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.     

Reception of PSK Signals Over Fading Channels Via Quadrature Amplitude Estimation

We consider here a new approach to PSK signal detection over a slow nonselective Rayleigh fading channel which does not require a carrier recovery loop. The receiver achieves coherent demodulation by making use of estimates of the quadrature amplitudes of the received PSK signals in its likelihood ratio test. The receiver is assumed to have a memory containing information on the past received signals which enables it to generate the estimates. The error rate of the receiver can be evaluated analytically and computer simulation results are presented to verify the predicted performance.     

On Improving Bit Error Probability of QPSK and 4-Level Amplitude Modulation Systems by Convolutional Coding

We consider Amplitude Modulation (AM) systems, PhaseShift-Keying (PSK) and Amplitude-Phase-Keying (APK) systems in which each symbol can take 2ⁿvalues. After a systematic search of(n, n - 1)binary convolutional codes with large values of free distance and minimal number of code words at that distance, simulations have been performed with an 8-symbol modulation system (n = 3). For a bit error probability of less2 times 10^{-4}, the saving in average power signal-signal-to-noise ratio over that required for an uncoded system with the same channel symbol rate was more than 2 dB with PSK and APK, and 1.5 dB with AM.     

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     

Effect of Intersymbol and Quadrature Channel Interference on Error Probability of 16-ary Offset Quadrature Amplitude Modulation with Sinusoidal and Rectangular Shaping

In this paper we study the effect of intersymbol and quadrature channel interference on the average error probability of 16-ary offset quadrature amplitude modulation with rectangular or sinusoidal shaping functions. We present numerical results assuming that the transmitter and receiver filters are identical Butterworth filters of orderN = 1,2,..., 6,and the decision rule is either fixed or adaptive.     

Bit Interleaved Time-Frequency Coded Modulation for OFDM Systems Over Time-Varying Channels

Bit Interleaved Time-Frequency Coded Modulation for OFDM Systems Over Time-Varying Channels Orthogonal frequency-division multiplexing (OFDM) is a promising technology in broadband wireless communications with its ability in transforming a frequency selective fading channel into multiple flat fading channels. However, the time-varying characteristics of wireless channels induce the loss of orthogonality among OFDM sub-carriers, which was generally considered harmful to system performance. In this paper, we propose a bit interleaved time–frequency coded modulation (BITFCM) scheme for OFDM to achieve both time and frequency diversity inherent in broadband time-varying channels. We will show that the time-varying characteristics of the channel are beneficial to system performance. Using the BITFCM scheme and for relatively low maximum normalized Doppler frequency, a reduced complexity Maximum Likelihood (ML) decoding approach is proposed to achieve good performance with low complexity as well. For high maximum normalized Doppler frequency, the inter-carrier interference (ICI) can be large and an error floor will be induced. To solve this problem, we propose two ICI mitigation schemes by taking advantage of the second order channel statistics and the complete channel information, respectively. It will be shown that both schemes can reduce the ICI significantly.     

Adaptive Minimum Symbol Error Rate Beamforming Assisted Detection for Quadrature Amplitude Modulation

We consider beamforming assisted detection for multiple antenna aided multiuser systems that employ the bandwidth efficient quadrature amplitude modulation scheme. A minimum symbol error rate (MSER) design is proposed for the beamforming assisted receiver, and it is shown that this MSER design provides significant performance enhancement, in terms of achievable symbol error rate, over the standard minimum mean square error (MMSE) design. A sample-by-sample adaptive algorithm, referred to as the least symbol error rate, is derived for adaptive implementation of the MSER beamforming solution. The proposed adaptive MSER scheme is evaluated in simulation using Rayleigh fading channels, in comparison with the adaptive MMSE benchmarker.     

Linear Diversity Analysis for M‐ary Square Quadrature Amplitude Modulation over Nakagami Fading Channels

We derive and analyze the exact closed‐form expression for the average bit error probability (BEP) of M‐ary square quadrature amplitude modulation (QAM) for diversity reception in frequency‐nonselective Nakagami fading. A maximal ratio combining (MRC) diversity technique with independent or correlated fading cases are considered. Numerical results demonstrate error performance improvement with the use of MRC diversity reception. The presented new expressions offer a convenient way to evaluate the performance of M‐ary square QAM with an MRC diversity combiner for various cases of practical interest.     

Quadrature Amplitude Modulation for Differential Space-Time Block Codes

Differential Space-Time Block Codes (DSTBC) do not require any radio channel measurement and channel state information neither on the transmitter nor at the receiver side. Therefore, they are an attractive alternative to coherent Multiple-Input Multiple-output (MIMO) systems. The classical technical proposal for differential techniques is based on M-ary phase shift keying (M-PSK) modulation schemes for DSTBC (PSK-DSTBC). One advantage of this scheme is the constant envelop of the transmit signal, but it is well known that higher-order PSK is less efficient due to the small distance between adjacent points in the constellation diagram. Therefore, in this paper an alternative modulation technique for DSTBC is discussed, which is based on quadrature amplitude modulation (QAM-DSTBC). The signal envelope of the transmit signal is not any more constant in this case. Therefore, the technical challenge of integrating QAM into the DSTBC system design is to control the transmit power in order to avoid an increase or a decrease in transmit power to some extreme values. The mechanism, which is used in this paper to control the transmit power is based on an extension of the original QAM constellation diagram. The additional points, which are integrated into the constellation diagram are used in this case for the mapping procedure to select one of the modulation symbols with high or alternatively low signal power. This means for each single bit pattern there are almost always two modulation symbols available in the mapping procedure one with low and one with high signal power, which gives the basis for a signal power control algorithm. The resulting bit-error-rate (BER) performance of QAM-DSTBC is compared finally to the performance figures of the original proposal of PSK-DSTBC.

Effect of Channel Estimation Error on Bit Error Probability in OFDM Systems over Rayleigh and Ricean Fading Channels

A characteristic function-based method is used to derive closed-form bit error probability (BEP) expressions for orthogonal frequency-division multiplexing (OFDM) systems in the presence of channel estimation error over frequency-selective Rayleigh fading channels and frequency-selective Ricean fading channels. Both single channel reception and diversity reception with maximal ratio combining (MRC) are examined. The BEP expressions are shown to be sums of several conditional probability functions which can be calculated by using proper complex Gaussian random variable theory and a characteristic function method. The closed-form BEP expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models. The performances of two interpolation methods, a sine interpolator with Hamming windowing and a Wiener interpolator, are compared.     

Performance of Quadrature Amplitude Modulation for Indoor Radio Communications

The performance ofM-QAM for indoor radio communications is evaluated via a realistic model for indoor multipath propagation [1]. It is found that the outage (BER < 10^-4) is about 0.3 percent at 1 Mbit/s and 20 percent at 4 Mbits/s. Two-antenna predetection diversity reduces the outage from 1.2 to 0.04 percent at 2 Mbits/s. Increasing the signaling pulse rolloff factor from 0.5 to 1.0 reduces the outage by not more than 35 percent.     

Bit Error Probability and Bit Outage Rate in Chaos Communication

This paper investigates the notion of the probability of bit error (PBE) and its distribution in chaos-based communication systems; these are seen as being the fundamental quantities to both the well-known bit error rate (BER) and the new concept in chaos communications of bit outage rate (BOR). The form of the distribution illustrates the degree to which bit error rate is a stable representation of performance. Bit outage rate is another measure of performance which gives practically helpful information about bit error. For a simple coherent chaos-shift-keying system the distribution of bit error probability is derived exactly, and theoretically exact formulas for the bit outage rate and bit error rate are presented. Two specific cases are developed to obtain useful qualitative and quantitative information. The cases concern independent Gaussian spreading, as a lower benchmark and logistic map spreading, as typical of effective chaotic spreading. Comparisons are obtained between these spreading distributions and between different extents of their spreading, calibrated against per bit signal to noise ratio. A general conclusion is that bit outage and bit error rates are complementary measures of performance.     

An Automatically Controlled Predistorter for Multilevel Quadrature Amplitude Modulation

In digital microwave transmission, the nonlinear characteristics in a high power amplifier, such as a TWT (traveling-wave tube) inhibit efficient output use. This note introduces a new predistorter control technique, and assesses the nonlinear compensation capability of a third-order predistorter incorporating this technique. Concerning 16-QAM (quadrature amplitude modulation) a 10 dB reduction in out-of-band emission and larger than 8 dBC/Nimprovement with respect to symbol error rate can be achieved at 3 dB TWT average output power backoff.     

Prony and Polynomial Approximations for Evaluation of the Average Probability of Error Over Slow-Fading Channels

A novel and simple semianalytical method for evaluating the average probability of transmission error for digital communication systems that operate over slow-fading channels is presented. The proposed method applies a sum of exponentials fit known as the Prony approximation to the conditional probability of error. Hence, knowledge of the moment-generating function of the instantaneous signal-to-noise ratio (SNR) at the detector input can be used to obtain the average probability of error. Numerical results show that knowledge of the conditional probability of error at only a small number of points and the sum of only two exponentials are sufficient to achieve very high accuracy; the relative approximation error of the exact average probability of error is less than 6% in most of the cases considered. Furthermore, a piecewise polynomial approximation of the conditional probability of error is investigated as an alternative to the sum of exponentials fit. In this case, knowledge of the partial moments of the instantaneous SNR at the detector input can be used to obtain the average probability of error. Numerical results indicate that, to achieve good accuracy, the method based on the polynomial approximation requires that the product of the polynomial degree and the number of approximation subintervals be larger than 10.      

Performance Analysis in Terms of Bit Error Rate Over Fluctuating Two-Ray (FTR) Fading Channels

Wireless Personal Communications - The fluctuating two-ray (FTR) channel is currently taken as a suitable small-scale fading model for fifth-generation millimeter-wave communications. This paper...     

Optimization of Trellis Codes with Multilevel Amplitude Modulation with Respect to an Error Probability Criterion

An easily computed upper bound on the error probability of a data communications system with combined trellis coding and multilevel/phase modulation is derived, assuming an additive white Gaussian noise channel and maximum-likelihood decoding. This bound is used to search for codes obtained by set-partitioning that minimize the bound for a fixed number of trellis states. Only amplitude modulated signals typically used in voiceband modem applications are considered. The signal levels that minimize the error probability bound subject to an average power constraint are presented for some specific codes.     

模拟面目标中频正交幅度调制系统

介绍了为某产品研制的模拟面目标中频正交幅度调制系统，其输出的调制信号频率为120MHz，1dB带宽较宽，合成输出脉冲宽度为9．145μs，杂波电平为-33dBm。可模拟的面目标最小高度为15m。     

The Effect of Mismatches and Delay on the Quadrature Error of a Cross-Coupled Relaxation Oscillator

Cross-coupled relaxation oscillators can produce two highly accurate quadrature output signals (Verhoeven, 1992). We present a high-level model of these oscillators in terms of circuit parameters, from which we obtain explicit equations for duty-cycle, oscillation frequency, and quadrature error. They show the influence on the oscillator performance of component mismatches and other nonideal effects, such as delays. The results provide useful guidelines for the design of high performance oscillators. The theoretical results are confirmed by simulation and by measurements on a test chip.     

Computing the Average Symbol Error Probability of the MPSK System Having Quadrature Error

When quadrature error exists, the shape of the M‐ary phase shift keying (MPSK) signal constellation becomes skewed‐elliptic. Each MPSK symbol takes on a different symbol error probability (SEP) value. The analytical results presented thus far have been derived from studies which examined the SEP problem assuming that the SEP of each MPSK symbol is equally likely; therefore, those results should not be treated as offering a complete solution. In this letter, we present a new and more complete solution to the SEP problem of MPSK by relaxing the above assumption and finding the expressions for the average as well as individual SEP in the presence of quadrature error.     

Effect of Microdiversity and Macrodiversity on Average Bit Error Probability in Gamma‐Shadowed Rician Fading Channels

In this letter, we analyze the error performance of a mobile communication system with microdiversity and macrodiversity reception in gamma‐shadowed Rician fading channels for a binary differential phase‐shift keying modulation scheme. Analytical expressions for the probability density function (PDF) and moment‐generating function (MGF) are derived. The average bit error probability can be calculated by averaging the conditional bit error probability over the PDF or using the MGF‐based approach. Numerical results are graphically presented to show the effects of macrodiversity, correlation, number of diversity branches, and severity of both fading and shadowing.