Optimizing quantize-map-and-forward in slow fading relay networks

In this paper, we study a simple question: when are dynamic relaying strategies essential in optimizing the diversity-multiplexing tradeoff (DMT) in half-duplex wireless relay networks? This is motivated by apparently two contrasting results even for a simple three-node network with a single half-duplex relay. When all channels in the system are assumed to be independent and identically fading, a static schedule where the relay listens half the time and transmits half the time combined with quantize-map-and-forward (QMF) relaying is known to achieve the full-duplex performance. However, when there is no direct link between the source and the destination, a dynamic decode-and-forward (DDF) strategy is needed to achieve the optimal tradeoff. In this case, a static schedule is strictly suboptimal and the optimal tradeoff is significantly worse than the full-duplex performance. In this paper, we study the general case when the direct link is neither as strong as the other links nor fully nonexistent, and identify regimes where dynamic schedules are necessary and those where static schedules are enough. We identify four qualitatively different regimes for the single-relay channel, where the tradeoff between diversity and multiplexing is significantly different. We show that in all these regimes one of the above two strategies is sufficient to achieve the optimal tradeoff by developing a new upper bound on the best achievable tradeoff under channel state information available only at the receivers. A natural next question is whether these two strategies are sufficient to achieve the DMT of more general half-duplex wireless networks with a larger number of relays. We propose a generalization of the two existing schemes through a dynamic QMF (DQMF) strategy, where the relay listens for a fraction of time depending on received channel state information but not long enough to be able to decode. We show that such a DQMF strategy is needed to achieve the optimal DMT in a parallel channel with two relays, outperforming both DDF and static QMF strategies.

We consider a precoding method in downlink multiuser multiple-input multiple-output (MIMO) transmission with multiple base station (BS) cooperation where some of the instantaneous channel state information (CSI) is not available at the BSs. The proposed precoding method is based on block diagonalization of the channel matrix. However, since some elements of the channel matrix are unknown, we allow a partially non-orthogonal transmission. More specifically, we allow inter-user interference to users with limited instantaneous CSI feedback from the channel where the instantaneous CSI of that user is not obtained at the BSs. The other inter-user interferences are set to zero based on the block diagonalization of the channel matrix. The proposed method efficiently uses the degree of freedom of the spatial channel compared to the case with full orthogonal transmission at the cost of increased inter-user interference to the users with limited instantaneous CSI feedback. Simulation results show that the proposed method increases the capacity for a given transmission power or decreases the transmission power for a given capacity requirement compared to the case with full orthogonal transmission.

In this paper, the ergodic sum rate and the outage probability of a downlink single-antenna channel with K users are analyzed in the presence of Rayleigh flat fading, where limited channel state information (CSI) feedback is assumed. Specifically, only 1-bit feedback per fading block per user is available at the base station. We first study the ergodic sum rate of the 1-bit feedback scheme and consider the impact of feedback delay on the system. A closed-form expression for the achievable ergodic sum rate is presented as a function of the fading temporal correlation coefficient. It is proved that the sum rate scales as log log K, which is the same scaling law achieved by the optimal nondelayed full CSI feedback scheme. The sum-rate degradation due to outdated CSI is also evaluated in the asymptotic regimes of either large K or low SNR. The outage performance of the 1-bit feedback scheme for both instantaneous and outdated feedback is then investigated. Expressions for the outage probabilities are derived, along with the corresponding diversity-multiplexing tradeoffs (DMTs). It is shown that, with instantaneous feedback, a power allocation based on the feedback bits enables doubling of the DMT compared with the case with short-term power constraint in which a dynamic power allocation is not allowed. However, with outdated feedback, the advantage of power allocation is lost, and the DMT reverts to that achievable with no CSI feedback. Nevertheless, for finite SNR, improvement in terms of outage probability can still be obtained.

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.

In this paper, the optimum tradeoff between diversity and multiplexing gains in a two-user quasi-static Rayleigh fading interference channel (IC) is studied. The diversity and multiplexing gains are two basic performance measures in wireless networks which characterize the transmission reliability and the data rate, respectively. It would be of interest to investigate the optimal tradeoff between these two measures. First, we develop a coding scheme for the two-user quasi-static Rayleigh fading Gaussian IC with interference level α := log INR/log SNR ≥ 1. Then, for this coding scheme the achievable diversity-multiplexing tradeoff (DMT) is characterized. Our achievable DMT coincides with its outer bound. In the low and high rate regions (to be defined later), the proposed coding scheme is a one-level Gaussian code, independent of the channel state information (CSI). In the middle rate region (to be defined later), the proposed coding scheme, depending on the partial CSI, can be a one-level or a two-level Gaussian code. We show that the relevant partial CSI can be represented by only one bit determined by the absolute value of the channel gain. In the middle rate region, we assume that the single-bit partial CSI for all the four channel gains of the Gaussian IC are available at both transmitters.

SUMMARYThis paper introduces limited feedback technique into physical‐layer network coding (PLNC) scheme, which is the most spectrally efficient protocol in two‐way relay channels, consisted of one relay and two end nodes (sources). Decode‐and‐forward (DF) and partial‐decode‐and‐forward (PDF) strategies are considered for PLNC, and all nodes are assumed to have two antennas to allow transmission by Alamouti's orthogonal space–time block code to provide diversity. In DF, by limited feedback, one of the sources is informed about instantaneous channel state information (CSI) to increase the bit error rate (BER) performance at relay. The closed‐form upper and lower bounds on the bit error probability are derived for binary phase‐shift keying (BPSK) and quadrature PSK (QPSK) modulations and approved via computer simulations. In PDF strategy, each source has to know CSI between relay and the other source for decoding, which causes extra protocol complexity. Moreover, for the system in which all nodes have two antennas, classical PDF strategy does not satisfy orthogonality at the end nodes. Therefore, in this paper, a modified‐PDF (MPDF) strategy with limited feedback is proposed. In MPDF, for decoding at the end nodes, differential phase information between channel fading coefficients having maximum amplitudes is fed back to the sources by relay. This approach enables single‐symbol decoding, besides full diversity, and sources do not need to know CSI between relay and the other source. It is shown via computer simulations that MPDF strategy provides significantly better BER performance than the classical PDF for BPSK and QPSK modulations.Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, we consider relay selection for turbo coded cooperative networks subject to Nakagami-m fading when the channel state information (CSI) is known at the receiver but is not necessarily ideal. This non-ideality may be due to a feedback delay caused by the difference between the instantaneous CSI during the transmission and the CSI at the time of relay selection, resulting in outdated CSI phenomena. The impact of the outdated CSI on the proposed scheme is well investigated. A closed-form expression for the exact outage probability is derived as well as its asymptotic expression in the high signal-to-noise (SNR) regime. Moreover, upper bounds on the bit-error rate (BER) are presented and a study of the diversity order reveals that for ideal CSI, full diversity in the number of relays and fading parameters m is achieved as opposed to outdated CSI where the achievable diversity is equivalent to the diversity of a coded cooperative network with a single relay.

In centralized massive multiple-input multiple-output (MIMO) systems, the channel hardening phenomenon can occur, in which the channel behaves as almost fully deterministic as the number of antennas increases. Nevertheless, in a cell-free massive MIMO system, the channel is less deterministic. In this paper, we propose using instantaneous channel state information (CSI) instead of statistical CSI to obtain the power control coefficient in cell-free massive MIMO. Access points (APs) and user equipment (UE) have sufficient time to obtain instantaneous CSI in a slowly time-varying channel environment. We derive the achievable downlink rate under instantaneous CSI for frequency division duplex (FDD) cell-free massive MIMO systems and apply the results to the power control coefficients. For FDD systems, quantized channel coefficients are proposed to reduce feedback overhead. The simulation results show that the spectral efficiency performance when using instantaneous CSI is approximately three times higher than that achieved using statistical CSI.

Resource allocation for half-duplex bidirectional relaying networks using partial channel state information (CSI) at the transmitters is considered, with an emphasis on the diversity-multiplexing tradeoff (DMT). It is assumed that there is a direct link between the sources. It is shown that decode-and-forward (DF) two-way relaying does not suffer from a diversity loss when the multiplexing gain is high, a significant improvement over the dynamic DF protocol for one-way relaying. In contrast to the case of no direct link, power control with CSI feedback from relay to sources provides strictly better performance over systems without power control. The best DMT is obtained when each source broadcasts CSI to the other nodes in the network, allowing them to partially adapt their transmit powers.

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.

This paper investigates the power allocation problem in a two-hop OFDM relay link with a nonregenarative relay where the available channel state information (CSI) is an outdated version of the actual instantaneous CSI. A power allocation method is proposed to maximize the expected capacity, assuming that the correlation between the outdated and instantaneous CSI is known. The performance is compared with that of the baseline method, where the power allocation is performed solely based on the outdated CSI. Results confirm that the proposed method outperforms the baseline method when the available CSI is highly outdated.

Recently, substantial attention has been paid to increase the achievable rates of wireless networks using different kinds of limited channel state information (CSI) feedback. This paper aims to investigate the effect of limited noisy CSI feedback on the achievable rates of power-limited block fading channels constrained to have limited outage probability. Considering different power allocation strategies and various fading conditions, the results are obtained for different outage probabilities and are compared with the case where there is no outage limitation. Moreover, considering different outage probability constraints, the effect of feedback channel noise on the average rates of the forward channel is studied and compared with the ones obtained under noise-free feedback link assumption. Simulation results show that 1) although the outage probability constraint reduces the channel average rate, its influence diminishes as the channel state information feedback or the input power increases, 2) the effect of the outage probability constraint decreases as the forward channel fading severity or the feedback channel noise is reduced.

Most prior studies on wireless spatial-reuse TDMA (STDMA) link scheduling for throughput optimization deal with the situation where instantaneous channel state information (CSI) is available. Under fast fading, however, the channel may change too quickly for the scheduler to track the instantaneous CSI. In this paper, instead of the instantaneous CSI, the scheduler performs its task according to the stochastic behavior of the channel state. A basic schedule consists of a set of simultaneously transmitting links. The essence of the scheduling problem is to determine a mixed schedule consisting of a weighted sum (TDMA mixture) of a number of basic schedules to optimize a certain utility objective. A key to reducing scheduling complexity is to identify the Pareto-efflcient basic schedules, referred to as the extreme-point schedules, so that the construction of the optimal mixed schedule can be based on the extreme-point schedules rather than all the basic schedules. The precise identification of the extreme-point schedules, however, is intractable computationally. We show in this paper that identifying a slightly larger superset of the extreme-point schedules can be highly efficient using a Perron-Frobenius condition: simulation experiments indicate that oftentimes there are only very few extraneous non-extreme-point schedules in the superset. Building on the effective identification method, we propose a fast scheduling algorithm. This algorithm beats the algorithm without using the identification method by a complexity-reduction factor of 166 in a 15-link network. In addition, numerical results suggest that our algorithm is robust to variations of system parameters.

We analyze the throughout achievable in transmission over block-fading channels when the instantaneous channel state information (CSI) is not available at the transmitter. Assuming operation with incremental redundancy hybrid ARQ (HARQ), we propose to adapt the transmissions rates using the outdated CSI, i.e., the one experienced by the receiver in the past transmissions that resulted in a packet decoding failure. We show that, even if the CSI is fully outdated, i.e., in independently block-fading channel, the adaptation provides notable gains over a non-adaptive HARQ and for high SNR, a few transmissions are necessary to approach closely the ergodic capacity.

This paper investigates the problem of relay selection in a non-reciprocal two-way relay network. To achieve full diversity, relay selection at a central node needs to gather all the instantaneous channel state information (CSI). Assume one of the source nodes is the central node, to make an accurate decision this node needs some more CSI which can not be estimated from the received signal. To solve this problem we can feed back the required CSI from the other source node. To effectively transmit the CSI, two quantization schemes, Llyod-Max and uniform quantization, are considered in this paper. In order to further improve the performance, some modified quantization methods are designed to adjust the quantization range. Simulation results indicate the effectiveness of the proposed schemes.