Performance of Quantized Equal Gain Transmission With Noisy Feedback Channels

In this paper, new results and insights are derived for the performance of multiple-input, single-output systems with beamforming at the transmitter, when the channel state information is quantized and sent to the transmitter over a noisy feedback channel. It is assumed that there exists a per-antenna power constraint at the transmitter, hence, the equal gain transmission (EGT) beamforming vector is quantized and sent from the receiver to the transmitter. The loss in received signal-to-noise ratio (SNR) relative to perfect beamforming is analytically characterized, and it is shown that at high rates, the overall distortion can be expressed as the sum of the quantization-induced distortion and the channel error-induced distortion, and that the asymptotic performance depends on the error-rate behavior of the noisy feedback channel as the number of codepoints gets large. The optimum density of codepoints (also known as the point density) that minimizes the overall distortion subject to a boundedness constraint is shown to be the same as the point density for a noiseless feedback channel, i.e., the uniform density. The binary symmetric channel with random index assignment is a special case of the analysis, and it is shown that as the number of quantized bits gets large the distortion approaches the same as that obtained with random beamforming. The accuracy of the theoretical expressions obtained are verified through Monte Carlo simulations.

Impact of HPA nonlinearity on MIMO systems with quantized equal gain transmission

In this paper, we investigate the performance of multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of nonlinear high-power amplifiers (HPAs). Due to the suboptimality of maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, quantized equal gain transmission (QEGT) is suggested as a feasible TB scheme. The effect of HPA nonlinearity on the performance of MIMO QEGT/MRC is evaluated in terms of the average symbol error probability (SEP) and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, such as the parameters of nonlinear HPA, cardinality of the beamforming weight vector codebook, and modulation order of quadrature amplitude modulation (QAM), on performance.

Second-order statistics for equal gain and maximal ratio diversity-combining reception

Exact and closed-form expressions for the level crossing rate and average fade duration are presented for equal gain combining and maximal ratio combining schemes, assuming an arbitrary number of independent branches in a Rayleigh environment. The analytical results are thoroughly validated by simulation.

Analysing energy detector diversity receivers for spectrum sensing

The analysis of energy detector systems is a well studied topic in the literature: numerous models have been derived describing the behaviour of single and multiple antenna architectures operating in a variety of radio environments. However, in many cases of interest, these models are not in a closed form and so their evaluation requires the use of numerical methods. In general, these are computationally expensive, which can cause difficulties in certain scenarios, such as in the optimisation of device parameters on low cost hardware. The problem becomes acute in situations where the signal to noise ratio is small and reliable detection is to be ensured or where the number of samples of the received signal is large. Furthermore, due to the analytic complexity of the models, further insight into the behaviour of various system parameters of interest is not readily apparent. In this thesis, an approximation based approach is taken towards the analysis of such systems. By focusing on the situations where exact analyses become complicated, and making a small number of astute simplifications to the underlying mathematical models, it is possible to derive novel, accurate and compact descriptions of system behaviour. Approximations are derived for the analysis of energy detectors with single and multiple antennae operating on additive white Gaussian noise (AWGN) and independent and identically distributed Rayleigh, Nakagami-m and Rice channels; in the multiple antenna case, approximations are derived for systems with maximal ratio combiner (MRC), equal gain combiner (EGC) and square law combiner (SLC) diversity. In each case, error bounds are derived describing the maximum error resulting from the use of the approximations. In addition, it is demonstrated that the derived approximations require fewer computations of simple functions than any of the exact models available in the literature. Consequently, the regions of applicability of the approximations directly complement the regions of applicability of the available exact models. Further novel approximations for other system parameters of interest, such as sample complexity, minimum detectable signal to noise ratio and diversity gain, are also derived. In the course of the analysis, a novel theorem describing the convergence of the chi square, noncentral chi square and gamma distributions towards the normal distribution is derived. The theorem describes a tight upper bound on the error resulting from the application of the central limit theorem to random variables of the aforementioned distributions and gives a much better description of the resulting error than existing Berry-Esseen type bounds. A second novel theorem, providing an upper bound on the maximum error resulting from the use of the central limit theorem to approximate the noncentral chi square distribution where the noncentrality parameter is a multiple of the number of degrees of freedom, is also derived.

Measurements, modeling and simulation of the off-body radio channel for the implementation of bodyworn antenna diversity at 868 MHz

This paper presents a systematic measurement campaign of diversity reception techniques for use in multiple-antenna wearable systems operating at 868 MHz. The experiments were performed using six time-synchronized bodyworn receivers and considered mobile off-body communications in an anechoic chamber, open office area and a hallway. The cross-correlation coefficient between the signal fading measured by bodyworn receivers was dependent upon the local environment and typically below 0.7. All received signal envelopes were combined in post-processing to study the potential benefits of implementing receiver diversity based upon selection combination, equal-gain and maximal-ratio combining. It is shown that, in an open office area, the 5.7 dB diversity gain obtained using a dual-branch bodyworn maximal-ratio diversity system may be further improved to 11.1 dB if a six-branch system was used. First-and second-order theoretical equations for diversity reception techniques operating in Nakagami fading conditions were used to model the postdetection combined envelopes. Maximum likelihood estimates of the Nakagami-parameter suggest that the fading conditions encountered in this study were generally less severe than Rayleigh. The paper also describes an algorithm that may be used to simulate the measured output of an M-branch diversity combiner operating in independent and identically-distributed Nakagami fading environments.

Characterization and modeling of on-body spatial diversity within indoor environments at 868 MHz

For the first time in the open literature we present a full characterization of the performance of receiver diversity for the on-body channels found in body area networks. The study involved three commonly encountered diversity combining schemes: selection combination (SC), maximal ratio combining (MRC) and equal gain combining (EGC). Measurements were conducted for both stationary and mobile user scenarios in an anechoic chamber and open office area environment. Achievable diversity gain for various on-body dual branch diversity receivers, consisting of horizontal and vertical spatially separated antennas, was found to be dependent upon transmitter-receive array separation, user state and level of multipath contribution from the local environment. The maximum diversity gain (6.4 dB) was observed for a horizontal two branch MRC combiner while the transmitter and receiver were on opposite sides of the body, and the user was mobile in the open office area. A novel statistical characterization of the fading experienced in on-body diversity channels is also performed using purposely derived first and second order diversity statistics for combiners operating in Nakagami fading.

Channel characterization for single- and multiple-antenna wearable systems used for indoor body-to-body communications

In this paper, an analysis of radio channel characteristics for single- and multiple-antenna bodyworn systems for use in body-to-body communications is presented. The work was based on an extensive measurement campaign conducted at 2.45 GHz representative of an indoor sweep and search scenario for fire and rescue personnel. Using maximum-likelihood estimation in conjunction with the Akaike information criterion (AIC), five candidate probability distributions were investigated and from these the kappa - mu distribution was found to best describe small-scale fading observed in the body-to-body channels. Additional channel parameters such as autocorrelation and the cross-correlation coefficient between fading signal envelopes were also analyzed. Low cross correlation and small differences in mean signal levels between potential dual-branch diversity receivers suggested that the prospect of successfully implementing diversity in this type application is extremely good. Moreover, using selection combination, maximal ratio, and equal gain combining, up to 8.69-dB diversity gain can be made available when four spatially separated antennas are used at the receiver. Additional improvements in the combined envelopes through lower level crossing rates and fade durations at low signal levels were also observed.

Inverse Gaussian Modeling of Turbulence-Induced Fading in Free-Space Optical Systems

We propose the inverse Gaussian distribution, as a less complex alternative to the classical log-normal model, to describe turbulence-induced fading in free-space optical (FSO) systems operating in weak turbulence conditions and/or in the presence of aperture averaging effects. By conducting goodness of fit tests, we define the range of values of the scintillation index for various multiple-input multiple-output (MIMO) FSO configurations, where the two distributions approximate each other with a certain significance level. Furthermore, the bit error rate performance of two typical MIMO FSO systems is investigated over the new turbulence model; an intensity-modulation/direct detection MIMO FSO system with Q-ary pulse position modulation that employs repetition coding at the transmitter and equal gain combining at the receiver, and a heterodyne MIMO FSO system with differential phase-shift keying and maximal ratio combining at the receiver. Finally, numerical results are presented that validate the theoretical analysis and provide useful insights into the implications of the model parameters on the overall system performance. © 2011 IEEE.

Improving signal reliability for indoor off–body communications using spatial diversity at the base station

In this paper, we investigate the potential improvement in signal reliability for indoor off-body communications when using spatial diversity at the base station. In particular, we utilize two hypothetical indoor base stations operating at 5.8 GHz each featuring four antennas which are spaced at either half- or one-wavelength apart. Three on-body locations are considered along with four types of user movement. The cross-correlation between the received signal envelopes observed at each base station antenna element was calculated and found to be always less than 0.5. Selection, maximal ratio, and equal gain combining of the received signal has shown that the greatest improvement is obtained when the user is mobile, with a maximum diversity gain of 11.34 dB achievable when using a four branch receiver. To model the fading envelope obtained at the output of the virtual combiners, we use diversity specific, theoretical probability density functions for multi-branch receivers operating in Nakagami-m fading channels. It is shown that these equations provide an excellent fit to the measured channel data.

Indoor off–body communications at 5.8 GHz with multiple antennas at the base station: a statistical characterization using the Nakagami–m fading model

In this paper we investigate the first and second order characteristics of the received signal at the output ofhypothetical selection, equal gain and maximal ratio combiners which utilize spatially separated antennas at the basestation. Considering a range of human body movements, we model the model the small-scale fading characteristics ofthe signal using diversity specific analytical equations which take into account the number of available signal branchesat the receiver. It is shown that these equations provide an excellent fit to the measured channel data. Furthermore, formany hypothetical diversity receiver configurations, the Nakagami-m parameter was found to be close to 1.

On the power amplifier nonlinearity in MIMO transmit beamforming systems

In this paper, single-carrier multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of high-power amplifier (HPA) nonlinearity are investigated. Specifically, due to the suboptimality of the conventional maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, we propose the optimal TB scheme with the optimal beamforming weight vector and combining vector, for MIMO systems with nonlinear HPAs. Moreover, an alternative suboptimal but much simpler TB scheme, namely, quantized equal gain transmission (QEGT), is proposed. The latter profits from the property that the elements of the beamforming weight vector have the same constant modulus. The performance of the proposed optimal TB scheme and QEGT/MRC technique in the presence of the HPA nonlinearity is evaluated in terms of the average symbol error probability and mutual information with the Gaussian input, considering the transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects on the performance of several system parameters, namely, the HPA parameters, numbers of antennas, quadrature amplitude modulation modulation order, number of pilot symbols, and cardinality of the beamforming weight vector codebook for QEGT.

Second-order statistics for diversity-combining, techniques in Nakagami-fading channels

Exact and closed-form expressions for the level crossing rate and average fade duration are presented for the M branch pure selection combining (PSC), equal gain combining (EGC), and maximal ratio combining (MRC) techniques, assuming independent branches in a Nakagami environment. The analytical results are thoroughly validated by reducing the general case to some special cases, for which the solutions are known, and by means of simulation for the more general case. The model developed here is general and can be easily applied to other fading statistics (e.g., Rice).

Liveweight gain and feed intake of weaned Bali cattle fed a range of diets in Central Sulawesi, Indonesia

Three experiments were conducted to determine liveweight (W) gain and feed and water intake of weaned Bali cattle offered a range of feed types. In each experiment, 18 weaned entire male Bali cattle were allocated to three treatment groups in a completely randomised block design, with six replicates (animals) per treatment. The dietary treatments were: Experiment 1, native grass fed ad libitum, native grass supplemented with rice bran at 10 g dry matter (DM)/kg W.day and native grass supplemented with a mixture of rice bran and copra meal in equal proportions fed at 10 g DM/kg W.day; Experiment 2, elephant grass hay fed ad libitum, elephant grass supplemented with gliricidia at 10 g DM/kg W.day, and gliricidia fed ad libitum; and Experiment 3, corn stover fed ad libitum, corn stover supplemented with gliricidia at 10 g DM/kg W.day, and corn stover supplemented with rice bran/copra meal in equal amounts (w/w) at 10 g DM/kg W.day. Each experiment was 10 weeks in duration, consisting of a 2-week preliminary period for adaptation to diets and an 8-week experimental period for the measurement of W change, feed and water intake and digestibility of the diet. Growth rates of 6-12-month-old, entire male Bali cattle fed a range of local diets ranged from 0.10 and 0.40 kg/day. Lowest growth rates occurred when the cattle were given the basal diets of native grass (0.104 kg/day), elephant grass (0.174 kg/day) and corn stover (0.232 kg/day). With the addition of supplements such as rice bran, rice bran/copra meal or gliricidia to these basal diets liveweight gains increased to between 0.225 and 0.402 kg/day. Forage DM intake was reduced with these supplements by on average 22.6% while total DM intake was increased by an average of 10.5%. The growth rate on gliricidia alone was 0.269 kg/day and feed DM intake was 28.0 g/kg W.day. Water intake was not affected by supplement type or intake. In conclusion, inclusion of small quantities of locally available, high quality feed supplements provide small-holder farmers with the potential to increase growth rates of Bali calves from 0.1 to 0.2 kg/day, under prevailing feeding scenarios, to over 0.4 kg/day.

Productive coexistence and gain in agroforestry systems.

Productive coexistence and coexistence gain of populations were studied using nine years' data from field experiments of Taxodium ascendens-intercrop systems in Lixiahe, Jiangsu Province, China. A theoretical framework for productive coexistence in agroforestry was developed. Interaction patterns between trees and intercrops were presented within this framework. A model framework was developed to describe the coexistence gain and interaction of populations in T. ascendens-intercrop systems. Facilitation and resource sharing were identified as main contribution to the advantage of species combination in agroforestry. The model of population interaction developed in the present study was accepted for describing the interaction of populations in T. ascendens-intercrop systems, because it explained a high proportion of the variance of experimental data and fitted well the observations in most intercropping types. The model developed in the present study provides flexibility for describing different patterns of intra- and inter-specific interactions. Model coefficients were applied to the determination of the ecological compatibility of species. Managed T. ascendens-intercrop systems were advantageous as compared to a monoculture of trees or arable crops. In T. ascendens stands up to the age of three, arable crops contributed about 50-80 % of the total biomass yield of agroforestry. The diameter or height growth of T. ascendens was not significantly influenced by intercrops, indicating that intercropping under trees produced extra yields but did not depress the tree growth. When the trees were young (during the first three years), T. ascendens did not depress the crop yields, and a land equivalent ratio greater than unity was obtained together with a high yield of both components. The diameter and height of the trees were similar in four spacing configurations with an equal number of trees per hectare up to the age of eight, but wider between-rows open range were beneficial for the intercrops. The relationship between open-ranges and species coexistence was also analysed and the distribution of soil nutrients studied.

A Low-Complexity, Full-Rate, Full-Diversity 2 x 2 STBC with Golden Code's Coding Gain

This paper presents a low-ML-decoding-complexity, full-rate, full-diversity space-time block code (STBC) for a 2 transmit antenna, 2 receive antenna multiple-input multiple-output (MIMO) system, with coding gain equal to that of the best and well known Golden code for any QAM constellation. Recently, two codes have been proposed (by Paredes, Gershman and Alkhansari and by Sezginer and Sari), which enjoy a lower decoding complexity relative to the Golden code, but have lesser coding gain. The 2 x 2 STBC presented in this paper has lesser decoding complexity for non-square QAM constellations, compared with that of the Golden code, while having the same decoding complexity for square QAM constellations. Compared with the Paredes-Gershman-Alkhansari and Sezginer-Sari codes, the proposed code has the same decoding complexity for non-rectangular QAM constellations. Simulation results, which compare the codeword error rate (CER) performance, are presented.