Showing papers on "Constellation diagram published in 1991"

A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations

Abstract: The author presents a simple integral expression for calculating the exact probability of a symbol error for an arbitrary array of signal points. The integrand contains only elementary functions and the range of integration is finite. The approach is introduced by applying it to M-ary phase shift keying (MPSK). The special case of M=2 gives novel and possibly useful expressions for calculating the Gaussian tail probability function and the related complementary error function. The approach is outlined for polygonal decision regions, and results are given for 16-point signal constellations. A method of obtaining, not exact, but even simpler and highly accurate expressions for symbol error probability when the latter is less than a few hundredths is presented. >

A data predistortion technique with memory for QAM radio systems

Abstract: The authors present an efficient data predistortion technique with memory for compensation of high-power amplifier (HPA) nonlinearities in digital microwave radio systems employing quadrature amplitude modulation (QAM) signal formats. A practical implementation method is described which trades off performance against complexity and which makes it possible to implement this kind of predistorter in 256-QAM, and higher-level QAM systems. Using the 16-, 64-, and 256-QAM signal constellations, it is shown that the proposed technique achieves a considerably higher performance than that of conventional memoryless data predistortion of the predistortion technique with memory based on finite-order inverses of nonlinear systems. Specifically, numerical results show that the proposed technique achieves a gain that is in excess of 2 dB over conventional memoryless data predistortion. >

Adaptive compensation for imbalance and offset losses in direct conversion transceivers

Abstract: It is pointed out that analog implementations of quadrature modulators and demodulators have deficiencies-primarily amplitude and phase imbalances and DC offset-that result in several troublesome problems for digital transceivers. An analysis and quantitative assessment of the losses due to analog implementations are presented. They include spurious tones and intermodulation products at the transmitter and a degraded BER (bit error rate) due to distortion of the signal constellation. The asymptotic degradation in BER performance in 16 QAM (quadrature amplitude modulation) for example is shown to be 1.1 dB for a 5 degrees phase imbalance and 0.65 dB for 5% gain imbalance. An adaptive procedure at the receiver for minimization of the imbalance and offset errors is developed. It is demonstrated that the LMS (least mean square) algorithm can be used to adapt the compensator in a manner similar to an equalizer, and that the computational load is the same as that of a three-tap equalizer. >

A 200-MHz all-digital QAM modulator and demodulator in 1.2- mu m CMOS for digital radio applications

Abstract: A 200-MHz universal all-digital quadrature modulator and demodulator are presented for implementing the front-end signal processing functions for high-bit-rate digital radio applications. The modulator chip accepts a pair of 8-b in-phase and quadrature data streams and generates a band-limited IF digital output. The demodulator chip accepts a digitized IF input signal and generates a pair of filtered in-phase and quadrature baseband signals. The modulator and demodulator chips each incorporate matched 40-tap finite-impulse-response (FIR) square-root Nyquist filters and can accommodate symbol rates up to Mbd. The modulator chip can generate any arbitrary signal constellation within a rectangular grid of 256*256 points, thus resulting in a generic chip set suitable for a wide variety of high-bit-rate digital modem designs using various advanced multilevel modulation formats such as M-ary QAM. Both chips were fabricated in a 1.2- mu m CMOS process. >

Device and method for precoding

Abstract: A novel precoding technique (900) and device (100) allows transmission of a stream of signal points over a channel h(D) to provide efficient data transfer in the presence of intersymbol interference and noise at data rates approaching channel capacity. This new technique may be combined with trellis-coded modulation and works with any signal constellation. In addition, the present invention allows decoupling signal constellation shaping, a significant improvement over prior precoding techniques. Thus, the present invention simplifies shaping and allows signaling at fractional rates without constellation switching.

Adaptive equalization for PAM and QAM signals with neural networks

Abstract: The authors investigate the application of neural networks to adaptive and blind equalization problems. The purpose is twofold: (1) to introduce a new realization structure of a multilayer perceptron (MLP) with a backpropagation training algorithm and show that it works well for both PAM and quadrature amplitude modulation (QAM) signals of any constellation size, and (2) to demonstrate the performance of self-organizing maps (SOMs) as blind equalizers and establish that they are simply not powerful enough for this problem, especially when the intersymbol interference is large. A new MLP structure for adaptive equalization of PAM and QAM signals is described and its performance, along with the simulation results of SOMs as blind equalizers, is demonstrated. >

Technique for compensating for intersymbol interference

Abstract: In a communications system, a generalized partial response signaling (GPRS) technique is employed to compensate for intersymbol interference. To this end, signal points representative of data to be transmitted are selected from a signal constellation. This signal constellation includes a multiplicity of signal points which are regularly spaced within a polygonal region having more than four sides. The selected signal points are precoded in the transmitter in accordance with the GPRS technique. Because of the particular choice of the signal constellation used, the precoded signal points for transmission occupies a region identical to the polygonal region.

Generalized data predistortion using intersymbol interpolation

Abstract: Intersymbol-interpolated digital data predistortion is an efficient countermeasure technique against the high-power amplifier non-linearity in digital microwave radio systems employing bandwidth-efficient quadrature amplitude modulation. This concept was recently introduced by the present authors using a specific transmit pulse shaping that leads to discrete signal levels at two or three points per symbol interval. Signal predistortion was then performed so as to cancel non-linear distortion at these equispaced points. In the present paper, we generalize the concept of intersymbol-interpolated data predistortion, and combine it with arbitrary transmit filters. Only a limited number of most significant bits at the transmit filter output are used as inputs to a random-access memory (RAM) which outputs the corresponding predistorted coordinates. The remaining bits are used to make a fine amplitude interpolation between the coarsely quantized RAM output levels. This allows us to define a range of predistorters corresponding to different complexity-performance trade-offs for a given signal constellation, transmit pulse shaping, and receive filtering. It is shown, by means of computer simulations, that this technique is considerably superior to conventional memoryless data predistortion.

On the performance of an asymmetrical digital subscriber lines QAM transceiver

Abstract: The author presents an analysis of an asymmetrical digital subscriber line (ADSL) transceiver that uses the quadrature amplitude modulation (QAM) passband transmission system. Output signal-to-noise ratio curves versus carrier and guardband frequencies are presented for the 16-, 64-, and 256-point rectangular constellations, assuming ADSL impairments consisting of self-far-end crosstalk, thermal noise generated by the loop, and receiver noise that is generated primarily by amplifiers in the front-end of the receiver. The simulation results show that an ADSL system with these impairments is viable even on loops that are at the extreme range of the loop plant. In addition, 16-QAM signaling generally performs better than any of the other constellations. The study assumed perfect timing and carrier recovery. >

The Random Coded Modulation: Performance And Euclidean Distance Spectrum Evaluation

Abstract: We apply the random coding argument to coded modulation. The well-known union bound on the error probability of general signaling schemes is revisited. The random coded modulation idea is introduced and a simple bound on the average performance of coded constellations is presented. A relationship between the union bound and the cut-off rate is exhibited by introducing the concept of N-dimensional partial cut-off rate. We define finite theta series for bounded finite-dimensional constellations and their related transfer functions. Bounds on the block and symbol error probability based on the transfer function are derived. The discussion is then focused on the squared Euclidean distance distribution. The evaluation of such parameters as its first two moments (average squared distance and squared distance variance) is considered by either finite theta series or transfer function of the bounded signal set. The Euclidean distance spectra of a few multidimensional coded modulation schemes based on square/cross constituent two-dimensional constellations are presented. Their respective partial cut-off rates are computed. We discuss the asymptotic behaviour and we show that almost all very long coded constellations are good (actually, they tend to become quasi-identical in a certain sense). Finally, we examine how to extend the initial union bound to Gallager-type bounds.

Shaping Multidimensional Signal Constellations

Abstract: Consider an optimally shaped N-dimensional (N even) signal constellation on a lattice. Assuming continuous approxima- tion, the boundary of the two-dimensional subconstellations is a cir- cle and the boundary of the whole constellation is a hypersphere. We derive analytical expressions for the optimum tradeoff between the shape gain and the Constellation-Expansion-Ratio and also between the shape gain and the Peak-to-Average-power-Ratio. We introduce a method for achieving a point on the optimum tradeoff curves. This is based on mapping the constellation to the Voronoi region of the lattice D;, n = N/2. The addressing com- plexity is essentially that of decoding 0; which using D;= ((2Z)") U ((2Z)" + (l)"}, where Z is the integer lattice, is simple. For dimen- sions up to 12 the point obtained is located on the knee of the curve. This coding method is less complex and has superior performance to that based on the Voronoi constellations. In a second method, n-dimensional subconstellations are first shaped using previous method. The N/n-fold Cartesian product of this subconstellations is further shaped by a lookup table. Analyti- cal expressions show that even for small lookup tables this method obtains results near the optimum tradeoff curves. Summary We study two methods for shaping an N-dimensional constellation. In the first method Sz(R) is the boundary of the two-dimensional subconstellations and S,(JpR) is the boundary of the whole con- stellation. This method provides the optimum tradeoff between ys (shape gain) and CER, (shaping Constellation-Expansion-Ratio) and also between ys and PAR (Peak-to-Average-power-Ratio). The pa- rameter p determines this tradeoff. Optimality is the result of the facts that, (i) CER, and PAR are measured on a two dimensional basis, (ii) the two-dimensional subconstellations are bounded within a circle, and (iii) for a fixed volume the signal constellation is the subset of the available signal space with the least second moment. The energy shells of the Sz's can be mapped to the coordinates of an n=N/2 dimensional space. Half of each shell is mapped to the positive values and half to the negative values. The region RN bounding the constellation will be mapped to R,. It is shown that, 0.88 1.4 3.26 0.92 1.5 3.53 0.82 1.2 2.76

Combined coding and shaping over a multitone channel

Abstract: The idea of combined shaping and coding of a signal constellation over a multitone channel is introduced. Two joint optimization methods, partly integer, for distributing the rate and the energy are introduced. In the first method, the minimum distance to noise ratio (protection) along all the dimensions is the same. The proposed method maximizes this protection. In the second method, this restriction is relaxed. The second method outperforms the first. As part of the calculations, a closed-form formula has been found for the weight distribution of the scaled E/sub 8/ lattice. >

Interleaved 5B20 code for insertion of carrier and clock pilots in 64-QAM systems

Abstract: An interleaved 5-binary to 2-octonary (5B2O) block code is proposed to insert carrier and clock pilots in 64-QAM systems with a spectrum efficiency of about 4.5bit/s/Hz. Its design is based on the rotated and scaled 64-QAM signal constellation. The spectral components of symbol sequences from this encoder are completely suppressed at DC and at the Nyquist frequency (NF).

An eight-dimensional phase invariant trellis coded modulation scheme with constant envelope

Abstract: An eight-dimensional trellis-coded-modulation (TCM) scheme which uses 512 points to transmit two information bits per signaling interval is presented. The system has constant envelope and, with only eight states on the trellis, yeilds an asymptotic gain of 6.02 dB without expanding the bandwidth over that of the equivalent uncoded system. The size of the coded constellation is doubled, but the minimum squared Euclidean distance (MSED) and the peak and average energies remain identical to those of the uncoded system, therefore avoiding the 3 dB loss in Ungerboeck's conventional codes. The novel constellation is formed by the union of an 8D QPSK and a rotated version of it. The new scheme achieves an effective gain of 5.64 dB and a small normalized redundancy of rho =0.25, has constant envelope, achieves spectral efficiency of 2b/s/Hz if Nyquist filtering is used, and uses simple and small constituent 2D constellation. >

The use of random coset coding for bounding the probability of error in coded modulations schemes

Abstract: A random coset coding for coded modulation structure is presented. This approach enables the authors to calculate easily an upper bound for the probability of decoding error of an average coset code. The random coding method they present, and the upper bound obtained, are applicable to most of the known coded modulation schemes, any transmitted signal constellation, and Gaussian as well as other (not necessarily additive noise) channels. Furthermore, by transmitting according to this method, an equal probability of decoding error is provided for each transmitted sequence. >

Combined concatenated coding and modulation schemes using a redundant signal alphabet

Abstract: Combined concatenated coding and modulation schemes using redundant signal alphabets are presented. A 2/sup m+1/-point signal constellation is employed to transmit m information bits per symbol (as in Ungerboeck schemes). To avoid a loss in spectral efficiency, the available redundancy (1 b/symbol duration) is shared between an outer error-correcting code and an inner code combined with a multidimensional modulation. The analytical performance of the schemes presented is evaluated on an additive white Gaussian noise (AWGN) channel. Simulation results indicate that 8 dB of coding gain at a bit error rate of 10/sup -11/ can be obtained with simple concatenated codes having a spectral efficiency of 3 b/s/Hz, thus achieving a better performance/complexity tradeoff than Ungerboeck codes. >

Error performance of triangular-shaped signal set

Abstract: The error performance of an amplitudephase shift keying system with triangularshaped signal set (TSSS) is discussed. Expressions for the probability of error performance of this scheme are derived for the case of 64, 128, 256, 512, 1024 states and compared to QAM and modified QAM (MQAM) for the same number of states. It is shown that this signal set outperforms both QAM and MQAM in the presence of an additive Gaussian noise channel. The performance improvement is attributed to the larger decision region obtained for each state in the signal constellation, as compared to QAM and MQAM. Degradation due to the phase error is also discussed in detail.