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Theoretical and practical aspects of diagonal algebraic space-time block codes over n transmit and m receive antennae are examined. These codes are obtained by sending a rotated version of the information symbols over the principal diagonal of the n x n space-time matrix over n transmit antennae and n symbol periods. The output signal-to-noise ratios of two predecoding filters and two decoding algorithms are derived. Analysis of the information loss incurred by using the codes considered is used to clarify their structures, and the expected performances. Different algebraic real and complex rotations presented in the literature are analyzed and compared as regards the achieved coding gains, the complexities, performances, and peak-to-mean envelope power ratios. Index Terms--Capacity, diversity methods, maximum-likelihood decoding (MLD), multiple-input/multiple-output (MIMO) systems, space-time (ST) codes.

The average level crossing rate and average fade duration of the output signal of a maximal ratio combiner (MRC) and equal gain combiner (EGC), operating on independent Ricean fading input branch signals, are derived. Exact, closed-form results are obtained for MRC diversity, while precise expressions for EGC diversity are presented with an infinite series method. The results are valid for an arbitrary number of independent, identically distributed diversity branches, isotropic scattering, and a specular component perpendicular to the line of motion of the mobile. Index Terms--Diversity methods, fade duration, fading channels, level crossing rate.

We examine some algebraic properties of two high-rate linear space-time block codes over M = 2, 3 transmit antennas. Although these high-rate codes have positive coding gain, the gain decreases when increasing the constellation size. We give tight upper and lower bounds on the achieved coding gains as functions of the size of the constellations used. We show that when using the irrational numbers [square root of 3] and [square root of 2], the coding gains express the approximation of these numbers by continued fractions depending on the constellations used. The poor approximation of these numbers by rational numbers is then shown to make the coding gains decrease slowly when increasing the constellation size. Index Terms--Block codes, continued fractions, diversity methods, multiple-input-multiple-output (MIMO) systems, number theory.

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.o] 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 [less than or equal to] 32), but not for larger sizes. Index Terms--Error rate, Gray map, joint source-channel coding, maximum a posteriori (MAP) and maximum-likelihood (ML) decoding, nonuniform sources, phase-shift keying (PSK) and quadrature amplitude modulation (QAM), signal mapping.

The lack of a well-defined and meaningful measure of the quality of computer-generated correlated random variates complicates the design and comparison of generation algorithms for communications system simulation applications. This paper presents quantitative quality measures for computer-generated random variates having a multivariate Gaussian distribution or having a distribution that derives from the multivariate Gaussian distribution. These measures are, in particular, useful for digital communication system simulation applications. A theoretical basis for the definition of the measures is given and it is shown that the measures also possess useful intuitive interpretations. Examples of the use of these quality measures are provided. Index Terms--Fading channels, random number generation, Rayleigh channels, simulation.

Analysis on the exact error rate of jointly optimal (JO) maximum likelihood (ML) multiuser detection is limited in the existing literature owing to its high computational complexity. In this paper, the JO ML detection of two quadrature phase-shift keying (QPSK) signals with an arbitrary relative phase offset is investigated. Exact, analytical symbol error rate (SER) and bit error rate (BER) formulas are derived for two users with no less than 3 dB power difference between them. Closed-form union bounds on the user SER and BER with an arbitrary phase offset and an arbitrary user power ratio are also given as a simpler approach to acquire the asymptotic error rate performance. Furthermore, insights on the potentials and properties of the JO ML detector regarding its error rate behaviors for each user are revealed through comparisons with the successive interference cancellation receiver. The accuracies of the obtained formulas are demonstrated through simulation. The results show the error rates for the two-user QPSK case no longer follow the classic knowledge on the error rate behaviors in the single signal detection. In addition, the performance and dB penalty employing different modulation types are also compared and discussed. [ABSTRACT FROM AUTHOR]

Recently, an improved Jakes' fading channel simulator was proposed by Pop and Beaulieu to eliminate the stationarity problem occurring in Jakes' original design. In this letter, second-order statistical properties of the improved Jakes' simulator are analyzed. Consistent with Pop and Beaulieu's caution about high-order statistics of the simulator, it is proved that some second-order statistics of both the quadrature components and the envelope do not match the desired ones even if the number of sinusoids approaches infinity. Therefore, care must be taken when the simulator is employed to evaluate algorithms and systems. Index Terms--Fading channel simulator, fading channels, Rayleigh fading, statistics.

This letter introduces two general relationships concerning the output signal-to-noise ratio distribution and the bit error performance of the nonideal maximal ratio combiner. The imperfections are modeled as Gaussian distributed weighting errors in the channel gain estimates used for coherent combination. The general form for the bit error rate is applicable to any modulation format. Index Terms - Combining techniques, diversity, fading channels.

A new exact method for computing the average symbol error probability of two-dimensional M-ary signaling in slow fading is presented. The method is generally applicable to polygonal decision regions. The exact average symbol error rate of coherent 16-star-QAM is obtained and compared to that of 16-rectangular-QAM. New results for optimum ring ratios of 16-star-QAM in additive white Gaussian noise (AWGN) and in slow fading are also given in this letter. Index Terms - Error probability, fading channels.

A semianalytical (SA) simulation method is proposed as a means to improve the efficiency of computer simulation in estimating block-error rates (BKER's) in the presence of Doppler fading and additive white Gaussian noise. Frequency-nonselective Rayleigh, Rician, and Nakagami fading with diversity combining for binary noncoherent frequency-shift keying (NCFSK) modulation are considered. The reduction in required computer simulation time of the SA method compared to the conventional Monte Carlo (MC) simulation is assessed. Index Terms - Error correction coding, fading channels, simulation.

The performances of selection diversity receiver structures in a slow flat Rayleigh-fading environment are assessed. A number of new and interesting results are obtained. Binary digital signaling using noncoherent frequency-shift keying (NCFSK), differential phase-shift keying (DPSK), coherent phase-shift keying (CPSK), and coherent frequency-shift keying (CFSK) is considered. The traditional analysis (the Traditional Selection Diversity Model) of a selection diversity system is based on choosing the branch with the largest signal-to-noise (SNR) power ratio while assuming that the noise power is constant across all branches. However, many practical selection systems choose the branch based on a largest signal-plus-noise (S + N selection) sample of a filter output. This paper comprises accurate analyses of such S + N selection systems. Results show that S + N selection systems perform better than predicted by the Traditional Selection Diversity Model. This is because the former includes the statistical nature of the noise, whereas the latter does not. The performance difference between the two models increases as the number of diversity branches increases. For each of DPSK and CPSK, the dual diversity equal gain (EG) combining and S + N selection systems perform identically. For each of NCFSK and CFSK, receiver structures which are equivalent when there is no diversity perform differently in a diversity environment. Certain dual diversity S + N selection systems give the same performances as EG combining or square law combining. The results are contingent upon perfect cophasing for the EG combining. In systems where estimates of the combining carrier phases contain noise, S + N selection outperforms EG combining for dual diversity. Index Terms - Combining techniques, diversity, fading channels.

We propose applying an approximate Fourier series to evaluate efficiently the bit-error-rate (BER) performance of finite-length linear equalization (LE) and decision feedback equalization (DFE). By extending the Fourier series, we enable BER calculations for quadrature phase-shift keying (QPSK) transmission on complex channels with in-phase and crosstalk intersymbol interference (ISI). The BER calculation is based on determining the residual ISI samples and background Gaussian noise variance at the equalizer output for static channels or for realizations of quasi-static fading channels. A simple bound on the series error magnitude in terms of the Fourier series parameters ensures the required accuracy and precision. Improved state transition probability estimates are derived and verified by simulation for an approximate Markov model of DFE error propagation for the case in which residual ISI exists even when the previous decisions stored in the feedback filter (FBF) are correct. We demonstrate the ease and widespread applicability of our approach by producing results which elucidate a variety of equalization tradeoffs. Our analysis includes symbol-spaced and fractionally spaced minimum mean-square error (MMSE)-LE, zero-forcing (ZF)-LE, and MMSE-DFE (with and without error propagation) on static ISI channels and multipath channels with quasi-static Rayleigh fading; a comparison between suboptimum and optimum receiver filtering in conjunction with equalization; and an assessment of the accuracy of some widely used equalization BER approximations and bounds. Index Terms - Decision feedback equalization, error propagation, intersymbol interference, linear equalization, Markov processes, quadrature phase-shift keying.

New upper and lower bounds on the mean recovery time of decision feedback equalization (DFE) are derived. The recovery time is defined as the time it takes the decision feedback equalizer (DFEQ) to reach the error-free state after an error has corrupted an error-free DFEQ. The derivations of the bounds assume a causal channel response, independent data symbols, and independent noise samples. The bounds are found to be tighter, especially at large SNR, than previous bounds in a numerical example. Index Terms - Decision feedback equalization, equalizer error statistics.

The average bit-error rate (BER) performance of [Pi]/4-shifted differential quadrature phase shift keying ([Pi]/4-DQPSK) in the presence of multiple independent cochannel interferers in frequency-nonselective fading environments is analyzed. Nyquist shaped pulses are used and post detection diversity combining is employed at the receiver. The use of both L-branch post detection equal gain combining (EGC) and L-branch post detection selection combining (SC) are considered. Two approaches for representing the cochannel interference are investigated. These are a Gaussian interference model and a synchronous interference model. The accuracies of both of these models are assessed by comparing their BER performances with precise BER results. The precise BER results are obtained by using a combination of analysis and simulation. Attention will be given, in particular, to the outdoor microcellular environment. The results of this paper indicate that the synchronous interference model may overestimate the effects of interference while the Gaussian interference model may underestimate the effects of interference.

Four methods that can be used to approximate the distribution function (DF) of a sum of independent lognormal random variables (RV's) are compared. The aim is to determine the best method to compute the DF considering both accuracy and computational effort. The investigation focuses on values of the dB spread, [Sigma], valid for practical problems in wireless transmission (6 dB [less than or equal to] [Sigma] [less than or equal to] 12 dB). Contrary to some previous reports, our results show that the simpler Wilkinson's approach gives a more accurate estimate, in some cases of interest, than Schwartz and Yeh's approach.

The performance of M-ary differential phase shift keying (MDPSK) on frequency-selective slow Rayleigh fading, lognormal shadowed channels with diversity combining is analyzed for mobile and portable applications. The use of L-branch equal gain postdetection microdiversity combining to mitigate the effects of fading and P-port macrodiversity to alleviate the effects of shadowing are investigated. Four performance criteria are considered for a frequency-selective multipath fading, intersymbol interference channel. These are, the short term bit error rate (BER), the irreducible BER, the complementary distribution over the lognormal shadowing of the average BER, and the probability that the instantaneous BER exceeds a threshold value, averaged over a spatial environment. Closed-form expressions for the four performance criteria are obtained. The BER and outage performance results show that diversity combining is an effective method for improving the system performance (and hence system reliability), when the normalized delay spread is not large. It is also seen that, in most cases, 4DPSK gives the best performance followed by 8DPSK and 2DPSK, respectively, for a given information throughput.

The performances of switched diversity systems operating on generalized (Nakagami)-fading channels are analyzed using a discrete-time model. The average bit error rate (BER) of binary noncoherent frequency shift keying (NCFSK) on slow, nonselective Nakagami-fading channels is derived. Closed-form expressions that can be used to determine optimum switching esholds (in a minimum error rate sense) are also derived. In addition, the use of optimum fixed thresholds is considered. It is found that a considerable amount of diversity gain can be obtained using an optimum fixed (rather than adaptive) switching threshold. Results are obtained for both independent and correlated Nakagami-fading branch signals. The effects of fading severity and the correlation coefficient on both the BER and on the optimum switching threshold are investigated. It is shown that useful diversity gain can be obtained with power correlation coefficients as high as 0.9 when the fading is strong. The results for a Rayleigh channel are obtained and presented as a special case of generalized-fading model.

The performances of switched dual diversity systems operating on independent and correlated Ricean fading channels are analyzed using a discrete time model. The average bit error rate (BER) of the discrete time switched diversity system using binary noncoherent frequency shift keying (NCFSK) on slow, nonselective Ricean fading channels is derived. A closed form expression that gives the optimum switching threshold in a minimum error rate sense is derived for the case of independent branch signals. Results for the optimum switching threshold for the case of correlated branch signals, obtained numerically, are also presented. Results using selection diversity combining are obtained for comparison. The effects of fading severity on both the BER and on the optimum switching threshold are investigated. The Ricean fading model may be used to model both the microcellular radio environment and the mobile satellite fading channel. Hence, the results of this paper are useful for both of these areas.

New upper and lower bounds on the mean recovery times of decision feedback equalizers are derived. The analysis uses an approach based on writing difference equations for conditional, state dependent, mean recovery times. This method is simple and leads to simple expressions for the bounds. Two different recovery times are investigated; the channel error recovery time and the startup, or reset, error recovery time. Quantitative relationships between the two recovery times are established. Both noiseless and noisy equalizer operating conditions are examined. The new upper bounds are several orders of magnitude smaller than previous upper bounds in some practical cases.

Currently, channels having large low-frequency attenuation are of much interest Low-frequency removal may result from transformer or capacitor coupling. Examples include ISDN loop transmission (transformer coupling) and wireless systems (capacitor coupled amplifiers). Despite this interest, few works have explicitly examined the problem of calculating the average probability of error for these systems, in which the intersymbol interference from a single pulse ma extend over hundreds or even thousands of symbols. Efficient series techniques for evaluation of the error probabilities of multilevel pulse amplitude modulations and multilevel duobinary signaling are derived. The method is applicable to any additive noise possessing an even probability density function. The Gaussian noise case is examined in detail. Examples of Nyquist I signaling and suboptimal detection of nonreturn-to-zero pulse codes are considered. The results are compared to previous published results. It is seen that an often cited upper bound, though within a factor of about ten in error probability for small to medium intersymbol interference conditions, may significantly overestimate the system degradation due to low-frequency attenuation when the intersymbol interference is large.

The improvements achievable using diversity with matched filter NCFSK (and DPSK receivers operating on log-normal shadowed Nakagami-fading channels are analyzed. Three microdiversity techniques, equal gain combining (EGC), maximal ratio combining (MRC) and selection combining (SC) are compared. The system performances are assessed by considering two measures of coverage; one well suited for mobile users and one well suited for portable users. The detrimental effects of multipath fading in cellular mobile radio systems can be mitigated b using a number of micro-diversity paths at the receiver. The effects of shadowing can be mitigated by using a number K of macrodiversity radio ports to serve each cell. The improvements gained by using microdiversity to combat multipath fading and macrodiversity to combat shadowing are investigated. The effects of the fading severity, the number of microdiversity branches at each port L and the number of macrodiversity ports K on the system performance are investigated in detail. The results, in most cases, are obtained by carrying ou a single numerical integration (for any order of diversity). The results show that although MRC gives the best performance, EGC and SC perform nearly as well for dual (L = 2) diversity. For larger L, i.e., L [is greater than or equal to] 4, the relative performance of SC deteriorates substantially whereas the performance of EGC remains close to that of MRC. Also, our results show that as the fading gets less severe, the performance of EGC gets closer to that of MRC, while the performance of SC worsens compared to that of MRC.

Several approaches that can be used to compute the distribution of a sum of correlated lognormal RVs are investigated. Specifically, Wilkinson's approach, an extension to Schwartz and Yeh's approach, and a cumulants matching approach are studied. The aim is to determine which method is best for computing the complementary distribution function (CDF) of a sum of correlated lognormal RVs considering both accuracy and computational effort. Then, using these techniques, we compute the outage probability of a desired lognormal shadowed signal in the presence of multiple correlated lognormal cochannel interferers. The outage results are presented as a function of the reuse factor. The reuse factor is defined as the distance between the centers of the two nearest cells using the same frequencies divided by the cell radius. It is a key parameter in the design of any frequency reuse system. Simulation results are used for verification and comparison. Overall, the results obtained in this paper show that among the three methods considered in this paper Wilkinson's approach may be the best method to compute the CDF of sums of correlated lognormal RVs (and hence the outage probability in correlated lognormal shadowed mobile radio environments). This is due to both its accuracy and computational simplicity over the range of parameters valid for practical applications.

The exact computation of the symbol error probability of systems using decision feedback equalization is difficult due to the propagation of errors. New upper bounds to the error probability of decision feedback equalization, which take error propagation into account, are developed. The derivations of the bounds assume a causal channel response, independent data symbols, and independent noise samples. The bounds are valid for any noise process that has a symmetric and unimodal probability density function. In some cases, the new bounds are significantly tighter than a well-known upper bound of Duttweiler, Mazo, and Messerschmitt.

Analytical, closed from expressions for cellular outage probabilities in generalized Nakagami fading are derived for three practical diversity combining schemes. The outage is defined as the probability that the signal-to-interference power ratio (SIR) is less than a power protection ratio. The analysis considers L-branch equal gain (EG), selection (SC), and switched (SW) diversity combining schemes. The analyses are not limited to a single interferer, but rather assume the presence of multiple independent cochannel interferers. Previous results have used some approximations to study the performance of the EG combiner. Here, a precise method is used to analyze the performance of an L-branch EG combiner. Selection diversity combining using the total power algorithm, the desired power algorithm, and the signal-to-interference power algorithm are analyzed. The effects of diversity on the reuse factor and on the spectrum efficiency of cellular mobile radio systems are considered in detail. The results for the Rayleigh fading channel are obtained and presented as a special case of the generalized Nakagami fading model.

The Cramer-Rao bound is often used to lower bound the mean square error of symbol timing estimators. However, the valid application of this bound requires that the estimator be unbiased and that the signaling waveform be sufficiently smooth. In some cases of practical interest, these conditions are not satisfied. Furthermore, the Cramer-Rao bound is known to yield poor results for small signal-to-noise ratios. A modified Cramer-Rao bound is derived that takes account of the fact that the symbol timing estimate is restricted to a finite interval of one symbol duration. A detection theory bound is also applied to the symbol timing problem. Results obtained using the Cramer-Rao and detection theory bounds are compared. It is shown that the detection theory bound is superior to the traditionally used Cramer-Rao bound. In particular, the detection theory bound gives useful results for sharp pulse shapes and shows a dependence of the mean square error on the data sequence. It also yields meaningful results for small signal-to-noise ratios.

It is known that the "better than" raised-cosine pulse has several advantages over the conventional raised-cosine pulse. In addition to the advantages previously reported, this letter reports that the "better than" raised-cosine pulse enables better performance of symbol timing estimation than the raisedcosine pulse. Both Cramer-Rao lower bounds and simulations of practical synchronizers show the superiority of the new pulse. The performance gain can be as much as 3.4 dB for a practical system. Index Terms--"Better than" raised-cosine pulse, Cramer-Rao lower bound, non-data-aided feedforward symbol timing estimation, raised-cosine pulse.

No closed--form expression is known for the lognormal characteristic function. Computation of the characteristic function using numerical integration is time consuming and often converges poorly. Alternative published numerical methods for its evaluation are complex and often valid only for particular values of the dB-spread. A novel definite integral form of the lognormal characteristic function is derived. This form lends itself to rapid and convenient computation of the lognormal characteristic function using simple, common methods of numerical integration. Index Terms--Characteristic function, lognormal, probability.

Single-input multiple-output non-orthogonal multiple access (SIMO-NOMA) is a promising technology for the uplink (UL) of the Internet of things (IoT). A rate splitting scheme to guarantee max-min fairness (MMF) of SIMO-NOMA is studied. First, the achievable data rate of the minimum mean square error successive interference cancellation (MMSE-SIC) detection is formulated. An upper bound for the minimum data rate of UL users is derived, and it is proved that the upper bound can be achieved by rate splitting with MMSE-SIC detection. Then, an exhaustive-search rate splitting algorithm to maximize the minimum data rate is designed. The existence of a lower bound for the minimum data rate with two-layer SIMO-NOMA is proved. A low-complexity two-layer rate splitting algorithm is designed with suitable detection order to exceed the lower bound. Numerical results verify that rate splitting SIMO-NOMA has higher minimum data rate and lower transmission latency than single-input multiple-output orthogonal multiple access (SIMO-OMA) and un-layered SIMO-NOMA. [ABSTRACT FROM AUTHOR]

Despite the usefulness of the bivariate (correlated) Nakagami-m cumulative distribution function (cdf) in communications systems analysis, an infinite series for the computation of this function is not known. In this letter, an infinite series representation of the bivariate cdf is derived. Bounds on the error resulting from truncation of the infinite series are also derived.

The equivalence of the simultaneous and separate minimum-mean-square-error (MMSE) optimizations of the feed-forward filter (FFF) and feedback filter (FBF) of a finite-length decision feedback equalizer (DFE) is established. Index Terms - Decision feedback equalization, minimum-mean-square-error optimization.