In this paper, we revisit a recently proposed receiver design, named the splitting receiver, which jointly uses coherent and non-coherent processing for signal detection. By considering an improved signal model for the splitting receiver as compared to the original study in the literature, we conduct a performance analysis on the achievable data rate under Gaussian signaling and obtain a fundamentally different result on the performance gain of the splitting receiver over traditional receiver designs that use either coherent or non-coherent processing alone. Specifically, the original study ignored the antenna noise and concluded on a 50% gain in achievable data rate in the high signal-to-noise ratio (SNR) regime. In contrast, we include the antenna noise in the signal model and show that the splitting receiver improves the achievable data rate by a constant gap in the high SNR regime. This represents an important correction of the theoretical understanding on the performance of the splitting receiver. In addition, we examine the maximum-likelihood detection and derive a low-complexity detection rule for the splitting receiver for practical modulation schemes. Our numerical results give further insights into the conditions under which the splitting receiver achieves significant gains in terms of either achievable data rate or detection error probability.
In the presence of multiple senders, one of the simplest decoding strategies that can be employed by a receiver is successive decoding. In a successive decoding strategy, the receiver decodes the messages one at a time using the knowledge of the previously decoded messages as side information. Recently, there have been two separate attempts to construct codes for the interference channel using successive decoding based on the idea of rate-splitting. In this note, we highlight a difficulty that arises when a rate-splitting codebook is to be decoded by multiple receivers. The main issue is that …
In this paper, we propose a novel splitting receiver, which involves joint processing of coherently and non-coherently received signals. Using a passive RF power splitter, the received signal at each receiver antenna is split into two streams which are then processed by a conventional coherent detection (CD) circuit and a power-detection (PD) circuit, respectively. The streams of the signals from all the receiver antennas are then jointly used for information detection. We show that the splitting receiver creates a three-dimensional received signal space, due to the joint coherent and non-cohe…
We consider a point-to-point system with simultaneous wireless information and power transfer (SWIPT) over a block fading channel. Each transmission block consists of a training phase and a data transmission phase. Pilot symbols are transmitted during the training phase for channel estimation at the receiver. To enable SWIPT, the receiver adopts a power-splitting design, such that a portion of the received signal is used for channel estimation or data detection, while the remaining is used for energy harvesting. We optimally design the power-splitting ratios for both training and data phases t…
Scavenging energy from ambient radio signals, namely wireless energy harvesting (WEH), has recently drawn significant attention. In this paper, we consider a point-to-point wireless link over the flat-fading channel, where the receiver replenishes energy via WEH from the signals sent by the transmitter. We consider a SISO (single-input single-output) system where the single-antenna receiver cannot decode information and harvest energy independently from the same signal received. Under this practical constraint, we propose a dynamic power splitting (DPS) scheme, where the received signal is spl…
To enhance the multiplexing gain of two-receiver Multiple-Input-Single-Output Broadcast Channel with imperfect channel state information at the transmitter (CSIT), a class of Rate-Splitting (RS) approaches has been proposed recently, which divides one receiver's message into a common and a private part, and superposes the common message on top of Zero-Forcing precoded private messages. In this paper, with quantized CSIT, we study the ergodic sum rate of two schemes, namely RS-S and RS-ST, where the common message(s) are transmitted via a space and space-time design, respectively. Firstly, we u…
Ultrasonic intra-body communication (IBC) is a promising enabling technology for future healthcare applications, due to low attenuation and medical safety of ultrasonic waves for the human body. A splitting receiver, referred to as the splitting-detection separate-decision (SDSD) receiver, is introduced for ultrasonic pulse-based IBCs, and SDSD can significantly improve bit-error rate (BER) performance over the traditional coherent-detection (CD) and energy detection (ED) receivers. To overcome the high complexity and improve the BER performance of SDSD, a splitting-detection joint-decision (S…
We present a low-complexity joint demapper-decoder scheme for coherent optical receivers with DQPSK modulation. The new technique reduces to 0.7dB the gap between QPSK and DQPSK in 100Gb/s coherent optical systems.
An achievable rate region is obtained for a primary multiple access network coexisting with a secondary link of one transmitter and a corresponding receiver. The rate region depicts the sum primary rate versus the secondary rate and is established assuming that the secondary link performs rate-splitting. The achievable rate region is the union of two types of achievable rate regions. The first type is a rate region established assuming that the secondary receiver cannot decode any primary signal, whereas the second is established assuming that the secondary receiver can decode the signal of on…
This letter deals with the joint information and energy processing at a receiver of a point-to-point communication channel. In particular, the trade-off between the achievable information rate and harvested energy for a multiple-antenna power splitting (PS) receiver is investigated. Here, the rate- energy region characterization is of particular interest, which is intrinsically a non-convex problem. In this letter, an efficient algorithm is proposed for obtaining an approximate solution to the problem in polynomial time. This algorithm is mainly based on the Taylor approximation in conjunction…
This paper focuses on $ K $-receiver discrete-time memoryless broadcast channels (DM-BCs) with private messages, where the transmitter wishes to convey $K$ private messages to $K$ receivers respectively. A general inner bound on the capacity region is proposed based on an exhaustive message splitting and a $K$-level modified Marton's coding. The key idea is to split every message into $ \sum_{j=1}^K {K\choose j} $ submessages each corresponding to a set of users who are assigned to recover them, and then send these submessages through codewords that are jointly typical with each other. To guar…
The problem of characterizing the capacity region for Gaussian broadcast channels with receiver message side information appears difficult and remains open for N >= 3 receivers. This paper proposes a joint network and Gelfand-Pinsker coding method for 3-receiver cases. Using the method, we establish a unified inner bound on the capacity region of 3-receiver Gaussian broadcast channels under general message side information configuration. The achievability proof of the inner bound uses an idea of joint interference cancelation, where interference is canceled by using both dirty-paper coding at …
Joint estimation of carrier frequency and direction of arrival (DOA) for multiple signals has been found in many practical applications such as Cognitive Radio (CR). However, Nyquist sampling mechanism is costly or implemented due to wide spectrum range. Taking advantage of sub-Nyquist sampling technology, some array receiver architectures are proposed to realize joint estimation of carrier frequency and DOA. To further decrease equivalent sampling rate and hardware complexity, we propose a simplifying receiver architecture based on our previous work. We come up with joint DOA and frequency es…
Internet of things (IoT) is an ever-growing network of objects that connect, collect and exchange data. To achieve the mission of connecting everything, physical layer communication is of indispensable importance. In this work, we propose a new receiver tailored for the characteristics of IoT communications. Specifically, our design is suitable for sporadic transmissions of small-to-medium sized packets in IoT applications. With joint design in the new receiver, strong reliability is guaranteed and power saving is expected.
Semi-definite relaxation (SDR) detector has been demonstrated to be successful in approaching maximum likelihood (ML) performance while the time complexity is only polynomial. We propose a new receiver jointly utilizing the forward error correction (FEC) code information in the SDR detection process. Strengthened by the code constraints, the joint SDR detector provides soft information of much improved reliability to downstream decoder and therefore outperforms existing receivers with substantial gain.
Simultaneous information and power transfer over the wireless channels potentially offers great convenience to mobile users. Yet practical receiver designs impose technical constraints on its hardware realization, as practical circuits for harvesting energy from radio signals are not yet able to decode the carried information directly. To make theoretical progress, we propose a general receiver operation, namely, dynamic power splitting (DPS), which splits the received signal with adjustable power ratio for energy harvesting and information decoding, separately. Three special cases of DPS, nam…
Pushing and caching hold the promise of significantly increasing the throughput of content-centric wireless networks. However, the throughput gain of these techniques is limited by the buffer size of the receiver. To overcome this, this paper presents a Joint Pushing and Caching (JPC) method that jointly determines the contents to be pushed to, and to be removed from, the receiver buffer in each timeslot. An offline and two online JPC policies are proposed respectively based on noncausal, statistical, and causal content Request Delay Information (RDI), which predicts a user's request time for …
This paper proposes a joint transmitter-receiver design to minimize the weighted sum power under the post-processing signal-to-interference-and-noise ratio (post-SINR) constraints for all subchannels. Simulation results demonstrate that the algorithm can not only satisfy the post-SINR constraints but also easily adjust the power distribution among the users by changing the weights accordingly. Hence the algorithm can be used to alleviates the adjacent cell interference by reducing the transmitting power to the edge users without performance penalty.
Nonlinear distortion in power amplifiers (PA) can significantly degrade performance of orthogonal frequency division multiplexed (OFDM) communication systems. This paper presents a joint maximum-likelihood channel frequency response and nonlinear PA model estimator for OFDM signals. Derivation of the estimator is based on Taylor-series representation of power amplifier nonlinearity and is suitable for wide range of memoryless PA models. A sub-optimal decision-aided algorithm for adaptive compensation of nonlinear distortion effects at the receiver-side is also presented. It is shown that the p…
In this paper, we consider a multihop wireless sensor network (WSN) with multiple relay nodes for each hop where the amplify-and-forward (AF) scheme is employed. We present a strategy to jointly design the linear receiver and the power allocation parameters via an alternating optimization approach that maximizes the sum rate of the WSN. We derive constrained maximum sum-rate (MSR) expressions along with an algorithm to compute the linear receiver and the power allocation parameters with the optimal complex amplification coefficients for each relay node. Computer simulations show good performan…
It is known that, as opposed to point-to-point channel, separate source and channel coding is not optimal in general for sending correlated sources over multiuser channels. In some works joint source-channel coding has been investigated for some certain multiuser channels; i.g., multiple access channel (MAC) and broadcast channel (BC). In this paper, we obtain a sufficient condition for transmitting arbitrarily correlated sources over a discrete memoryless BC with cooperating receivers, where the receivers are allowed to exchange messages via a pair of noisy cooperative links. It is seen that …
In this paper, a joint power allocation algorithm with minimum mean-squared error (MMSE) receiver for a cooperative Multiple-Input and Multiple-Output (MIMO) network which employs multiple relays and a Decode-and-Forward (DF) strategy is proposed. A Distributed Space-Time Coding (DSTC) scheme is applied in each relay node. We present a joint constrained optimization algorithm to determine the power allocation parameters and the MMSE receive filter parameter vectors for each transmitted symbol in each link, as well as the channel coefficients matrix. A Stochastic Gradient (SG) algorithm is deri…
This paper presents the development of a joint optimization of an automatic gain control (AGC) algorithm and a linear \textit{minimum mean square error} (MMSE) receiver for multi-user multiple input multiple output (MU-MIMO) systems with coarsely quantized signals. The optimization of the AGC is based on the minimization of the \textit{mean square error} (MSE) and the proposed receive filter takes into account the presence of the AGC and the effects due to quantization. Moreover, we provide a lower bound on the capacity of the MU-MIMO system by deriving an expression for the achievable rate. T…
In this paper, we address the message-passing receiver design for the 3D massive MIMO-OFDM systems. With the aid of the central limit argument and Taylor-series approximation, a computationally efficient receiver that performs joint channel estimation and decoding is devised by the framework of expectation propagation. Specially, the local belief defined at the channel transition function is expanded up to the second order with Wirtinger calculus, to transform the messages sent by the channel transition function to a tractable form. As a result, the channel impulse response (CIR) between each …
We propose a deep-learning approach for the joint MIMO detection and channel decoding problem. Conventional MIMO receivers adopt a model-based approach for MIMO detection and channel decoding in linear or iterative manners. However, due to the complex MIMO signal model, the optimal solution to the joint MIMO detection and channel decoding problem (i.e., the maximum likelihood decoding of the transmitted codewords from the received MIMO signals) is computationally infeasible. As a practical measure, the current model-based MIMO receivers all use suboptimal MIMO decoding methods with affordable …
Joint optimization of nonlinear precoders and receive filters is studied for both the uplink and downlink in a cellular system. For the uplink, the base transceiver station (BTS) receiver implements successive interference cancellation, and for the downlink, the BTS station pre-compensates for the interference with Tomlinson-Harashima precoding (THP). Convergence of alternating optimization of receivers and transmitters in a single cell is established when filters are updated according to a minimum mean squared error (MMSE) criterion, subject to appropriate power constraints. Adaptive algorith…
In this work, we consider a scenario wherein an energy harvesting wireless radio equipment sends information to multiple receivers alongside powering them. In addition to harvesting the incoming radio frequency (RF) energy, the receivers also harvest energy from {its environment (e.g., solar energy)}. This communication framework is captured by a fading Gaussian Broadcast Channel (GBC) with energy harvesting transmitter and receivers. In order to ensure {some quality of service (QoS)} in data reception among the receivers, we impose a \textit{minimum-rate} requirement on data transmission. For…
In a superimposed unicast and multicast transmission system, one layer of Successive Interference Cancellation (SIC) is required at each receiver to remove the multicast stream before decoding the unicast stream. In this paper, we show that a linearly-precoded Rate-Splitting (RS) strategy at the transmitter can efficiently exploit this existing SIC receiver architecture. By splitting the unicast message into common and private parts and encoding the common parts along with the multicast message into a super-common stream decoded by all users, the SIC is used for the dual purpose of separating …
This paper considers orthogonal frequency division multiple access systems with simultaneous wireless information and power transfer. We study the resource allocation algorithm design for maximization of the energy efficiency of data transmission. In particular, we focus on power splitting hybrid receivers which are able to split the received signals into two power streams for concurrent information decoding and energy harvesting. Two scenarios are investigated considering different power splitting abilities of the receivers. In the first scenario, we assume receivers which can split the recei…
This letter proposes a joint pilot and payload power allocation (JPA) scheme to mitigate the error propagation problem for uplink multiple-input multiple-output non-orthogonal multiple access (MIMO-NOMA) systems. A base station equipped with a maximum ratio combining and successive interference cancellation (MRC-SIC) receiver is adopted for multiuser detection. The average signal-to-interference-plus-noise ratio (ASINR) of each user during the MRC-SIC decoding is analyzed by taking into account the error propagation due to the channel estimation error. Furthermore, the JPA design is formulated…
A novel linear blind adaptive receiver based on joint iterative optimization (JIO) and the constrained constant modulus (CCM) design criterion is proposed for interference suppression in direct-sequence ultra-wideband (DS-UWB) systems. The proposed blind receiver consists of two parts, a transformation matrix that performs dimensionality reduction and a reduced-rank filter that produces the output. In the proposed receiver, the transformation matrix and the reduced-rank filter are updated jointly and iteratively to minimize the constant modulus (CM) cost function subject to a constraint. Adapt…
In this work, with combined belief propagation (BP), mean field (MF) and expectation propagation (EP), an iterative receiver is designed for joint phase noise (PN) estimation, equalization and decoding in a coded communication system. The presence of the PN results in a nonlinear observation model. Conventionally, the nonlinear model is directly linearized by using the first-order Taylor approximation, e.g., in the state-of-the-art soft-input extended Kalman smoothing approach (soft-in EKS). In this work, MF is used to handle the factor due to the nonlinear model, and a second-order Taylor app…
We consider a cache-aided communications system in which a transmitter communicates with many receivers over an erasure broadcast channel. The system serves as a basic model for communicating on-demand content during periods of high network congestion, where some content can be pre-placed in local caches near the receivers. We formulate the cache-aided communications problem as a joint cache-channel coding problem, and characterise some information-theoretic tradeoffs between reliable communications rates and cache sizes. We show that if the receivers experience different channel qualities, th…
When classical information is sent over a channel with quantum-state modulation alphabet, such as the free-space optical (FSO) channel, attaining the ultimate (Holevo) limit to channel capacity requires the receiver to make joint measurements over long codeword blocks. In recent work, we showed a receiver for a pure-state channel that can attain the ultimate capacity by applying a single-shot optical (unitary) transformation on the received codeword state followed by simultaneous (but separable) projective measurements on the single-modulation-symbol state spaces. In this paper, we study the u…
The problem of joint source-channel coding in transmitting independent sources over interference channels with correlated receiver side information is studied. When each receiver has side information correlated with its own desired source, it is shown that source-channel code separation is optimal. When each receiver has side information correlated with the interfering source, sufficient conditions for reliable transmission are provided based on a joint source-channel coding scheme using the superposition encoding and partial decoding idea of Han and Kobayashi. When the receiver side informati…
In ultra-wideband (UWB) communication systems with impulse radio (IR) modulation, the bandwidth is usually 1GHz or more. To process the received signal digitally, high sampling rate analog-digital-converters (ADC) are required. Due to the high complexity and large power consumption, monobit ADC is appropriate. The optimal monobit receiver has been derived. But it is not efficient to combat intersymbol interference (ISI). Decision feedback equalization (DFE) is an effect way dealing with ISI. In this paper, we proposed a algorithm that combines Viterbi decoding and DFE together for monobit rece…
In this paper, the transmission of an improper-complex second-order stationary data sequence is considered over a strictly band-limited frequency-selective channel. It is assumed that the transmitter employs linear modulation and that the channel output is corrupted by additive proper-complex cyclostationary noise. Under the average transmit power constraint, the problem of minimizing the mean-squared error at the output of a widely linear receiver is formulated in the time domain to find the optimal transmit and receive waveforms. The optimization problem is converted into a frequency-domain …
In this paper, a joint transmitter and receiver design for pattern division multiple access (PDMA) is proposed. At the transmitter, pattern mapping utilizes power allocation to improve the overall sum rate, and beam allocation to enhance the access connectivity. At the receiver, hybrid detection utilizes a spatial filter to suppress the inter-beam interference caused by beam domain multiplexing, and successive interference cancellation to remove the intra-beam interference caused by power domain multiplexing. Furthermore, we propose a PDMA joint design approach to optimize pattern mapping base…
We consider a basic communication and sensing setup comprising a transmitter, a receiver and a sensor. The transmitter sends an encoded sequence to the receiver through a discrete memoryless channel, and the receiver is interested in decoding the sequence. On the other hand, the sensor picks up a noisy version of the transmitted sequence through one of two possible discrete memoryless channels. The sensor knows the transmitted sequence and wishes to discriminate between the two possible channels, i.e. to identify the channel that has generated the output given the input. We study the trade-off…
This paper introduces multiuser multiple-input multiple-output (MU-MIMO) architectures based on non-linear precoding and stream combining techniques using rate-splitting (RS), where the transmitter often has only partial knowledge of the channel state information (CSI). In contrast to existing works, we consider deployments where the receivers may be equipped with multiple antennas. This allows us to employ linear combining techniques based on the Min-Max, the maximum ratio and the minimum mean-square error criteria along with Tomlinson-Harashima precoders (THP) for RS-based MU-MIMO systems to…
A general inner bound is given for the discrete memoryless broadcast channel with an arbitrary number of users and general message sets, a setting that accounts for the most general form of concurrent groupcasting, with messages intended for any set of subsets of receivers. Achievability is based on superposition coding and rate-splitting without and with binning, where each receiver jointly decodes both its desired messages as well as the partial interference assigned to it via rate-splitting. The proof of achievability builds on the techniques for the description and analysis of superpositio…
In this paper, we propose a turbo receiver for joint activity detection and data decoding in grant-free massive random access, which iterates between a detector and a belief propagation (BP)-based channel decoder. Specifically, responsible for user activity detection, channel estimation, and soft data symbol detection, the detector is developed based on a bilinear inference problem that exploits the common sparsity pattern in the received pilot and data signals. The bilinear generalized approximate message passing (BiG-AMP) algorithm is adopted to solve the problem using probabilities of the t…
In this work, we propose the joint optimization of the automatic gain control (AGC), which works in the remote radio heads (RHHs), and a low-resolution aware (LRA) linear receive filter based on the minimum mean square error (MMSE), which works on the baseband unit (BBU) pool, for large-scale multi-user multiple-input multiple-output (MU-MIMO) systems with coarsely quantized signals in cloud radio access networks. We develop successive interference cancellation receivers based on the proposed joint AGC and LRA-MMSE (AGC-LRA-MMSE) approach. An analysis of the achievable sum rates is also carrie…
In this paper, we consider a time-switching (TS) co-located simultaneous wireless information and power transfer (SWIPT) system consisting of multiple multi-antenna access points which serve multiple single antenna users. In this scenario, we propose a multi-objective optimization (MOO) framework to design jointly the Pareto optimal beamforming vector and the TS ratio for each receiver. The objective is to maximize the utility vector including the achieved data rates and the harvested energies of all users simultaneously. This problem is a non-convex rank-constrained MOO problem which is relax…
Modern communication systems organize receivers in blocks in order to simplify their analysis and design. However, an approach that considers the receiver design from a wider perspective rather than treating it block-by-block may take advantage of the impacts of these blocks on each other and provide better performance. Herein, we can benefit from machine learning and compose a receiver model implementing supervised learning techniques. With this motivation, we consider a one-to-one transmission system over a flat fast fading wireless channel and propose a support vector machines (SVM)-based r…
This work presents joint iterative power allocation and interference suppression algorithms for DS-CDMA networks which employ multiple relays and the amplify and forward cooperation strategy. We propose a joint constrained optimization framework that considers the allocation of power levels across the relays subject to individual and global power constraints and the design of linear receivers for interference suppression. We derive constrained minimum mean-squared error (MMSE) expressions for the parameter vectors that determine the optimal power levels across the relays and the parameters of …
We build a realistic Simultaneous Wireless Information and Power Transfer (SWIPT) prototype and experimentally analyse the harvested energy and throughput trade-off. Both time-switching and power splitting receiver architectures are implemented, and the performance comparison is carried out. Systematic SWIPT transmission signal design methods are also considered and implemented on the prototype. The harvested energy-throughput (E-T) performance with different transmission signal designs, modulation schemes, and receiver architectures are evaluated and compared. The combination of the power spl…
In a Non-Orthogonal Unicast and Multicast (NOUM) transmission system, a multicast stream intended to all the receivers is superimposed in the power domain on the unicast streams. One layer of Successive Interference Cancellation (SIC) is required at each receiver to remove the multicast stream before decoding its intended unicast stream. In this paper, we first show that a linearly-precoded 1-layer Rate-Splitting (RS) strategy at the transmitter can efficiently exploit this existing SIC receiver architecture. We further propose multi-layer transmission strategies based on the generalized RS an…
Large-scale multi-user multiple-input multiple-output (MU-MIMO) systems and cloud radio access networks (C-RANs) are considered promising technologies for the fifth generation (5G) of wireless networks. In these technologies, the use of low-resolution analog-to-digital converters (ADCs) is key for energy efficiency and for complying with constrained fronthaul links. Processing signals with few bits implies a significant performance loss and, therefore, techniques that can compensate for quantization distortion are fundamental. In wireless systems, an automatic gain control (AGC) precedes the A…
We consider the problem of Simultaneous Wireless Information and Power Transfer (SWIPT) over a fading multiple access channel with additive Gaussian noise. The transmitters as well as the receiver harvest energy from ambient sources. We assume that the transmitters have two classes of data to send, viz. delay sensitive and delay tolerant data. Each transmitter sends the delay sensitive data at a certain minimum rate irrespective of the channel conditions (fading states). In addition, if the channel conditions are good, the delay tolerant data is sent. {Along with data, the transmitters also tr…
Recently, joint wireless information and energy transfer (JWIET) methods have been proposed to relieve the battery limitation of wireless devices. However, the JWIET in a general K-user MIMO interference channel (IFC) has been unexplored so far. In this paper, we investigate for the first time the JWIET in K-user MIMO IFC, in which receivers either decode the incoming information data (information decoding, ID) or harvest the RF energy (energy harvesting, EH). In the K-user IFC, we consider three different scenarios according to the receiver mode -- i) multiple EH receivers and a single ID rec…
In this paper, we formulate and solve a weighted-sum transmitter and receiver energy minimization (WSTREMin) problem in the downlink of an orthogonal frequency division multiplexing (OFDM) based multiuser wireless system. The proposed approach offers the flexibility of assigning different levels of importance to base station (BS) and mobile terminal (MT) power consumption, corresponding to the BS being connected to the grid and the MT relying on batteries. To obtain insights into the characteristics of the problem, we first consider two extreme cases separately, i.e., weighted-sum receiver-sid…
We study the joint transmit (Tx) power allocation and receive (Rx) power splitting for simultaneous wireless information and power transfer (SWIPT). Considering the practical scenario of nonlinear energy harvesting (EH), we adopt the realistic nonlinear EH model for analysis. To address the critical nonlinearity issue due to the saturation, we propose to use multiple EH circuits in parallel. An important problem is to maximize the achievable rate by jointly optimizing Tx power allocation and Rx power splitting, which is a nonconvex problem. In this paper, we first derive the optimal solution f…
This paper investigates the optimal transmit beamforming design of simultaneous wireless information and power transfer (SWIPT) in the multiuser multiple-input-single-output (MISO) downlink with specific absorption rate (SAR) constraints. We consider the power splitting technique for SWIPT, where each receiver divides the received signal into two parts: one for information decoding and the other for energy harvesting with a practical non-linear rectification model. The problem of interest is to maximize as much as possible the received signal-to-interference-plus-noise ratio (SINR) and the ene…
