive modulation and coding (AMC) and hybrid automatic repeat request (HARQ) schemes, with limited channel state information (CSI) feedback. Since they exploit CSI differently, they have different characteristics, which make the comparison study (in terms of energy efficiency) challenging. Using the notion of energy-delay tradeoff (EDT), we derive approaches to compare them with given equivalent quality-of-service (QoS) constraints. The derived approaches are important as they allow us to choose energy-efficient transmission schemes under certain conditions. It is shown that AMC is more energy efficient than HARQ with incremental redundancy (HARQ-IR) in the low-power regime. However, in the high-power regime, HARQ-IR has better energy efficiency than AMC.

On the Energy Delay Tradeoff of HARQ-IR in Wireless Multiuser Systems

Energy delay tradeoff (EDT) is a fundamental tradeoff that plays a crucial role in understanding the energy efficiency of various transmission schemes. In particular, for hybrid automatic repeat request (HARQ) protocols, the EDT can be well defined. In this paper, in order to understand the EDT for a wireless multiuser system, we consider various downlink transmission schemes where the HARQ with incremental redundancy (HARQ-IR) protocol is employed for reliable transmissions to users. For a given total power, the impact of different transmission schemes in conjunction with power allocation on EDT is extensively studied. Among the transmission schemes, it is shown that the threshold-based transmission (TBT) scheme efficiently lowers the minimum energy per bit (EB) in spite of limited prior channel state information (CSI) feedback. The study is further extended to a more plausible scenario where users have different channel statistics. In doing so, we consider a proportional fairness scheduling based on relative channel gain that can be easily accommodated in the proposed TBT scheme, and study its EDT behaviors. Performance evaluations show that the schemes incorporating proportional fairness achieve good EDT performances while guaranteeing the fairness among users.

Limited Feedback-Based Multi-Antenna Relay Broadcast Channels with Block Diagonalization

The relay technology is effective in extending radio coverage and improving the performance of cell edge users. In multi-antenna relay channels, good knowledge of the channel state information (CSI) at the transmitter is important to achieve multiplexing gains of the multiple-input multiple-output technique. In this paper, we study the multi-antenna relay downlink channel with limited feedback CSI from both two-hop links. Data streams from the base station (BS) are first transmitted to a relay station (RS) with singular value decomposition-based precoding and receiver pulse shaping at the BS and RS, respectively. The block diagonalization precoding is then applied at the RS to forward the received signals to the remote multi-antenna users. We derive an upper bound for the system throughput loss due to CSI quantization error, and then propose a feedback quality control strategy to maintain a bounded rate loss relative to the perfect CSI case. It reveals that the feedback size B_1 from the RS to BS needs to scale in proportion to both transmit power at the BS and RS while the feedback size B_2 from each user to the RS only needs to scale linearly with the transmit power at the RS.

Cooperative Relaying at Finite SNR—Role of Quantize-Map-and-Forward

Quantize-Map-and-Forward (QMF) relaying has been shown to achieve the optimal diversity-multiplexing trade-off (DMT) for arbitrary slow fading full-duplex networks as well as for the single-relay half-duplex network. A key reason for this is that quantizing at the noise level suffices to achieve the cut-set bound approximately to within an additive gap, without any requirement of instantaneous channel state information (CSI). However, DMT only captures the high SNR performance and potentially, limited CSI at the relay can improve performance at moderate SNRs. In this work we propose an optimization framework for QMF relaying over slow fading channels. Focusing on vector Gaussian quantizers, we optimize the outage probability for the full-duplex and half-duplex single relay by finding the best quantization level and relay schedule according to the available CSI at the relays. For the N-relay diamond network, we derive an universal quantizer that sharpens the additive approximation gap of QMF from the conventional \Theta(N) bits/s/Hz to \Theta(log(N)) bits/s/Hz using only network topology information. Analytical solutions to channel-aware optimal quantizers for two-relay and symmetric N-relay diamond networks are also derived. In addition, we prove that suitable hybridizations of our optimized QMF schemes with Decode-Forward (DF) or Dynamic DF protocols provide significant finite SNR gains over the individual schemes.

A Stochastic Geometry Framework for Analyzing Pairwise-Cooperative Cellular Networks

Cooperation in cellular networks has been recently suggested as a promising scheme to improve system performance, especially for cell-edge users. In this work, we use stochastic geometry to analyze cooperation models where the positions of Base Stations (BSs) follow a Poisson point process distribution and where Voronoi cells define the planar areas associated with them. For the service of each user, either one or two BSs are involved. If two, these cooperate by exchange of user data and channel related information with conferencing over some backhaul link. Our framework generally allows variable levels of channel information at the transmitters. In this paper we investigate the case of limited channel state information for cooperation (channel phase, second neighbour interference), but not the fully adaptive case which would require considerable feedback. The total per-user transmission power is further split between the two transmitters and a common message is encoded. The decision for a user to choose service with or without cooperation is directed by a family of geometric policies depending on its relative position to its two closest base stations. An exact expression of the network coverage probability is derived. Numerical evaluation allows one to analyze significant coverage benefits compared to the non-cooperative case. As a conclusion, cooperation schemes can improve system performance without exploitation of extra network resources.

Successive orthogonal beamforming for cooperative multi‐point downlinks

This study considers successive orthogonal beamforming (SOBF) for multicell downlink transmissions. A group of base stations (BSs) are in cooperation for effective downlink transmissions to cell-edge users, which is usually referred to as cooperative multi-point. As the number of cell-edge users is small and varying, conventional beamforming schemes, for example, zero-forcing beamforming (ZFBF), are not suitable for the multicell scenario. In the SOBF scheme considered here, the beamforming vectors are found in a successive manner when a new user comes in, so that the beamforming vectors of the existing users remain unchanged. With limited channel state information at the group of BSs, a new successive beam allocation (SBA) scheme is proposed for SOBF. In SBA, the candidate beams are broadcasted to all the users through downlink before the index of the best beam is sent back to the BS by each user. The sum rate performance of a system with two users is studied analytically. The numerical results are presented to show that the proposed SOBF with SBA outperforms ZFBF with conventional feedback strategy.

Energy-Delay Tradeoff Comparison of Transmission Schemes with Limited CSI Feedback

Due to increasing energy cost and various environmental issues, energy efficiency becomes an important issue in wireless communications where spectral efficiency has been considered as a key performance measure. If transmission schemes can be flexible to allow varying average transmission delay (or throughput), the energy-delay tradeoff (EDT) can be exploited. In general, the longer (average) transmission delay, the better energy efficiency can be achieved. In this paper, we study various transmission schemes with limited channel state information (CSI) feedback that can have flexible transmission delay in wireless communications, including hybrid automatic repeat request (HARQ) protocols, and derive EDT characteristics over fading channels. An opportunistic transmission scheme that relies on prior CSI feedback is studied for comparisons with HARQ protocols in terms of EDT. In order to improve the energy efficiency of HARQ, a modified transmission scheme that employs prior CSI feedback is proposed and analyzed to understand its EDT characteristics.

Adaptive minimum bit feedback for sum-rate analysis in multi-user distributed antenna systems

The paper mainly studies the sum-rate performance of limited feedback (LFB) block-diagonalization (BD) in multi-user distributed antenna system (DAS). As the channel state information (CSI) fed back to base station (BS) is limited, multi-user interference (MUI) is caused inevitably because of the quantization error. Considering the influence of the MUI to the capacity of DAS, we propose a parameter of effective sum-rate ratio (ESRR) to denote the capacity offset under the condition of the BS can get perfect CSI and limited CSI first, then we confirm that the approximated ESRR is very close to actual ESRR got through simulations. After that, based on the approximated ESRR, an adaptive minimum bit feedback scheme which can effectively reduce the overhead of feedback channel and the complexity of the system is proposed. Simulation results show the effectiveness of the proposed scheme.

Robust {MISO Transmit} Optimization under Outage-Based QoS Constraints in Two-Tier Heterogeneous Networks

To improve wireless heterogeneous network service via macrocell and femtocells that share certain spectral resources, {this paper studies} the transmit beamforming design for femtocell base station (FBS), {equipped with multiple antennas}, under an outage-based quality-of-service (QoS) constraint at the {single-antenna} femtocell user equipment characterized by its signal-to-interference-plus-noise ratio. {Specifically}, we {focus on} the practical case of {imperfect} downlink {multiple-input single-output (MISO)} channel state information (CSI) at the FBS due to limited CSI feedback or CSI estimation errors. By characterizing the CSI uncertainty probabilistically, we formulate an outage-based robust beamforming design. This nonconvex optimization problem can be relaxed into a convex semidefinite programming problem, which reduces to a power control problem when all CSI vectors are independent {and} identically distributed. We also investigate the performance gap between the optimal transmission strategy (that allows maximum transmission degrees of freedom (DoF) equal to the number of transmit antennas) and the proposed optimal beamforming design (with the DoF equal to one) and provide some feasibility conditions, followed by their performance evaluation and trade-off through simulation results.

A new reduced-complexity detection scheme for zero-padded OFDM transmissions

Recently, zero-padding orthogonal frequency division multiplexing (ZP-OFDM) has been proposed as an alternative solution to the traditional cyclic prefix (CP)-OFDM, to ensure symbol recovery regardless of channels nulls. Various ZP-OFDM receivers have been proposed in the literature, trading off performance with complexity. In this paper, we propose a novel low-complexity (LC) receiver for ZP-OFDM transmissions and derive an upper bound on the bit error rate (BER) performance of the LC-ZP-OFDM receiver. We further demonstrate that the LC-ZP-OFDM receiver brings a significant complexity reduction in the receiver design, while outperforming conventional minimum mean-square error (MMSE)-ZP-OFDM, supported by simulation results. A modified (M)-ZP-OFDM receiver, which requires the channel state information (CSI) knowledge at the transmitter side, is presented. We show that the M-ZP-OFDM receiver outperforms the conventional MMSE-ZP-OFDM when either perfect or partial CSI (i.e., limited CSI) is available at the transmitter side.Index Terms-Zero-padding, orthogonal frequency division multiplexing (OFDM), equalization.

Outage Analysis of Distributed Scheme on Opportunistic Relaying with Limited CSI

In this letter, we propose a distributed scheme on opportunistic amplify-and-forward (AF) relaying to minimize the system outage probability with low feedback overhead. Only the subset of relays report the calculated outage probability information to the source based on the outage probability threshold with the limited channel state information (CSI). We present the approximate expressions for the system outage probability under two scenarios, the statistical CSI and the statistical quantized CSI of the relay-destination links, respectively. Numerical results indicate that the derived analytic results are reasonable and the outage performance is better for the statistical quantized CSI case with acceptable feedback cost.

Interference-aware receiver structure for multi-user MIMO and LTE

In this paper, we propose a novel low-complexity interference-aware receiver structure for multi-user MIMO that is based on the exploitation of the structure of residual interference. We show that multi-user MIMO can deliver its promised gains in modern wireless systems in spite of the limited channel state information at the transmitter (CSIT) only if users resort to intelligent interference-aware detection rather than the conventional single-user detection. As an example, we focus on the long term evolution (LTE) system and look at the two important characteristics of the LTE precoders, i.e., their low resolution and their applying equal gain transmission (EGT). We show that EGT is characterized by full diversity in the single-user MIMO transmission but it loses diversity in the case of multi-user MIMO transmission. Reflecting on these results, we propose a LTE codebook design based on two additional feedback bits of CSIT and show that this new codebook significantly outperforms the currently standardized LTE codebooks for multi-user MIMO transmission.

Diversity-Multiplexing Tradeoff of Symmetric MIMO Interference Channels with Partial CSIT

In this paper, we propose a transmission scheme for the two-user symmetric multiple antenna interference channel (IFC) and show that the proposed transmission scheme can achieve the optimal diversity-multiplexing tradeoff (DMT) of the channel. The proposed transmission scheme requires only limited channel state information at the transmitter (CSIT) and is suitable for practical implementation. The limited CSIT is obtained by letting the destinations quantize the required information and feed back to the sources. Rules for implementing the quantization are proposed and the number of bits needed to represent the quantization is calculated. It is shown that for the proposed transmission scheme to be DMT optimal, the number of feedback bits should increase in log scale with respect to signal-to-noise ratio.

Energy-Efficient Relaying Strategy with Network Coding in Two-Way Parallel Channels

We consider a two-way communication assisted by parallel regenerative decode-and-forward relays operating in orthogonal channels. In a system with limited channel state information at each source and relay node, an optimum distributed power allocation strategy is proposed to minimize the total transmit power, providing a target signal-to-noise ratio at each destination with a target outage probability. Moreover, combined with opportunistic relaying and network coding, a distributed decision mechanism is proposed for the relay node to decide whether to help the transmission or not. In this proposal, each source works out the transmit power and the decision threshold then broadcasts them. The selected relay compares the decision threshold with the channel gain of its weaker relay-to-destination link, then determines whether to forward the networkcoded data or not. Simulation results show the advantage of this strategy in terms of energy efficiency for a two-hop two-way communication scenario. The proposed strategy is very flexible as it can trade outage to power consumption and vice versa.

Combined Transceiver Optimization for Uplink Multiuser MIMO with Limited CSI

Joint precoder and decoder optimization is considered for uplink multiuser multiple-input multiple-output (MU-MIMO) systems with limited channel state information (CSI) at both the transmitters and receivers. Instead of counting on complex iterative-based algorithms, an efficient and noniterative QR-based linear transceiver pair design is employed. In addition, an equal power distribution (EPD) scheme is applied to adjust transmit power allocation of each mobile station (MS) between its symbols under the total transmit-power constraint. Simulations are conducted to provide a comparative evaluation of the proposed QR-EPD algorithm with other transceiver designs on the sum mean-squared error (SMSE) and the averaged bit-error-rate (BER) performance.

Partially Non-orthogonal Block Diagonalization-Based Precoding in Downlink Multiuser MIMO with Limited Channel State Information Feedback

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.