Symbol error rate calculation and data pre‐distortion for 16‐QAM transmission over nonlinear memoryless satellite channels

This paper presents a simplified mathematical approach to evaluate the performance of any given circular constellation of 16‐level quadrature amplitude modulation (16‐QAM) in terms of symbol error rate (SER). Following this approach, with the aim to work with memoryless nonlinear satellite channels, a model is derived as a generalized form for both linear and nonlinear channels in the presence of down link additive white Gaussian noise (AWGN). The analysis provides means to calculate the optimal ring ratio (RR) and phase difference (PD) for several possible candidates of 16‐QAM circular constellations. The effects of RR and PD on the SER performance are investigated in the analysis. To overcome the nonlinear distortion, data pre‐distortion is taken into account in the study. The paper gives a general procedure for data pre‐distortion implementation for all circular 16‐QAM constellations. The analytical formulation has been extended for total degradation (TD) performance measure as a function of input back‐off (IBO) of the nonlinear amplifier. A SER performance‐comparison between different constellations for 16‐QAM systems has also been presented in this paper. The analytical results are validated by simulation. Copyright © 2006 John Wiley & Sons, Ltd.     

On the Performance of Combined Quadrature Amplitude Modulation and Convolutional Codes for Cross-Coupled Multidimensional Channels

The performance of cross-coupled,M-ary quadrature amplitude modulation (QAM) systems is determined when bandwidth efficient trellis codes are used to combat interference. Performance with and without compensation for cross-coupled interference is presented. It is found that simple trellis codes can maintain the error probability at an acceptable level for cross-coupling parameters that render uncoded systems unusable. Up to two-dimensional trellis codes are considered for four-dimensional QAM signals, and possibilities of obtaining diversity advantages in the form of higher total system throughput by prolonged availability of the two signals are explored. This is accomplished through joint coding over two different constellations. The probability of the most likely error events is calculated by using the method of moments. The results are applicable to any digital communication system using multidimensional quadrature amplitude modulation, e.g., voiceband modems, cross-polarized radio systems and, to some extent, optical systems. In the paper the analysis is restricted to nondispersive cross-coupling models. In most cases the coding gain is larger than in the absence of cross-coupling interference. Specifically, it is found that simple codes have coding gains increased by at least 2 dB with cross-coupling interference relative to that obtained on the additive white Gaussian noise channel.     

Six-dimensional trellis-coding with QAM signal sets

A family of 6-D trellis-coded modulation (TCM) schemes which involve a 2-step partitioning of the constituent QAM signal alphabet is presented. With infinite constellations without shaping, the asymptotic coding gain is 3 dB for the 2-state code, 4 dB for the 4- and 8-state codes, and 5 dB for the 16- and 32-state codes which involve a smaller alphabet expansion. The authors also describe a rotationally invariant 16-state code that achieves the same asymptotic gain as its linear counterpart. Practical signal constellations are described for 6-D TCM with the spectral efficiency of uncoded 64-QAM, and the performance of these schemes is studied by means of computer simulations. It was found that they achieve an additional coding gain of 0.2-0.3 dB over infinite hypercube-type constellations. The performance of the presented schemes at practical signal-to-noise ratio values is evaluated using transfer function techniques     

Better performance of OFDM using three special triangular constellations over AWGN and fading channels

Orthogonal frequency division multiplexing (OFDM) has been adopted as a major data transmission technique by many wireless communication standards. In this research, 3 new triangular constellations schemes, which are named as TRI1, TRI2, and TRI3, are introduced to replace for the well‐known rectangular quadrature amplitude modulation (QAM) constellation in OFDM modulation. In this study, it has been shown that these new schemes have 3 major advantages with respect to the QAM. The first advantage is their lower bit error rate, which results from the better usage of the constellation space with longer minimum distances. The 2 other advantages are a lower peak to average ratio and higher noise immunity. Both mathematical analysis and simulation results demonstrate that by applying high fading channels with additive white Gaussian noise and intersymbol interference impairment simultaneously, the proposed constellations exhibit a superior performance in criteria compared to the commonly used rectangular 16QAM and 64QAM constellations. As a result, they are good choice for high speed and real‐time multicarrier applications such as digital video broadcasting terrestrial at no extra cost.     

A data predistortion technique with memory for QAM radio systems

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     

Multidimensional constellations. I. Introduction, figures of merit,and generalized cross constellations

The authors discuss the major attributes desired in signal constellations, such as signal-to-noise ratio (SNR) efficiency, simplicity of mapping bits to points and vice versa, compatibility with coded modulation schemes, and compatibility with quadrature amplitude modulation (QAM). The capability of supporting a so-called opportunistic secondary channel, often used for internal control signaling, is considered. The gain in SNR efficiency of a multidimensional constellation (lattice code) consisting of the points from a lattice Λ within a region R compared to a cubic constellation is shown to be approximately separable into the coding gain of Λ and the shape gain of R, for large constellations. Similarly, the expansion of the associated constituent 2-D constellation is shown to be approximately separable into a constellation expansion ratio (CER) coding component CER_c(Λ) and a shaping component CER _s(R). The N sphere is the region R with the best shape gain, but N also has large constellation expansion. Bounds for the best possible shape gain versus CER_s(R) or peak-to-average-power ratio (PAR) are given. Generalized cross constellations are discussed. These constellations yield a modest shape gain with very low CER_s(R) or PAR, are easily implemented, are well suited for use with coded QAM modems, and can be readily adapted to support an opportunistic secondary channel     

Phase Noise Effects on High Spectral Efficiency Coherent Optical OFDM Transmission

There are three major advantages for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) transmission using digital signal processing. First, coherent detection is realized by digital phase estimation without the need for optical phase-locked loop. Second, OFDM modulation and demodulation are realized by the well-established computation-efficient fast Fourier transform (FFT) and inverse FFT. Third, adaptive data rates can be supported as different quadrature amplitude modulation (QAM) constellations are software-defined, without any hardware change in transmitter and receiver. However, it is well-known that coherent detection, OFDM, and QAM are all susceptible to phase noise. In this paper, theoretical, numerical, and experimental investigations are carried out for phase noise effects on high spectral efficiency CO-OFDM transmission. A transmission model in the presence of phase noise is presented. By using simulation, the bit error rate floors from finite laser linewidth are presented for CO-OFDM systems with high-order QAM constellations. In the experiments, the phase noise effects from both laser linewidth and nonlinear fiber transmission are investigated. The fiber nonlinearity mitigation based on receiver digital signal processing is also discussed.     

Joint blind equalization, carrier recovery and timing recovery forhigh-order QAM signal constellations

Two existing blind equalization tap update recursions for 64-point and greater QAM (quadrature amplitude modulation) signal constellations are studied, along with existing and novel carrier and timing recovery techniques. It is determined that the superior tap update recursion is the one known as the constant modulus algorithm. Carrier recovery requires a modified second-order decision-directed digital phase-locked loop. An all-digital implementation of band-edge timing recovery is used. With 14.4 kb/s outbound transmission using CCITT V.33 trellis-coded 128-QAM signals having 12.5% excess bandwidth, a prototype blind retrain procedure is developed to demonstrate the feasibility of the techniques for high-speed multipoint modems. A WE DSP32-based real-time digital signal processor was employed to test the retrain over a set of severely impaired channels. For each channel in the set, the retrain succeeded at least 90% of the time     

Variable rate QAM for mobile radio

Quadrature amplitude modulation (QAM) schemes which vary the number of modulation levels in accordance with the mobile radio fading channel variations are investigated. Important parameters considered are the fading rate and the block size used. We describe how the adaptive QAM modems can be employed and consider their use in a DECT-like TDD packet structure. System performance in the presence of cochannel interference is also considered. Simulations show that the variable rate system has about 5 dB improvement in channel SNR over a fixed 16-level QAM system for BER's between 10^-2 and 10^-5 and channel SNR's between 25 and 40 dB     

Triangular Quadrature Amplitude Modulation

The square quadrature amplitude modulation (QAM) has been widely used for decades. Though it is not optimum in the sense of power efficiency, simple detection makes it in use for numerous digital communication systems deploying high-order modulation. In this paper, we propose new signal sets which make an effective use of limited power resource. We also suggest simple detection methods for the proposed signal sets to be meaningful from a point of view of implementation. The newly proposed constellations can provide advantages of 0.46 dB and 0.55 dB in signal-to-noise ratio over the square QAM in 16-ary and 64-ary signal sets while keeping low complexity for detection     

Multidimensional Signal Constellations for Voiceband Data Transmission

A significant improvement in noise immunity can be achieved for digital transmission over band-limited channels by the use of multidimensional signal constellations. Conventional 16-point QAM signaling, such as that used in many digital transmission systems, is a two-dimensional modulation scheme where in each signaling interval a group ofNbits is used to determine the amplitudes of the in-phase and quadrature dimension or coordinate, i.e.,N/2bits are conveyed per dimension. In a2M-dimensional QAM system, a group ofMNbits is used to determine the in-phase and quadrature ampllitudes forMconsecutive, symbol intervals whereN/2bits are still conveyed by each dimension. It is the purpose of this paper to describe the basic theory and implementation for a particular 2 bits/dimension four-dimensional (two-symbol interval) encoding which readily lends itself to simple encoding and decoding. For this encoding, theory predicts a 1.2 dB gain in noise margin over conventional 16-point (two-dimensional) QAM signaling. Experimental results agreed with the theoretical predictions, and have demonstrated an order of magnitude reduction in block error rate. Extension to eight-dimensional signaling offers a theoretical gain of 2.4 dB over conventional 16-point QAM.     

Constellation mappings for two-dimensional signaling of nonuniform sources

The design of two-dimensional constellation mappings for the transmission of binary nonuniform memoryless sources over additive white Gaussian noise channels using standard M-ary PSK and QAM modulation schemes is investigated. The main application of this problem is the incorporation of an adaptive mapping assignment in modem devices that employ fixed PSK/QAM modulation schemes for the transmission of heterogenous data (such as multimedia information) containing various levels of nonuniformity. In general, the optimal mapping depends on both the probability distribution of the input signals and the signal-to-noise ratio (SNR) in the channel, in addition to the geometry of the signal constellation. We show that constellation mappings which follow the objective of minimizing the average symbol energy and, given this, maximizing the decoding probability of the most likely signals, can yield symbol-error-rate and bit-error-rate performance that is substantially better than Gray encoding maps. Gains as high as 3.5 dB in SNR E/sub b//N/sub 0/ are obtained for highly nonuniform sources. Finally, we note that the mappings techniques result in nonzero mean constellations and briefly consider their performances when they are converted to zero mean constellations by shifting. In this case, we observe that the shifted zero-mean Gray map outperforms our shifted maps for small- to medium-sized constellations (M/spl les/32), but not for larger sizes.     

Compensation of Frequency Offset for Differentially Encoded 16- and 64-QAM in the Presence of Laser Phase Noise

The compensation of frequency offset for differentially encoded 16- and 64-ary quadrature amplitude modulation (QAM) in the presence of laser phase noise is investigated. Differential encoding is employed to solve the four-fold phase ambiguity problem in a nondata-aided transmission system with square QAM constellations. Simulation results show that frequency offset and phase noise can successfully be compensated using a second-order digital filter loop for the square QAM constellations.      

Performance characteristics and applications of hybrid multichannelANI-VSB/M-QAM video lightwave transmission systems

The performance characteristics and applications of hybrid multichannel amplitude modulation vestigal sideband (AM-VSB)/M-quadrature amplitude modulation (QAM) video lightwave transmission systems operating at either 1310 or 1550 nm are reviewed. These systems can transport up to 80 AM-VSB video channels and more than 30 64/256-QAM digital video channels over a standard single-mode fiber (SMF) using a single laser transmitter. Five main transmission impairment mechanisms for these systems are reviewed as follows: (a) clipping-induced impulse noise, (b) bursty nonlinear distortions, (c) multiple optical reflections, (d) stimulated Brillouin scattering, and (e) self-phase modulation. For AM-QAM video lightwave trunking applications, the in-line erbium-doped fiber amplifier (EDFA) selection is discussed using a frequency-domain simulation model. Such lightwave trunking systems can provide an AM carrier-to-noise ratio (CNR) greater than 50 dB with composite second order (CSO) and composite-triple-beat (CTB) distortions less than -65 dBc, and nearly error-free transmission (BER⩽10^-9) for the 64-QAM channels with signal-to-noise ratio (SNR) of 30-dB or better. Comparison between 64-QAM and 256-QAM video channel transmission and the effect of the QAM channels on the AM-VSB channels are also presented. The implications of these results and others in hybrid multichannel AM-QAM video lightwave trunking systems are discussed     

A comparison of passband and baseband transmission schemes for HDSL

Using an ideal decision feedback equalizer (DFE), the SNR of quadrature amplitude modulation (QAM) and baseband pulse amplitude modulation (PAM) in the presence of self near-end crosstalk is computed for a large sample of loops within a carrier serving area (CSA). When baud-space feedforward filters are used, PAM has 1-2 dB more SNR than QAM, where the type of PAM is the 2B1Q line code. However, when using fractionally spaced feedforward equalizers (FSEs), the SNRs of 2B1Q and QAM are almost equal for loops at the extreme range of a CSA. Four- and 16-state trellis-coded modulation is applied to PAM and QAM. Coded and uncoded PAM and QAM are simulated with parallel decision feedback estimation. Viterbi receivers and coding gains are computed. QAM has up to 1 dB higher coding gains that PAM. However, the higher coding gains of QAM do not compensate for the lower SNR of uncoded QAM, and coded QAM has worse performance than coded PAM in the presence of self near-end crosstalk. The error rates of PAM and QAM with impulse noise are computed using a collection of measured impulse noise events. Results indicate that QAM has a lower error rate than PAM in the presence of impulse noise     

On differentially encoded star 16QAM with differential detectionand diversity

Star 16QAM is a modulation method that transmits 4 bits per symbol and has the advantage that it may be differentially encoded and detected. It is very robust to fast multiplicative Rayleigh fading and is suitable for mobile telephone systems and personal communication networks. The main contribution of this paper is the derivation and bit error probability simulation of the maximum likelihood differential detector using phase differences and amplitude ratios from L diversity branches for bit decisions. As a comparison, much simpler previously known post detection combining techniques are generalized for star 16QAM and optimized. The bit error probability is simulated for both diversity detectors on a multiplicative Rayleigh fading channel with additive white Gaussian noise. It is found that the bit error probability of the ML detector may also be obtained by the simple combining detector. This is also true for the error floor due to the maximum Doppler frequency. The diversity gain is almost 8 dB, measured in signal to noise ratio per diversity branch, at a bit error probability of 1 percent. The diversity detector can sustain an almost 3 times larger Doppler frequency again at a bit error probability of 1 percent. We also show that star 16QAM offers, at most, 3 subchannels with different bit error probabilities     

Differential space time block codes using nonconstant modulus constellations

We propose differential space time block codes (STBC) using nonconstant modulus constellations, e.g., quadrature amplitude modulation (QAM), which cannot be utilized in the conventional differential STBC. Since QAM constellations have a larger minimum distance compared with the phase shift keying (PSK), the proposed method has the advantage of signal-to-noise ratio (SNR) gain compared with conventional differential STBC. The QAM signals are encoded in a manner similar to that of the conventional differential STBC. To decode nonconstant modulus signals, the received signals are normalized by the channel power estimated forgoing training symbols and then decoded with a conventional QAM decoder. Assuming the knowledge of the channel power at the receiver, the symbol error rate (SER) bound of the proposed method under independent Rayleigh fading assumption is derived, which shows better SER performance than the conventional differential STBC. When the transmission rate is more than 3 bits/channel use in time-varying channels, the simulation results demonstrate that the proposed method with the channel power estimation outperforms the conventional differential STBC. Specifically, the posed method using the channel power estimation obtains a 7.3 dB SNR gain at a transmission rate of 6 bits/channel use in slow fading channels. Although the performance gap between the proposed method and the conventional one decreases as the Doppler frequency increases, the proposed method still exhibits lower SER than the conventional one, provided the estimation interval L is chosen carefully.     

Signal space diversity: a power- and bandwidth-efficient diversitytechnique for the Rayleigh fading channel

The increasing need for high data-rate transmissions over time- or frequency-selective fading channels has drawn attention to modulation schemes with high spectral efficiency such as QAM. With the aim of increasing the “diversity order” of the signal set we consider multidimensional rotated QAM constellations. Very high diversity orders can be achieved and this results in an almost Gaussian performance over the fading channel, This multidimensional modulation scheme is essentially uncoded and enables one to trade diversity for system complexity, at no power or bandwidth expense     

Transmission of SDH signals through future satellite channels usinghigh-level modulation techniques

The authors discuss the possibility of transmitting synchronous digital hierarchy (SDH) signals through two-link nonlinear satellite channels. Transmitting such high bit rate signals through a standard 54 MHz or 36 MHz transponder bandwidth requires the use of high-level modulation schemes. The techniques and technologies needed to make the use of 16-ary quadrature amplitude modulation (QAM) and 64-ary QAM transmissions feasible for future satellite communication systems are examined. It is shown that it is possible to transmit a synchronous transport module-level 1 (STM-1) signal through a standard 54 or 36 MHz transponder bandwidth using 16-ary QAM or 64-ary QAM transmission, respectively, for the 6/4 GHz band. However, for higher frequency bands, due to high fade margins needed to achieve the high availability and performance for SDH systems, is not practical to transmit the STM-1 signal through such standard transponder bandwidths