Showing papers on "Constellation diagram published in 2011"

On Two-User Gaussian Multiple Access Channels With Finite Input Constellations

Abstract: Constellation Constrained (CC) capacity regions of two-user Single-Input Single-Output (SISO) Gaussian Multiple Access Channels (GMAC) are computed for several Non-Orthogonal Multiple Access schemes (NO-MA) and Orthogonal Multiple Access schemes (O-MA). For NO-MA schemes, a metric is proposed to compute the angle(s) of rotation between the input constellations such that the CC capacity regions are maximally enlarged. Further, code pairs based on Trellis Coded Modulation (TCM) are designed with PSK constellation pairs and PAM constellation pairs such that any rate pair within the CC capacity region can be approached. Such a NO-MA scheme which employs CC capacity approaching trellis codes is referred to as Trellis Coded Multiple Access (TCMA). Then, CC capacity regions of O-MA schemes such as Frequency Division Multiple Access (FDMA) and Time Division Multiple Access (TDMA) are also computed and it is shown that, unlike the Gaussian distributed continuous constellations case, the CC capacity regions with FDMA are strictly contained inside the CC capacity regions with TCMA. Hence, for finite constellations, a NO-MA scheme such as TCMA is better than FDMA and TDMA which makes NO-MA schemes worth pursuing in practice for two-user GMAC. Then, the idea of introducing rotations between the input constellations is used to construct Space-Time Block Code (STBC) pairs for two-user Multiple-Input Single-Output (MISO) fading MAC. The proposed STBCs are shown to have reduced Maximum Likelihood (ML) decoding complexity and information-losslessness property. Finally, STBC pairs with reduced sphere decoding complexity are proposed for two-user Multiple-Input Multiple-Output (MIMO) fading MAC.

Superposition modulation: myths and facts

Abstract: Traditionally, digital modulation schemes are bijective (i.e., the signal constellation points are disjunct), and the mapping is unique. Only recently it has been discovered that non-bijective modulation schemes may outperform bijective modulation schemes when employed in conjunction with suitable channel coding and iterative processing. In this in-depth tutorial, we clarify myths and facts about non-bijective modulation. Emphasis is on superposition modulation (SM). Without active signal shaping, SM outperforms bit-interleaved coded modulation with PSK or square QAM modulation at even lower receiver complexity.

Four-dimensional optical multiband-OFDM for beyond 1.4Tb/s serial optical transmission

Abstract: Systems and methods are disclosed to perform four-dimensional optical multiband OFDM communication by organizing an N-dimensional (ND) signal constellation points as a signal matrix; performing 2D-inverse FFT and 2D-FFT to perform modulation and demodulation, respectively; and applying both orthogonal polarizations in the OFDM communication to deal with chromatic dispersion, PMD and PDL effects, and multidimensional signal constellation to improve optical signal-to-noise ratio (OSNR) sensitivity.

Energy-efficient spatial-domain-based hybrid multidimensional coded-modulations enabling multi-Tb/s optical transport.

Abstract: In addition to capacity, the future high-speed optical transport networks will also be constrained by energy consumption. In order to solve the capacity and energy constraints simultaneously, in this paper we propose the use of energy-efficient hybrid D-dimensional signaling (D>4) by employing all available degrees of freedom for conveyance of the information over a single carrier including amplitude, phase, polarization and orbital angular momentum (OAM). Given the fact that the OAM eigenstates, associated with the azimuthal phase dependence of the complex electric field, are orthogonal, they can be used as basis functions for multidimensional signaling. Since the information capacity is a linear function of number of dimensions, through D-dimensional signal constellations we can significantly improve the overall optical channel capacity. The energy-efficiency problem is solved, in this paper, by properly designing the D-dimensional signal constellation such that the mutual information is maximized, while taking the energy constraint into account. We demonstrate high-potential of proposed energy-efficient hybrid D-dimensional coded-modulation scheme by Monte Carlo simulations.

Estimating OSNR of equalised QPSK signals.

Abstract: We propose and demonstrate a technique to estimate the OSNR of an equalised QPSK signal based on the radial moments of the complex signal constellation. The technique is compared through simulation with maximum likelihood estimation and the effect of the block size used in the estimation is also assessed. The technique is verified experimentally and when combined with a single point calibration the OSNR of the input signal was estimated to within 0.5 dB.

Direction dependent antenna modulation using a two element array

Abstract: A direction dependent antenna modulation system based on a simple two element phased array is presented By applying discrete phase shifts to the elements of the array, data modulation can be imparted on to the transmitted signal The form of the modulation then becomes dependent on the transmission angle It is shown that such a system provides a degree of transmission security and this is demonstrated by calculating the error rate of the system as a function of observation angle

Multidimensional Hybrid Modulations for Ultrahigh-Speed Optical Transport

Abstract: From Shanon's theory, we know that information capacity is a logarithmic function of signal-to-noise ratio (SNR) but a linear function of the number of dimensions By increasing the number of dimensions D, we can dramatically improve the spectral efficiency At the same time, in D-dimensional space (D >; 2), for the same average symbol energy, we can increase the Euclidean distance between signal constellation points compared with the conventional in-phase (I)/quadrature (Q) 2-D signal space The 4-D space, with two phase coordinates per polarization, has already been intensively studied To satisfy the ever-increasing bandwidth demands, in this paper, we propose the D-dimensional signaling (D >; 4) by employing all available degrees of freedom for transmission over a single carrier including amplitude, phase, polarization, and orbital angular momentum (OAM) The proposed modulation scheme can be called hybrid D-dimensional modulation as it employs all available degrees of freedom The proposed hybrid 8-D coded-modulation scheme outperforms its 4-D counterpart by 397 dB at a bit error rate (BER) of 10-8 while outperforming its corresponding polarization-division-multiplexed (PDM) iterative polar quantization (IPQ)-based counterpart by even a larger margin of 641 dB (at the same BER) The improvement of the proposed scheme for two amplitude levels per dimension and D = 8 over conventional PDM 64-quadrature amplitude modulation (QAM) is indeed a striking 828 dB at a BER of 2 × 10-8

Partial Marginalization Soft MIMO Detection With Higher Order Constellations

Abstract: A new method for multiple-input multiple-output (MIMO) detection with soft-output, the partial marginalization (PM) algorithm, was recently proposed. Advantages of the method are that it is straightforward to parallelize, and that it offers a fully predictable runtime. PM trades performance for computational complexity via a user-defined parameter. In the limit of high computational complexity, the algorithm becomes the MAP demodulator. The PM algorithm also works with soft-input, but until now it has been unclear how to apply it for other modulation formats than binary phase-shift keying (BPSK) per real dimension. In this correspondence, we explain how to extend PM with soft-input to general signaling constellations, while maintaining the low complexity advantage of the original algorithm.

On Generalized MIMO Y Channels: Precoding Design, Mapping, and Diversity Gain

Abstract: In this paper, we first study the design of network coding for the generalized multiple-input-multiple-output (MIMO) Y channels, where K users wish to exchange information with each other within two time slots. Precoding at each user and the relay is carefully constructed to ensure that the signals from the same user pair are grouped together and that cross-pair interference can be canceled. In addition, a simple mapping function is proposed to ensure low-complexity detection at the relay. Exact expressions of symbol error rate (SER) are then developed to establish the explicit relationship between the diversity gain and the number of node antennas. Monte Carlo simulation is also provided to demonstrate the performance of the proposed scheme.

Initial performance evaluation of spatial modulation OFDM in LTE-based systems

Abstract: In this paper, we explore the spatial modulation (SM) orthogonal frequency division multiplexing (SM-OFDM) transmission to achieve good performance in Long Term Evolution (LTE) based systems For assessment purposes, the performance results of SM-OFDM systems are compared with the popular Alamouti-coded OFDM systems and vertical Bell Labs layered space-time (V-BLAST) OFDM systems Simulation results show that SM-OFDM systems achieve better performance than other systems at low spectral efficiencies However, at high spectral efficiencies, the performance of SM depends on a trade-off between the spatial constellation size and signal constellation size Furthermore, the results also show that SM provides a flexible transceiver configuration, especially for an unbalanced multiple-input multiple-output (MIMO) channel

Signal Constellation Distortion and BER Degradation Due to Hardware Impairments in Six-Port Receivers with Analog I/Q Generation

Abstract: Since its introduction in 1994 direct conversion sixport receivers have attracted a considerable attention at microwave frequencies, with most recent work focusing on the so called sixport receivers with analog I/Q generation. Besides its applications at microwave frequencies, six-port receivers with I/Q regeneration play a crucial role in the optical communications field, as they are the most promising candidates for optical coherent receivers that are being developed for 100 Gigabit Ethernet transceivers. In this paper we analytically model the influence of six-port junction hardware impairments on receiver performance. New analytical expressions are developed which give geometrical interpretation of signal constellation distortion due to hardware impairments and allow for the definition of several interesting figures of merit. Closed formulas are also proposed to analytically calculate BER degradation, under AWGN conditions, from these figures of merit. Finally, the proposed formulas are validated by means of simulation, and it is shown that they can be of practical interest to set the specifications of the six-port junction components.

RF Directional Modulation Technique Using a Switched Antenna Array for Communication and Direction-Finding Applications

Abstract: A RF directional modulation technique using a switched antenna array is proposed for communication and direction-flnding applications. The main idea is that a baseband modulation signal is transmitted by the switched antenna array. The phase center of the transmit signal is moved by the feeding line of each element from the left to the right. In this way, the data information and Doppler frequency shift information are modulated into a transmit signal constellation simultaneously. Therefore, this constellation is a scrambled constellation compared with traditional baseband modulation signal, which varies with the azimuth angle information of the receiver. For the receiver with a single antenna, a difierential correlation algorithm is employed to demodulate the data information, and an azimuth angle estimation algorithm is also developed to extract the azimuth angle information from this scrambled constellation. Simulation results show that this RF directional modulation technique ofiers a comprehensive scheme for communication and direction-flnding from the point view of RF modulation technique.

Design of Flower Constellations for Telecommunication Services

Abstract: Satellite constellation designers take into consideration the entire telecommunication network and their design choices are influenced by many factors including: number of satellites, orbital characteristics, coverage area, network interconnections, system cost, and complexity. When the satellite constellation design method does not include a large number of possible configurations, then the final result of the design process is a suboptimal solution. Flower Constellation (FC) design provides a relatively new design approach which can overcome this problem. The time evolution of the FC theory is here summarized and the fundamental mathematics allowing the constellation design is provided. In particular, the theory is applied to the design and optimization of constellations maximizing the global coverage and the network connectivity via intersatellite links. Performance results are compared to the classical type of satellite constellations, i.e., the Walker Constellations. The performance improvement provided by FC design with respect to Walker Constellation design is shown. Finally, considerations regarding the cost for deployment and orbital control are also provided.

50.53-Gb/s PDM-1024QAM-OFDM transmission using pilot-based phase noise mitigation

Abstract: We demonstrate the largest signal constellation reported to date for optical transmission with 50.53-Gb/s PDM-1024-QAM-OFDM over 2×80-km ULAF. A spectral efficiency of 11.7 b/s/Hz was achieved.

Generalized OFDM (GOFDM) for ultra-high-speed optical transmission

Abstract: We propose a coded N-dimensional modulation scheme suitable for ultra-high-speed serial optical transport. The proposed scheme can be considered as a generalization of OFDM, and hence, we call it as generalized OFDM (GOFDM). In this scheme, the orthogonal subcarriers are used as basis functions and the signal constellation points are defined over this N-dimensional linear space. To facilitate implementation, we propose using N-dimensional pulse-amplitude modulation (ND-PAM) as the signal constellation diagram, which is obtained as the N-ary Cartesian product of one-dimensional PAM. In conventional OFDM, QAM/PSK signal constellation points are transmitted over orthogonal subcarriers and then they are multiplexed together in an OFDM stream. Individual subcarriers, therefore, carry N parallel QAM/PSK streams. In the proposed GOFDM scheme instead, an N-dimensional signal constellation point is transmitted over all N subcarriers simultaneously. When some of the subcarriers are severely affected by channel impairments, the constellation points carried by those subcarriers may be lost in the conventional OFDM. In comparison, under such conditions, the overall signal constellation point will face only small distortion in GOFDM and it can be recovered successfully using the information on the other high fidelity subcarriers. Furthermore, because the channel capacity is a logarithmic function of signal-to-noise ratio but a linear function of the number of dimensions, the spectral efficiency of optical transmission systems can be improved with GOFDM.

2-User multiple access spatial modulation

Abstract: Spatial modulation (SM) is a recently proposed approach to multiple-input-multiple-output (MIMO) systems which entirely avoids inter-channel interference (ICI) and requires no synchronisation between the transmit antennas, while achieving a spatial multiplexing gain. SM allows the system designer to freely trade off the number of transmit antennas with the signal constellation. Additionally, the number of transmit antennas is independent from the number of receive antennas which is an advantage over other multiplexing MIMO schemes. Most contributions thus far, however, have only addressed SM aspects for a point-to-point communication systems, i.e. the single-user scenario. In this work we seek to characterise the behaviour of SM in the interference limited scenario. The proposed maximum-likelihood (ML) detector can successfully decode incoming data from multiple sources in an interference limited scenario and does not suffer from the near-far problem.

Coded multidimensional pulse amplitude modulation for ultra-high-speed optical transmission

Abstract: We propose a coded N-dimensional pulse-amplitude modulation (ND-PAM) suitable for ultra-high-speed serial optical transport. The polarization-multiplexed-ND-PAM significantly outperforms corresponding polarization-multiplexed-QAM counterpart in terms of OSNR sensitivity (> 4 dB at symbol rate 31.25 GS/s), while enabling beyond 400 Gb/s transmission.

Development and Performance Evaluation of Hierarchical Quadrature Amplitude Modulation (HQAM) for Image Transmission over Wireless Channels

Abstract: Asymmetric modulation techniques like Quadrature Amplitude Modulation system is one of the key techniques in building a broadband mobile communication network because of increasing shortage of wireless communication channels. It provides alternative means of Equal Error Protection (EEP) to the transmitted bits without increasing the bandwidth. Hierarchical Quadrature Amplitude Modulation (HQAM), a modification of QAM, provides Unequal Error Protection (UEP) to the transmitted bits for increasing the protection to the sensitive and non-sensitive bits and is also efficient in power and bandwidth. This paper presents an analysis and simulation of HQAM in order to bring out its merits over QAM. The simulation is carried out using MATLAB & Simulink for different values of modulation parameter. A Simulink-based simulation system is designed for the transmission of gray image as test image over AWGN wireless channel. Keywords-Wireless Channels, HQAM, Error Protection

Optimized Nonuniform Constellation Rearrangement for Cooperative Relaying

Abstract: The performance of cooperative relaying networks can be significantly enhanced by using constellation rearrangement (CoRe). In CoRe, the base-station and the relay-station use different constellations, each having the same number of signal points, to communicate with the user terminal. A number of CoRe schemes have been proposed in the literature based on uniform quadrature-amplitude modulation (QAM) constellations. However, it is still unclear whether nonuniform QAM constellations can further enhance the performance of CoRe. Toward this end, we investigate the problem of designing the optimum nonuniform QAM constellations for CoRe. Our motivation is that nonuniform constellations have the potential to outperform their uniform counterparts because the set of nonuniform constellations is a superset of uniform constellations. Nonuniform QAM constellations can be categorized as either decomposable or nondecomposable . Unlike nondecomposable QAM constellations, decomposable QAM constellations are generated from the Cartesian product of two pulse-amplitude modulation (PAM) constellations. We formulate an optimization problem to find the nonuniform constellations that have the minimum union bound on the uncoded symbol error rate (SER). Using convex analysis, we devise a search method to find globally optimum nonuniform decomposable constellations. We also devise a simple heuristic to find good locally optimum nonuniform nondecomposable constellations, which perform better than their decomposable counterparts.

Construction of Higher-Level 3-D Signal Constellations and Their Accurate Symbol Error Probabilities in AWGN

Abstract: A simple and straightforward method of constructing higher-level three-dimensional (3-D) signal constellations for a reliable digital communication system is proposed in this paper. The new method expands basic 8-ary constellation into 3-D signal space systematically so that it produces lattice configurations. We also derive accurate closed-form symbol error probability (SEP) of cross-lattice constellations in additive white Gaussian noise (AWGN). It is verified that the theoretical SEPs are almost the same as simulation results. Minimum Euclidean distance (MED) of the higher-level 3-D constellations is increased at least 49% in comparison with quadrature amplitude modulation (QAM). When the number of symbols is 256, the 3-D constellation has around 105% longer MED than the 2-D QAM. Due to increase in MED, the 3-D constellations have much improved error performance compared to the QAM configurations. It is, therefore, considered that the higher-level 3-D constellations are appropriate for high-quality digital communications.

Simplified Quantisation in a Reduced-Lattice MIMO Decoder

Abstract: Symbol detection in a lattice-reduction aided MIMO receiver depends upon appropriate quantisation in the reduced lattice and this has previously been achieved using a shift-and-scale method. This paper describes a novel parity-based method that avoids the need to perform inversion of the reduction matrix and simplifies the computation involved in symbol estimation in MIMO receivers using QAM and PAM modulation schemes. The new algorithm is shown to be functionally identical to the shift-and-scale method.

New BER Expression of MPSK

Abstract: This paper provides a new, exact, and general expression involving 1-D and 2-D Q-functions for the bit error probability of M-ary phase-shift keying (MPSK) under additive white Gaussian noise (AWGN) and fading channels when Gray code bit mapping is employed. Regular patterns in the error probability expression of the kth bit are observed while developing the bit error rate (BER) expression. From these patterns, we then derive a new BER expression for the MPSK constellation.

Robustness of digitally modulated signal features against variation in HF noise model

Abstract: High frequency (HF) band has both military and civilian uses. It can be used either as a primary or backup communication link. Automatic modulation classification (AMC) is of an utmost importance in this band for the purpose of communications monitoring; e.g., signal intelligence and spectrum management. A widely used method for AMC is based on pattern recognition (PR). Such a method has two main steps: feature extraction and classification. The first step is generally performed in the presence of channel noise. Recent studies show that HF noise could be modeled by Gaussian or bi-kappa distributions, depending on day-time. Therefore, it is anticipated that change in noise model will have impact on features extraction stage. In this article, we investigate the robustness of well known digitally modulated signal features against variation in HF noise. Specifically, we consider temporal time domain (TTD) features, higher order cumulants (HOC), and wavelet based features. In addition, we propose new features extracted from the constellation diagram and evaluate their robustness against the change in noise model. This study is targeting 2PSK, 4PSK, 8PSK, 16QAM, 32QAM, and 64QAM modulations, as they are commonly used in HF communications.

Generalized OFDM (GOFDM) for ultra-high-speed serial optical transport networks

Abstract: A coded multidimensional modulation system called generalized OFDM (GOFDM) uses orthogonal subcarriers as bases functions, and the signal constellation points of corresponding multidimensional constellation diagram are obtained as N-dimensional Cartesian product of one-dimensional PAM/two-dimensional QAM In GOFDM, the N-dimensional/2N-dimensional signal constellation point is transmitted over all N subcarriers/2N-subcarriers, which serve as individual bases functions Even if some of the subcarriers are severely affected by channel distortion, the overall signal constellation point will face only small distortion, when strong channel capacity achieving channel codes are used In addition, because the channel capacity is a linear function of number of dimensions, the spectral efficiency of optical transmission systems is significantly improved Finally, since Euclidean distance of multidimensional signal constellation is much larger that that of two-dimensional signal constellations, OSNR sensitivity is dramatically improved

Optimization of Fast-Decodable Full-Rate STBC with Non-Vanishing Determinants

Abstract: Full-rate STBC (space-time block codes) with non-vanishing determinants achieve the optimal diversity-multiplexing tradeoff but incur high decoding complexity. To permit fast decoding, Sezginer, Sari and Biglieri proposed an STBC structure with special QR decomposition characteristics. In this paper, we adopt a simplified form of this fast-decodable code structure and present a new way to optimize the code analytically. We show that the signal constellation topology (such as QAM, APSK, or PSK) has a critical impact on the existence of non-vanishing determinants of the full-rate STBC. In particular, we show for the first time that, in order for APSK-STBC to achieve non-vanishing determinant, an APSK constellation topology with constellation points lying on square grid and ring radius √m2+n2 (m,n integers) needs to be used. For signal constellations with vanishing determinants, we present a methodology to analytically optimize the full-rate STBC at specific constellation dimension.

Method for realizing MQAM (Multiple Quadrature Amplitude Modulation) signal modulation mode identification of any constellation diagram on basis of clustering

Abstract: The invention discloses a method for realizing MQAM (Multiple Quadrature Amplitude Modulation) signal modulation mode identification of any constellation diagram on the basis of clustering. For an MQAM signal, a modulation order can be big theoretically, the modulated constellation diagram can have various types, thus the possible range of the modulation mode of a signal to be identified is hard to determine, and people may face unknown modulation modes. The method puts forward a two-step clustering algorithm to reconstruct the constellation diagram, and the modulation mode identification is finished on the basis of the reconstructed constellation diagram; the self-adaption subtractive clustering based on a signal to noise ratio gives an initial clustering result, and the primary constellation diagram reconstruction is finished; on the basis, fuzzy C mean value clustering is adopted for finishing the constellation point reconstruction of the final modulation signal; after constellation point reconstruction is finished, the modulation order of the signal is judged according to the number of the constellation points; and for a modulation mode set of different orders, the modulation mode identification is carried out by a generalized likelihood ratio. The method disclosed by the invention can realize the MQAM signal modulation mode identification of any constellation diagram by the reconstructed constellation diagram.

Constellation shaping for broadcast channels in practical situations

Abstract: This paper analysis the problem of constellation shaping for degraded broadcast channels using a finite dimension constellation, where a single source communicates simultaneously with two receivers. We are interested in a particular situation where the private message to be sent to each user is limited to unity. This corresponds to a very practical situation, and hierarchical modulation is a special case of this framework. We investigate if higher achievable rates can be obtained by using non uniform constellations following a nonequiprobable distribution. Achievable rates regions are derived for Additive White Gaussian Noise (AWGN) and for finite input Pulse Amplitude Modulation (PAM) constellations. A noticeable shaping gain (compared with the equiprobable case) is observed with 4 PAM symbols, when achievable rates are maximized over the probability distribution of the input signals, the shape of the constellation, and the labeling.

Moment-Based Parameter Estimation and Blind Spectrum Sensing for Quadrature Amplitude Modulation

Abstract: Knowing accurate noise variance and signal power is crucial to most spectrum-sensing algorithms such as energy detection, matched filter detection, and cyclostationary detection. In this paper, we consider a practical scenario when these two parameters are unknown and are needed to be estimated before the spectrum sensing. This task is non-trivial without knowing the status of the primary user, and we categorize the related spectrum sensing as a blind one. We develop the estimation algorithms for unknown parameters by exploiting the signal constellation of the primary user. Three different parameter estimators that do not require any training are then proposed based on the moments of the received signals. Since the secondary user may not know the primary user's signal constellation, we develop a robust approach that approximates a finite quadrature amplitude modulation (QAM) constellation by a continuous uniform distribution. We also derive the modified Cramer-Rao bound (CRB) for noise variance estimation. Then the optimal moment pair is found from minimizing the mean squared error (MSE) of the signal-to-noise ratio (SNR). The method of choosing the spectrum sensing threshold by taking into consideration the estimation error is also discussed.

Model-based software-defined radio(SDR) design using FPGA

Abstract: A software-defined radio (SDR) allows for digital communication systems to easily adopt more sophisticated coding and modulation technologies, which is extremely important in meeting the ever-increasing demands of the wireless communication industry. In this study, an SDR has been constructed using Xilinx system generator tools and implemented on the Virtex-II Field Programmable Gate Array (FPGA). The Xilinx system generator allows for fixed-point logic system design, hardware/software co-simulation, and board implementation through a model-based approach. In the SDR, Quadrature Phase Shift Keying (QPSK) is chosen as the modulation scheme for demonstration. Through a wireless link, the QPSK signal experiences amplitude attenuation, frequency and phase shifts causing rotation of the signal constellation. A phase-locked loop (PLL) circuit is designed for carrier and symbol synchronization for recovery of data from the received signal. In order to resolve the phase ambiguity of the QPSK system, a differential encoding scheme is also implemented.

Modulation classification of linearly modulated signals in a cognitive radio network using constellation shape

Abstract: In this paper we intend to classify linear digital modulations in a cognitive radio network using constellation shape of the received signal as a feature. In our method, we perform the clustering of the base-band symbols to recognize the constellation and evaluate the result by some validation method. For clustering, K-Means, one of the simplest and fastest clustering methods, and the Fuzzy Hyper Volume (FHV), a well-known, simple and fast index for validating fuzzy C-Means clustering method, are employed. The presented approach is fully unsuper-vised and performs its task despite the slowly-varying flat Rayleigh fading channel and without the knowledge of the parameters such as SNR, carrier phase and timing offset. Using this fast and accurate pair of method-index and introducing a novel idea for refining K-Means initial values that considerably increases accuracy and decreases the number of iterations required for K-Means clustering, guarantees high performance and low computational complexity of the aforementioned algorithm. It is shown via simulations that the algorithm performs correct classification when the SNR is over 10dB for most practical linear modulation schemes under the presence of AWGN.