Vandermonde-subspace Frequency Division Multiplexing Research Articles

Unitary Matrix Method for PAPR Reduction of IDFT-VFDM Signals

To enable the frequency reuse between the new radio (NR) and the long-term evolution (LTE) systems, inverse discrete Fourier transform-based Vandermonde-subspace frequency division multiplexing (IDFT-VFDM) has been proposed to exploit the guard intervals of the conventional orthogonal frequency division multiplexing (OFDM) system. One important issue of the IDFT-VFDM system is the high peak-to-average power ratio (PAPR), which distorts the transmitted signal and causes severe performance degradation. Compared to OFDM, the method to reduce the PAPR in IDFT-VFDM requires unique design to guarantee zero interference to the legacy LTE system. To deal with this problem, a unitary matrix based method is proposed to design the precoder at the NR users to reduce the PAPR, which can also guarantee the minimum residual interference to the LTE system. Simulation results are demonstrated to verify the effectiveness of the proposed scheme.

IDFT-VFDM for Supplementary Uplink and LTE-NR Co-Existence

During the first phase of the deployment of new radio (NR) networks, base station (BS) and user equipment (UE) are expected to operate alongside the pre-existing long-term evolution (LTE) networks. This paper proposes a solution to be adopted by NR UE to perform an uplink transmission towards NR BS over the same time and frequency resources as the legacy LTE system, which would extend the uplink coverage when operating at the supplementary uplink band. In order to guarantee the absence of interference towards LTE BS, we design a new waveform termed as inverse discrete Fourier transform-based Vandermonde-subspace frequency division multiplexing (IDFT-VFDM) with the following important features. On one hand, an NR UE communicating with an NR BS through IDFT-VFDM would not generate any interference at the legacy LTE BS, regardless of the number of antennas present at both ends of the interference channel. On the other hand, an IDFT-VFDM signal can always be designed to occupy the same signal bandwidth as a legacy single-carrier frequency division multiple access signal for LTE uplink transmission. Numerical results demonstrate the merit of IDFT-VFDM and confirm its potential as a candidate solution to achieve LTE-NR co-existence in multi-antenna multi-user scenarios.

Robust Rate-Maximization Precoder Design for VFDM System

The new radio (NR) system is recently proposed to deploy alongside the long term evolution (LTE) system to improve the wireless communication capacity. The Vandermonde-subspace frequency division multiplexing (VFDM) is an efficient technique for such a two tier network, whereby the NR transmitter can reuse the frequency spectrum of LTE system meanwhile guaranteeing interference free to LTE. In this paper, we first investigate the robust rate-maximization problem in the VFDM system. In the condition of imperfect channel state information (CSI), the precoder is optimized to satisfy both non-interference to LTE system and rate-maximization in the NR system. To tackle the challenge in solving such a non-convex problem, an iterative algorithm is proposed based on the block coordinate descent (BCD) and penalty dual decomposition (PDD) methods. Finally, simulation results demonstrate the superiority of the proposed algorithm in terms of robustness and achievable rate over the conventional SVD-based VFDM technique.

Spectral Efficiency Improvement based on Small-cell Deployments Toward 5G Communications Technologies

This paper emphasizes a method for improving spectral efficiency based on small cells (SCs) deployed in an existing macrocell (MC), which ultimately results in overall enhancement of the network capacity and coverage area. In addition, it allows an unlicensed secondary network to deliver messages through opportunistic access to the licensed network spectrum. By deploying SCs, users either inside or outside high residential buildings and/or commercial buildings can acquire signals during communications without interruption. The connectivity in the alliance of the two-tier networks becomes abundant, resulting in spectral efficiency improvement. In this paper, we first recall performance based on the Vandermonde-subspace frequency division multiplexing (VFDM) spectrum-sharing technique for spectrum management under both conventional (single-user) and enhanced scenarios; subsequently, the proposed method is introduced for comparison purposes. The performance of both methods is manifested in simulation results for the achievable rate, which demonstrate that the proposed approach outperforms enhanced VFDM and is a potential candidate in next-generation cellular technology. The motivation for the preference for SC deployment in the proposed approach is due to worthy characteristics (low power, low cost, very light weight, and self-organization). Unlike MCs, which need a considerable budget, they are installed anywhere without a lot of expense, and hence, save the network infrastructure.

On the SINR statistics of a VFDM cognitive spectrum sharing system

An analytical precise approximation of the SINR statistics of the two-tier Vandermonde-subspace frequency division multiplexing (VFDM) cognitive spectrum sharing systems over frequency-selective Rayleigh fading channels is presented. It is shown that the gamma distribution provides the best fitting accuracy and that its use leads to simple, yet accurate, closed-form expressions for evaluating the ergodic capacity (EC) and average bit error probability (ABEP) performance of such systems. In deriving these expressions, the parameters of the gamma distribution have been obtained for various operating conditions of the considered VFDM system using distribution fitting. Furthermore, regression analysis has been used to obtain approximate analytical expressions for these parameters in relation to the system operating parameters. Performance evaluation results, obtained for various system implementations, including the standardized IEEE 802.11 and 3GPP LTE, are presented to demonstrate the validity of the proposed methodology. Its accuracy has been verified by means of computer simulations.

Cooperative Precoding for Cognitive Transmission in Two-Tier Networks

In this paper, we study cooperative precoder design in two-tier networks, consisting of a macro-cell (MC) and several small-cells (SCs). By exploiting multiuser Vandermonde-subspace frequency division multiplexing (VFDM) transmission, an MC downlink can co-exist with cognitive SCs. In this paper, we first propose a cooperative cross-tier precoder (CTP) among the transmitters in the SCs to increase the transmitted dimension. The cooperative CTP allows us to use more efficient intra-tier precoder (ITP) in SCs to handle intracell interference and improve the throughput of the cognitive system. And then, three ITPs, a block-diagonal zero-forcing (BD-ZF) ITP, a capacity-achieving (CA) ITP, and a generalized MMSE channel inversion (GMI) ITP, are developed. Complexities of all CTPs and ITPs are discussed and compared. The overhead of channel state information (CSI) exchange is analyzed. Numerical results are presented to demonstrate the throughput improvement of the proposed schemes and to discover the impact of the imperfect CSI. From the complexity comparison and the numerical results, the GMI ITP offers a good tradeoff between complexity and throughput.

Optimized BD-ZF Precoder for Multiuser MIMO-VFDM Cognitive Transmission

In this paper, we study an optimized block-diagonal zeroforcing (BD-ZF) precoder in two-tiered cognitive networks, consisting of a macro-cell (MC) and a small-cell (SC). By exploiting multi-user multiple input multiple outputVandermonde-subspace frequency division multi-plexing (MIMO-VFDM) transmission, a cognitive SC can coexist with an MC. We first devise a cross-tier precoder (CTP) based on the idea of Vandermonde-subspace frequency division multiplexing (VFDM) to cancel the interference from SC to MC. And then, we adopt BD-ZF intra-tier precoder (ITP) to suppress the multi-user interference among SC. In the case that the dimension of the provided null space is larger than what BD-ZF ITP requires, we develop an optimized ITP. By optimizing the rotating and selecting matrix, all limited channel gain is collected, which results in a good performance of throughput. Numerical results are presented to demonstrate the throughput improvement of the proposed optimized BDZF ITP and to discover the impact of imperfect channel state information (CSI).

Vandermonde-Subspace Frequency Division Multiplexing for Two-Tiered Cognitive Radio Networks

Vandermonde-subspace frequency division multiplexing (VFDM) is an overlay spectrum sharing technique for cognitive radio. VFDM makes use of a precoder based on a Vandermonde structure to transmit information over a secondary system, while keeping an orthogonal frequency division multiplexing (OFDM)-based primary system interference-free. To do so, VFDM exploits frequency selectivity and the use of cyclic prefixes by the primary system. Herein, a global view of VFDM is presented, including also practical aspects such as linear receivers and the impact of channel estimation. We show that VFDM provides a spectral efficiency increase of up to 1 bps/Hz over cognitive radio systems based on unused band detection. We also present some key design parameters for its future implementation and a feasible channel estimation protocol. Finally we show that, even when some of the theoretical assumptions are relaxed, VFDM provides non-negligible rates while protecting the primary system.

Cognitive Orthogonal Precoder for Two-Tiered Networks Deployment

In this work, the problem of cross-tier interference in a two-tiered (macro-cell and cognitive small-cells) network, under the complete spectrum sharing paradigm, is studied. A new orthogonal precoder transmit scheme for the small base stations, called multi-user Vandermonde-subspace frequency division multiplexing (MU-VFDM), is proposed. MU-VFDM allows several cognitive small base stations to coexist with legacy macro-cell receivers, by nulling the small- to macro-cell cross-tier interference, without any cooperation between the two tiers. This cleverly designed cascaded precoder structure, not only cancels the cross-tier interference, but avoids the co-tier interference for the small-cell network. The achievable sum-rate of the small-cell network, satisfying the interference cancelation requirements, is evaluated for perfect and imperfect channel state information at the transmitter. Simulation results for the cascaded MU-VFDM precoder show a comparable performance to that of state-of-the-art dirty paper coding technique, for the case of a dense cellular layout. Finally, a comparison between MU-VFDM and a standard complete spectrum separation strategy is proposed. Promising gains in terms of achievable sum-rate are shown for the two-tiered network w.r.t. the traditional bandwidth management approach.

On the Practical Implementation of VFDM-based Opportunistic Systems: Issues and Challenges

Vandermonde-subspace frequency division multiplexing (VFDM) is a physical layer technique for cognitive two-tiered networks, allowing for the coexistence of an orthogonal frequency division multiplexing (OFDM) legacy system and a cognitive secondary system in a time division duplex mode. It consists of a linear null-space precoder used by the secondary transmitter to effectively cancel the interference towards one or more primary receivers, while guaranteeing a non-negligible rate to a served secondary receiver. In this work, we propose an implementation of an experimental test-bed using the new SDR4All platform developed at the Alcatel-Lucent Chair on Flexible Radio (SUPELEC) to take a step towards a proof of concept of a VFDM-based system. We focus on the secondary link, where an opportunistic transmitter/receiver pair communicates over moderately frequency selective channels, characterized by very short root mean square (r.m.s.) delay spreads and non uniform power delay profiles (PDP). The obtained results show the practical feasibility of a VFDM transmission over a secondary link. However, a significant bit error rate (BER) loss with respect to the previously shown achievable theoretical performance is evident. A thorough analysis of the structure of the VFDM precoder is carried out and the impact of the channel characteristics on the performance of the opportunistic system is discussed. Numerical findings demonstrate that the potential BER drop can be addressed by designing a suitable flexible receiver able to deal with the effect induced by non uniform PDP and short r.m.s. delay spread channels.