Abstract: A method for determining timing synchronization for demodulating a signal by a receiver, comprises the steps of: generating a channel response for the signal; transforming the signal into the time domain using an inverse fast fourier transform (“IFFT”); determining a signal power for the transformed signal as a function of the generated channel response; and calculating the timing synchronization by the receiver as a function of the determined signal power.

Abstract: Methods and apparatuses to reduce resource consumption by a mobile wireless device when decoding control channel information, such as a physical downlink control channel (PDCCH), in a subframe received from an LTE wireless network are disclosed. Representative methods include demodulating a first set of one or more PDCCH OFDM symbols contained in the subframe based on a first channel estimate; obtaining a second channel estimate based on a second OFDM symbol before demodulating a second set of one or more PDCCH OFDM symbols contained in the subframe based on both the first channel estimate and the second channel estimate. When the PDCCH indicates no downlink assignments for the subframe, the mobile wireless device enters a reduced power consumption mode after demodulating the PDCCH.

Abstract: A digital-to-analog conversion circuit operates by selectively discharging members of a plurality of capacitors. Charging of the capacitors occurs during a reset period while digital-to-analog conversion occurs as the capacitors are discharged. Those capacitors that are discharged are selected from the plurality of capacitors based on a digital input. The analog output includes the charge discharged from the capacitors. The capacitors are optionally divided into separate capacitor banks.

Abstract: Provided are a soft demapping apparatus and method that may cancel interference included in a rotated quadrature amplitude modulation (QAM) signal, using at least one interference cancellation unit, and may perform one-dimensional (1D) soft demapping of the interference-cancelled rotated QAM signal.

Abstract: In one aspect, the teachings herein disclose a method and apparatus for signal quality reporting from a wireless apparatus that better reflects the actual interference cancellation efficiency expected at the wireless apparatus for a given transmission interval. In one example, the wireless apparatus knows or predicts the particular modulation and coding schemes (MCSs) that will be used in the transmission of one or more interferer signals for a transmission interval of interest. In turn, it uses those MCS values to estimate the actual interference cancellation efficiency the wireless apparatus will achieve with respect to those interferers. The wireless apparatus estimates and reports signal quality according to its estimated interference cancellation efficiency.

Abstract: A first network device detects at least a first orthogonal code included in a preamble of a network packet received at the first network device from a second network device in an orthogonal frequency division multiplexing (OFDM) communication network. The first network device determines whether the first orthogonal code included in the preamble is associated with an assigned orthogonal code for the first network device. The assigned orthogonal code for the first network device is orthogonal to other assigned orthogonal codes for other network devices in the OFDM communication network. An operational mode of the first network device is changed from a sleep mode to an awake mode in response to determining the first orthogonal code is associated with the assigned orthogonal code for the first network device.

Abstract: Apparatus for measurement of the reception time of a pulse in a receiving system, which contains at least one receiving channel with a non-linear transmission response, which receiving channel produces at its output a received signal, having a memory, in which the received signals of reference pulses with a predetermined different amplitude are available as reference signals with respect to a time scale, and having an evaluation device, which is connected to the receiving system and to the memory and compares a received signal with each reference signal with a variant time offset in order to determine that reference signal and that time offset for which the comparison discrepancy is a minimum, and outputs this time offset as the reception time with respect to the time scale.

Abstract: The invention relates to a method for estimating frequency bias negatively affecting a digital signal representative of a symbol frame, wherein said method comprises the steps of: generating the digital signal at a sampling period Te that is shorter than a predefined period of each of the symbols of the frame; calculating values for a plurality of pairs of samples of the digital signal, each value being representative of a phase difference between the samples of a pair; estimating the frequency bias negatively affecting the digital signal on the basis of the values calculated for Np pairs of samples selected such that a plurality of said Np pairs belong strictly to a single symbol in the frame. The present invention also relates to a module for implementing the estimation method, as well as to a telecommunication method and system.

Abstract: An analog-to-digital converter (ADC) and a receiver that includes the ADC is disclosed. The ADC includes a first filter configured to receive a signal in an I-signal path of the receiver and a second filter configured to receive a signal in a Q-signal path of the receiver. The ADC further includes a quantizer alternatingly in connection with the first and second filters, and at least one DAC alternatingly in connection with the first and second filters. Switches in the ADC are configured to alternate connection between an input of the quantizer and outputs of the first and second filters, and are also configured to alternate connection between an output of the at least one DAC and inputs of the first and second filters.

Abstract: A receiver apparatus includes a propagation channel estimating unit that estimates a propagation channel. The propagation channel estimating unit includes a path detector unit that repeatedly performs a process of detecting paths in the order of increase in a propagation channel goodness of fit. The receiver apparatus that estimates a propagation channel at a high accuracy level with a small amount of calculation operation involved is thus provided.

Abstract: A technique for decoding a signal in a communication network is provided. A method implementation of the technique comprises the steps of receiving a signal; identifying a position in the signal; initializing a Viterbi state metric; and decoding the encoded signal by means of a wrap-around Viterbi algorithm. The received signal comprises information, wherein the signal is encoded by a tail-biting convolutional code. The identified position relates to a known portion of the information. The initialized Viterbi state metric is consistent with the known portion of the information. The decoding uses the initial Viterbi state metric, wherein the decoding starts at a decoding step following the identified position.

Abstract: In one embodiment, a transmitter includes a binary sequence generator unit configured to provide a sequence of reference signal bits, wherein the sequence is an inseparable function of a cell identification parameter, a cyclic prefix mode corresponding to the transmitter and one or more time indices of the sequence. The transmitter also include a mapping unit that transforms the sequence of reference signal bits into a complex reference signal, and a transmit unit configured to transmit the complex reference signal. In another embodiment, a receiver includes a receive unit configured to receive a complex reference signal and a reference signal decoder unit configured to detect a sequence of reference signal bits from the complex reference signal, wherein the sequence is an inseparable function of a cell identification parameter, a cyclic prefix mode corresponding to a transmitter and one or more time indices of the sequence.

Abstract: A method and an apparatus for transmitting broadcast signals thereof are disclosed. The apparatus for transmitting broadcast signals, the apparatus comprises an encoder for encoding service data corresponding to each of a plurality of data transmission path, wherein each of the data transmission path carries at least one service component, an encoder for encoding signaling data, a frame builder for building at least one signal frame including the encoded service data, a modulator for modulating the at least one signal frame by an OFDM (Orthogonal Frequency Division Multiplex) scheme and a transmitter for transmitting the broadcast signals carrying the at least one modulated signal frame.

Abstract: A transmission method simultaneously transmitting a first modulated signal and a second modulated signal at a common frequency performs precoding on both signals using a fixed precoding matrix and regularly changes the phase of at least one of the signals, thereby improving received data signal quality for a reception device.

Abstract: There is provided a reception device including a reception unit configured to receive an OFDM (Orthogonal Frequency Division Multiplexing) signal, an acquisition unit configured to acquire a transmission parameter concerning the OFDM signal contained in the OFDM signal, and a selection unit configured to select a demodulation mode of the OFDM signal in accordance with the acquired transmission parameter.

Abstract: Systems, methods, and other embodiments associated with preamble detection based on repeated preamble codes are described. According to one embodiment, an apparatus is provided that wirelessly receives a signal and calculates a differential output corresponding to a multiplication of the signal and a delayed version of the signal. A cross correlation is performed between the differential output and a known preamble pattern to produce a cross correlation output. One or more peaks are detected in the cross correlation. The detected peaks are used in subsequent processing to detect the known preamble pattern in the wirelessly received signal.

Abstract: To detect a victim signal in an ultra wideband communication system, fast Fourier transform of a received signal including a plurality of time symbols is performed to generate a signal including a plurality of frequency symbols, it is determined whether a first signal is present in a first region of the signal, and if a first signal is present, the first signal is detected as a first victim signal. Next, an error signal is generated based on the signal including the plurality of frequency symbols, it is determined whether a second signal is present in a second region of the error signal, and if a second signal is present, the second signal is detected as a second victim signal.

Abstract: Wireless receiver circuits and methods include algorithms for switching between a least-squares/minimum mean-square error method of channel estimation known as the CE algorithm, and a continuous plot method of channel estimation known as the CPCE algorithm based upon channel characteristics to improve reception of wireless communications in different reception conditions. In an embodiment, the CPCE algorithm may be selected by a processor for use in channel estimation when a calculated number of candidate paths is less than or equal to a first threshold value, a calculated power ratio of the L strongest paths to the total of all paths is greater than or equal to a second threshold value, and the maximum Automatic Gain Control variation is greater than or equal to a third threshold value. Threshold values may be based on field testing, and set to values at which the CE or CPCE algorithm exhibits better performance.

Abstract: Disclosed is a relay method including: receiving, as input, respective reception signals by two receive antennas, the reception signals each including a reception signal resulting from multiplexing respective transmission signals transmitted by two transmission antennas in a first frequency band; performing frequency conversion on the reception signal received by one of the receive antennas so as to obtain a signal of a third frequency band; and performing frequency multiplexing on the signal having the third frequency band and the reception signal received by the other of the receive antennas.

Abstract: An efficient decoding of vector signaling codes is obtained using a circuit that ranks received signal levels, designates ranked values as representing particular code elements, and translates those particular code elements into a decoded result. An optimized ranking circuit combines analog crossbar switching of signal values with comparators that provide digital results. These elements may be repetitively tiled into processing arrays capable of larger ranking operations, or iteratively applied to selected portions of the data set under control of a sequencer or controller.

Abstract: A broadcasting-communication data receiving apparatus for receiving mixed signals including original signals and additional signals.

Abstract: A detecting circuit includes: a first offset generating circuit, arranged to apply a first offset to an input signal pair and accordingly generate a first output signal pair; and a first sampling circuit, coupled to the first offset generating circuit, the first sampling circuit arranged to sample the first output signal pair to generate a first sampling signal, wherein the first sampling signal is utilized to identify a data signal on the input signal pair, and the first sampling circuit is controlled by a first signal that is irrelevant to the input signal pair.

Abstract: An optical communication system, a transmitter, a receiver, and methods of operating the same are provided. In particular, a transmitter is disclosed as being configured to encode optical signals in accordance with a multi-level coding scheme. The receiver is configured to provide receive and decode to the optical signals received from the transmitter. One or both of the receiver and transmitter are configured to compensate for non-idealities or non-linearities introduced into the communication system by optical components of the system.

Abstract: A method includes determining a correlation between a first residual error and multiple columns in a sensing matrix according to a measured value of an original signal and the sensing matrix, and determining a first array most correlative to the measured value of the original signal in the sensing matrix according to the correlation between the first residual error and the multiple columns; determining a correlation between a kth residual error and the multiple columns according to a correlation between a (k?1)th residual error and the multiple columns, and determining a kth array most correlative to the measured value of the original signal according to the correlation between the kth residual error and the multiple columns in the sensing matrix, where 2?k?K; and recovering the original signal after determining a Kth array most correlative to the measured value of the original signal.

Abstract: Systems and methods for decoding data transmitted by RFID tags are disclosed. One embodiment of the invention includes an analyzer and equalizer configured to filter an input signal, an estimation block configured to obtain a baseband representation of the modulated data signal by mixing the filtered input signal with the carrier wave, and a coherent detector configured to perform phase and timing recovery on the modulated data signal in the presence of noise and to determine a sequence of data symbols.

Abstract: A binary allocation in a hierarchical coding/decoding comprising a coding/decoding of a digital signal enhancement layer. The signal comprises a succession of L samples, each sample being represented by a mantissa and an exponent. The method comprises the allocation of a predetermined number Nb of enhancement bits to a part at least of the L samples of highest exponent values. In particular, the method comprises the steps: a) enumerating the exponents of the L samples each having a given value, b) calculating at least one aggregate of enumerations of exponents by decreasing values of exponent until the predetermined number Nb is approximated from above, for c) determining a threshold value of largest exponent iexp0 of sample for which no more enhancement bit is available, and allocating the Nb enhancement bits, according to chosen rules, to the samples whose exponent is greater than the aforesaid threshold value iexpo.

Abstract: Wireless communication wherein channel estimation accuracy is improved while keeping the position of each bit in a frame, even when a modulation system having a large modulation multiple value is used for a data symbol. An encoding operation encodes and outputs transmitting data (bit string) and a bit converting operation converts at least one bit of a plurality of bits constituting a data symbol to be used for channel estimation, among the encoded bit strings, into or ‘0’ or ‘0’. A modulating operation modulates the bit string inputted from the bit converting operation by using a single modulation mapper and a plurality of data symbols are generated.

Abstract: In one aspect, a method for mitigating an effect of an interfering radio signal at a multiple antenna receiver includes forming an estimate of a relationship of the interfering signal among signals received from the multiple antennas. In general, the interfering signal does not share the same communication technology as a desired signal. The signals received from the multiple antennas filtered and combined according to the estimate of the relationship of the interfering channels to reduce an effect of the interfering signal. Desired data present in the desired signal represented in the filtered and combined signals is decoded and the estimate of the relationship of the interfering signals is updated according to the decoding of the desired signal.

Abstract: Receiver synchronization techniques (RST), contributing more accurate synchronization of receiver clock to OFDM composite frame combined with much faster acquisition time and better stability of the receiver clock, and phase and frequency recovery techniques, comprising a software controlled clock synthesizer (SCCS) for high accuracy phase & frequency synthesis producing synchronized low jitter clock from external time referencing signals or time referencing messages wherein SCCS includes a hybrid PLL (HPLL) enabling 1-50,000 frequency multiplication with very low output jitter independent of reference clock quality.

Abstract: An orthotope sphere decoding method of a multiple antenna system is disclosed. The method includes performing tree search using a depth-first method by performing an OC-test on the nodes on which the tree search of orthotope sphere decoding will be performed and performing an SC-test on nodes passing the OC-test; and selecting a transmission symbol having a smallest PED value as a final signal as a result of the search.

Abstract: The present invention discloses a method and system for adaptively identifying signal bandwidth. The method includes: performing digitizing intermediate frequency processing to the received signal and outputting in-phase/quadrature (I/Q) signals; identifying signal bandwidth of the I/Q signals according to at least two signal identification templates and outputting the synchronized signal flows after a successful identification. A system for adaptively identifying signal bandwidth is also disclosed. The present invention can be compatible with at least two bandwidth modes, and the software can automatically perform identification and switch of the modulation bandwidth, when manual invention is not necessary and the operation is simple.

Abstract: A receiver apparatus includes a first frequency response estimator configured to calculate a first frequency response estimation value using a reference signal, a duration extractor configured to determine an estimation duration by extracting at least one duration from among a plurality of duration candidates into which a predetermined maximum delay time is divided, and a second frequency response estimator configured to calculate a second frequency response estimation value as a frequency response estimation value for demodulation using the first frequency response and the estimation duration. The receiver apparatus thus performs high-precision channel estimation even if a variety of PDPs occur with time.

Abstract: A transmitting apparatus, a receiving apparatus and a method of controlling these apparatus are provided. The transmitting apparatus includes: a frame generator configured to generate a plurality of frames which include one or more kinds of data; a preamble symbol inserter configured to insert at least one preamble symbol in each of the plurality of frames, and insert, in a preamble symbol of a frame, location information about at least one frame, among the plurality of frames, which includes a same kind of data as a kind of data included in the frame; and a transmitter configured to transmit the plurality of frames in each of which the preamble symbol is inserted.

Abstract: According to one embodiment, a receiver, which is configured to receive a radio signal having a preamble including a synchronization pattern and a payload containing data, includes an antenna, a low noise amplifier, a down-conversion module, a variable gain amplifier, an auto gain controller, a synchronization acquisition module, and a demodulator. The antenna is configured to receive the radio signal. The low noise amplifier is configured to amplify an output from the antenna by applying a first variable gain. The down-conversion module is configured to down-convert an output from the low noise amplifier. The variable gain amplifier is configured to amplify an output from the down-conversion module by applying a second variable gain. The auto gain controller is configured to, in accordance with strength of the radio signal, firstly adjust the first variable gain, and after fixing the first variable gain, adjust the second variable gain.

Abstract: A transmitter includes a frame generator which generates a plurality of frames each of which includes a preamble symbol and a data symbol, a pilot inserter which inserts a plurality of first pilots in the preamble symbol according to a predetermined first arrangement pattern and inserts a plurality of second pilots in a data symbol according to a second arrangement pattern, and a transmitting unit which transmits the plurality of frames in which the first and second pilots are inserted. Accordingly, a memory needed to store pilots may be reduced and precise synchronization may be performed based on an extended number of pilots.

Abstract: A receiver of a signal frame such as T2 frame used in a DVB-T2 system is provided. The receiver includes: a receiving unit configured to receive a frame including a preamble symbol in which a pseudo random noise (PN) sequence is inserted; a PN sequence detector configured to detect the PN sequence from the received frame; a controller configured to measure a start point of the preamble symbol and frequency offset of the PN sequence inserted in the preamble symbol, based on the detected PN sequence; and a preamble symbol detector configured to detect the preamble symbol according to the measured start point of the preamble symbol and the measured frequency offset of the PN sequence. Therefore, the receiver accurately measures the start point of the preamble symbol and the frequency offset and estimates a channel based on the PN sequence inserted in the preamble symbol.

Abstract: A method of processing data of an Orthogonal Frequency Division Multiplexing (OFDM) symbol, a transmitter and a receiver processing the OFDM symbol are provided. The method performed by the transmitter includes: mapping first data and second data to an OFDM symbol and transmitting a frame including the OFDM symbol. The mapping includes additionally mapping at least a portion of the second data to cells of the OFDM symbol which remain after the first data and the second data are mapped to the OFDM symbol.

Abstract: A transmitting apparatus is disclosed that adjusts an occupied bandwidth for each transmission rate, and thus can prevent deterioration of an S/N ratio while preventing a situation in which frequency components are cut and cannot be demodulated, without increasing the manufacturing cost. The transmitting apparatus is capable of performing communication at multiple different transmission rates. A modulation section modulates transmission data to generate a modulated signal and adjusts an occupied bandwidth in a passband of a channel selection filter for each of the transmission rates. An occupied bandwidth control section outputs to the modulation section bandwidth setting information that causes a bandwidth to approximate to the bandwidth of a passband of a channel selection filter based on the inputted transmission rate setting information. An RF transmitting section transmits the modulated signal obtained by adjusting the occupied bandwidth via an antenna.

Abstract: A method operates to transmit a data signal by a transmission unit of a wireless multiple-input/multiple-output (MIMO) communication system. The communication system includes the transmission unit and a reception unit, the transmission unit having a plurality of transmission antennas and the reception unit having a plurality of reception antennas. The method includes performing a first transmission of a data signal, the first transmission including transmitting the data signal by each one of the plurality of transmission antennas, and performing a second transmission of the data signal at a time later than the first transmission, the second transmission including transmitting at least one spectrally modified signal variant of the data signal by at least one antenna of the plurality of transmission antennas.

Abstract: A system including a receiver to receive, over a wireless channel, a packet including a preamble portion that includes a plurality of training fields and a first signal field and a controller to generate a first estimate of the wireless channel based on one or more of the plurality of training fields, and decode the first signal field based on the first estimate. Subsequent to decoding the first signal field, the controller re-encodes the first signal field to generate a second signal field. The controller verifies whether the first signal field was properly decoded by comparing the second signal field to the first signal field prior to being decoded. In response to the first signal field being correctly decoded, the controller generates a second estimate of the wireless channel based on the first signal field as decoded. The second estimate is usable to refine the first estimate.

Abstract: A communications device includes an input that receives a communications signal having in-phase (I) and Quadrature (Q) signal components. A bit synchronization circuit detects the symbol timing error in the communications signal and includes a symbol mapper circuit configured to receive I and Q signal components and determine transition samples of vectors within the signal constellation. A rotation generator circuit is coupled to the symbol mapper circuit and configured to rotate the trajectory of the transition samples at their midpoints to determine the symbol timing error.

Abstract: A receiver communicating according to a wireless communication protocol standard for filtering a signal received at a single antenna. The receiver includes filter modules, receiver modules, and a summer. The filter modules receive from antennas multipath components of the signal as transmitted to the receiver. The signal includes bits of data. Each of the filter modules: receives corresponding ones of the multipath components of the signal as received at a respective one of the antennas; and according to the wireless communication protocol standard, filters the signal as received at the respective one of the antennas to generate a filtered signal. The receiver modules respectively receive the filtered signals. Each of the receiver modules combines the multipath components in the respective filtered signal to generate an output signal. Each of the output signals includes a respective version of the bits of data. The summer sums the output signals.

Abstract: A non-linear detector for detecting signals with signal-dependent noise is disclosed. The detector may choose a data sequence that maximizes the conditional probability of detecting the channel data. Since the channel may be time-varying and the precise channel characteristics may be unknown, the detector may adapt one or more branch metric parameters before sending the parameters to a loading block. In the loading block, the branch metric parameters may be normalized and part of the branch metric may be pre-computed to reduce the complexity of the detector. The loading block may then provide the branch metric parameters and any pre-computation to the detector. The detector may then calculate the branch metric associated with the input signal and output the channel data.

Abstract: A multi-carrier signal is typically comprised of many equidistant sub-carriers. This results in periodicity of spectrum within the bandwidth of such a multi-carrier signal. An unknown multi-carrier signal with equidistant sub-carriers can thus be sensed together with its sub-carrier spacing by finding a discernible local maximum in the cepstrum (Fourier transform of the log spectrum) of the multi-carrier signal.

Abstract: A system for correcting gain imbalance and phase imbalance between first (IOUT) and second (QOUT) signals which are 90° out of phase, including circuitry for estimating the phase mismatch (?) and gain mismatch (?) between the first signal and the second signal signals in a plurality of frequency bands. An inverse fast Fourier transform is performed on each of a number of arrays of the phase mismatch estimates and the gain mismatch estimates to generate correction filter coefficients (h[N]) for a N tap correction filter. The N tap correction filter filters an uncorrected value of the second signal to generate a corrected value of the second signal.

Abstract: The present invention discloses a method for uplink multi-user cooperation communication, including a first, and a second source node and a target node. When transmitting a signal to the target node, the first source node also transmits the signal to the second source node, the second source node changing to a relay node of the first source node and forwarding the signal to the target node; the target node obtains its reception Signal Noise Ratio (SNR) by using a maximal ratio combining mode according to the signal directly transmitted from the first source node and the signal forwarded from the second source node, sets a precoding policy according to the reception SNR, and selects the optimal precoding as a precoding vector which is used when the first source node transmits a signal to the target node.

Abstract: A decoding apparatus including an operation unit to calculate a branch metric between first and second instants of time based on receiving likelihood data and an anterior likelihood, and to use, in a state transition in a butterfly represented by first and second states at the first instant of time and third and fourth states at the second instant of time, a first anterior cumulative metric for the first state, a second anterior cumulative metric for the second state and a first difference based on the branch metric between the first state and the third state and on a second difference between the first anterior cumulative metric and the second anterior cumulative metric to calculate a third anterior cumulative metric for the third state and a fourth anterior cumulative metric for each butterfly and at each instant of time, and a storage unit to store the second difference.

Abstract: A method and system for a sequence estimation in a receiver, such as for use when receiving a sample of a received inter-symbol correlated (ISC) signal corresponding to a transmitted vector of L symbols, with L being a integer greater than 1, and with symbol L being a most-recent symbol and symbol 1 being least recent symbol of the vector. A plurality of candidate vectors may be generated, wherein element L?m of each candidate vector holding one of a plurality of possible values of the symbol L?m, with m is an integer greater than or equal to 1, and elements L?m+1 through L of each candidate vectors holding determined filler values. A plurality of metrics may be generated based on the plurality of candidate vectors, and based on the generated plurality of metrics, a best one of the possible values of the symbol L?m may be selected.

Abstract: According to one embodiment, an adjacent-channel interference reject filter comprises a short-pulse inverter which includes a short-pulse sensor configured to detect a pulse in an intermediate frequency signal supplied to the device. The short-pulse sensor detects pulses having a pulse width less than or equal to some predetermined width. The short-pulse inverter also includes a pulse inverter configured to invert the pulse detected by the short-pulse sensor. The adjacent-channel interference reject filter may also include an inversion controller to control the inverting of detected short pulses. An adjacent-channel interference reject filter may be included in various devices such as wireless communication devices.

Abstract: Methods and systems to vary an erasure slicer threshold based on a measure computed from prior soft and/or hard symbol decisions, identify reliable symbol estimates based on the threshold, identify unreliable symbol estimates for erasure based on the threshold, modify the identified symbol estimates, output the reliable symbol estimates and the modified symbol estimates as erasure slicer decisions, and filter the decisions in a feedback filter of a decision feedback equalizer (DFE). The erasure slicer threshold may be based on signal-to-noise ratio (SNR) or mean-squared-error (MSE). A symbol estimate may be identified for erasure when a coordinate of the corresponding soft decision is within an erasure area defined by the threshold. Symbol modification may include replacing a corresponding coordinate of the symbol estimate with a coordinate of a decision boundary associated with the erasure area.