Optimum diversity combining and equalization in digital datatransmission with applications to cellular mobile radio II. Numericalresults

For Pt.I, see ibid., vol.40, no.5, p.885-94 (1992). The probability distributions of the data rates that can be supported by optimum receiver structures as well as the distribution of the Shannon capacity are studied. The dependences among the important system parameters are exhibited graphically for several illustrative examples including QPSK. At outage probabilities <10^-2 and at operating SNRs of 15-25 dB, the Shannon capacity with optimal dual diversity reception is about 2 bit/s/Hz higher than without diversity. Alternatively, at typical operations of QPSK with 1.5 bit/s/Hz, two orders of magnitude in outage probability can be gained by diversity reception. Comparing the uncoded average probability of error for the optimized MSE systems, at most an order-of-magnitude difference is found among the different equalizers investigated except for the zero-forcing equalizer, whose performance is drastically inferior. Dual diversity can provide two-orders-of-magnitude improvement in the average error rate or in outage probability for the uncoded optimized systems     

Optimum diversity combining and equalization overinterference-limited cellular radio channel

This paper presents the comparative analysis of Nth-order diversity combining and equalization over an interference-limited cellular radio channel. The method of combining diversity and equalization has been analyzed previously. However, cochannel interference (CCI) was not considered, and the number of equalization taps was assumed to be infinite. A quadrature amplitude modulation (QAM) is used in our signal analysis. In modeling the multipath radio, we take into account CCI generated by frequency reuse and additive white Gaussian noise (AWGN). The performance evaluations are made of average error probability and outage probability. The average error rate is determined by using a Monte Carlo simulation for a set of channel parameters such as signal-to-noise ratio (SNR), signal-to-interference ratio (SIR), and equalization coefficients determined for this channel. In the error-rate estimation, we analyze and compare the results of system performance obtained by the upper bound approach and the moment estimation method. We also investigate the tradeoff of the performance improvement in terms of average error probability and equalizer complexity (the number of equalization taps)     

Dual diversity combining and equalization in digital cellularmobile radio

The performance of digital data transmission over frequency-selective fading channels is investigated. For statistically independent diversity paths, estimates of average attainable error rates and outage probabilities as functions of system parameters are provided. The dependences among the important system parameters are exhibited graphically for several examples, including quaternary phase-shift keying (QPSK). In the optimized uncoded QPSK with 1.5 b/s/Hz, two orders of magnitude in outage probability can be gained by diversity reception. When one compares the uncoded average probability of error for the optimized mean squared error (MSE) systems one finds at most an order-of-magnitude difference among the different equalizers investigated except for the zero-forcing equalizer, whose performance is drastically inferior to the others. Again, dual diversity can provide two orders of magnitude improvement in the average error rate or in outage probability for the uncoded optimized systems     

Optimum combining in digital mobile radio with cochannel interference

This paper studies optimum signal combining for space diversity reception in cellular mobile radio systems. With optimum combining, the signals received by the antennas are weighted and combined to maximize the output signal-to-interference-plus-noise ratio. Thus, with cochannel interference, space diversity is used not only to combat Rayleigh fading of the desired signal (as with maximal ratio combining) but also to reduce the power of interfering signals at the receiver. We use analytical and computer simulation techniques to determine the performance of optimum combining when the received desired and interfering signals are subject to Rayleigh fading. Results show that optimum combining is significantly better than maximal ratio combining even when the number of interferers is greater than the number of antennas. Results for typical cellular mobile radio systems show that optimum combining increases the output signal-to-interference ratio at the receiver by several decibels. Thus, systems can require fewer base station antennas and/or achieve increased channel capacity through greater frequency reuse. We also describe techniques for implementing optimum combining with least mean square (LMS) adaptive arrays.     

MMSE diversity combining for wide-band digital cellular radio

A study of minimum mean-square error (MMSE) diversity combining for wide-band digital cellular radio, designed to combat intersymbol interference (ISI) caused by frequency selective fading is outlined. The systems analyzed use binary phase-shift keying (BPSK), quarternary phase-shift keying (QPSK) or 16-level quadrature amplitude modulation (16-QAM) with cosine rolloff spectral shaping, and space diversity with selection, maximal ratio or MMSE combining. A set of performance curves is presented for selected combining schemes showing the influence of the following system parameters: the diversity order (1 to 4); the cosine rolloff factor; the power delay spectrum (with its associated delay spread); the signal-to-interference ratio; and the number of modulation levels (2, 4 and 16)     

Adaptive equalization for TDMA digital mobile radio

Adaptive equalization for a TDMA (time-division multiple-access) digital cellular system is discussed. A survey of adaptive equalization techniques that includes their performance characteristics and limitations and their implementation complexity is presented. The design of adaptive equalization algorithms for a narrowband TDMA system is considered. It is concluded that, on the basis of implementation complexity and performance in the presence of multipath distortion and signal fading, MLSE (maximum-likelihood sequence estimation) and DFE (decision feedback equalization) are viable equalization methods for mobile radio     

Matched filter performance bounds for diversity combining receiversin digital mobile radio

By employing the technique known as the matched filter bound, the authors derive analytical expressions for the distribution and average of the bit-error-rate in an ideal space diversity mobile radio receiver. Each diversity branch receives from a frequency-selective Rayleigh fading channel of arbitrary delay profile, and is subjected to additive Gaussian noise of arbitrary spectral shape. Numerical results calculated from the analytical expressions give insight into the relative benefits of antenna diversity and wideband transmission over the mobile radio channel     

Equalization of digital radio channels with large multipath delayfor cellular land mobile applications

A new maximum a posteriori (MAP) equalizer is proposed for digital radio links affected by large multipath delays. The “sparse” nature of the channel, where a few nonzero powerful taps are spaced by many negligible taps, is exploited to achieve a complexity proportional to the number of nonzero taps. When the channel is time-varying, an efficient nonlinear Kalman like channel estimator is employed to track only the nonzero taps     

Optimal diversity combining under correlated noise in mobile radio

In this paper the performance of predetection maximal ratio and equal gain combiners are investigated under conditions of correlated branch noise. A statistical model is devised to determine the spatial noise correlation coefficients at metropolitan‐area base stations, and the cases where significant correlation is likely are clarified. Optimal weighting coefficients for a maximal ratio combiner with two‐branch space diversity are derived under correlated noise. Based on this result it is shown that correlation in branch noise can be used to improve the combiner performance by dynamically adjusting the weightings so as to partially cancel the noise. Performance of equal gain combiners is also shortly discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Adaptive equalization and diversity combining for mobile radiousing interpolated channel estimates

The authors demonstrate the feasibility of a digital cellular radio (DCR) system which employs a jointly adaptive decision-feedback equalizer and diversity combiner. In particular, the authors utilize the current estimates of the channel impulse response (CIR) at each diversity branch to compute the receiver parameters periodically. The authors propose a novel block-adaptive strategy which computes the time-varying CIR by interpolating a set of CIR estimates obtained through periodic training. Although incurring some inherent processing delay and throughput reduction, this interpolation strategy has the advantage of immunity to decision errors which would quite likely occur during a deep fade. It is shown that the system performance is limited, in the form of an irreducible bit error rate at high signal-to-noise ratios (SNRs), by the CIR estimation of the rapidly fading channel     

Two-stage maximum likelihood estimation for diversity combining indigital mobile radio

For space diversity, it is shown that it is related to maximal-ratio combining (MRC). Unlike MRC, it allows the receiver to collect diversity signals without gain adjustments or cophasing. Some worst-case bit error rate (BER) simulation results that show the influence of time delay spread, Doppler, shadow loss, and diversity for a seven-cell cluster using quadrature modulation are presented     

Postdetection selection diversity effects on digital FM land mobile radio

The postdetection selection diversity effects on a binary digital FM system are theoretically analyzed in the fast Rayleigh fading signal environment encountered in the typical UHF or microwave land mobile radio channels. Both differential and discriminator detections are considered for demodulation of digital FM signal. The average error rate is presented by a simple closed form including both effects of Rayleigh envelope fading and random FM noise. A few examples of numerical results for minimum shift keying (MSK) are graphically presented.     

Effects of diversity reception on BCH-coded QPSK cellular land mobile radio

Bit error rate performance of BCH-coded QPSK with coherent demodulation and multiple-branch selection diversity reception is calculated in the presence of fast Rayleigh fading and a cochannel interface environment. How diversity reception affects the optimum code rate and coding gain is investigated from power and spectrum efficiencies points of view.<>     

Adaptive frequency-domain equalization and diversity combining forbroadband wireless communications

We introduce a new kind of adaptive equalizer that operates in the spatial-frequency domain and uses either least mean square (LMS) or recursive least squares (RLS) adaptive processing. We simulate the equalizer's performance in an 8-Mb/s quaternary phase-shift keying (QPSK) link over a frequency-selective Rayleigh fading multipath channel with ~3 μs RMS delay spread, corresponding to 60 symbols of dispersion. With the RLS algorithm and two diversity branches, our results show rapid convergence and channel tracking for a range of mobile speeds (up to ~100 mi/h). With a mobile speed of 40 mi/h, for example, the equalizer achieves an average bit error rate (BER) of 10 ^-4 at a signal-to-noise ratio (SNR) of 15 dB, falling short of optimum linear receiver performance by about 4 dB. Moreover, it requires only ~50 complex operations per detected bit, i.e., ~400 M operations per second, which is close to achievable with state-of-the-art digital signal processing technology. An equivalent time-domain equalizer, if it converged at all, would require orders-of-magnitude more processing     

Known and novel diversity approaches as a powerful means to enhancethe performance of cellular mobile radio systems

The main requirements to be met by third generation mobile radio systems are high cellular spectrum efficiency and high flexibility. The authors focus on high cellular spectrum efficiency, which is difficult to achieve due to the time variance and frequency selectivity of the mobile radio channel and due to interference. It is known that the degrading effects of these adverse characteristics of the mobile radio channel and of interference can be mitigated by diversity. The way how diversity influences cellular spectrum efficiency is derived in general. As a reference point, the types of diversity used in GSM are analyzed. In GSM, the potential for diversity enhancement inherent in code-division multiple-access (CDMA) is not exploited. A joint detection code-division multiple-access (JD-CDMA) system concept aimed at third generation mobile radio systems has been proposed which introduces a CDMA feature into systems based on time-division multiple-access (TDMA) and frequency-division multiple-access (FDMA) like GSM and also advanced TDMA (ATDMA). The gains achievable by different types of diversity in GSM as well as in the JD-CDMA system concept are investigated. It is shown that considerable gains can be achieved by different types of antenna diversity and by exploiting the additional diversity potential of CDMA. Therefore, third generation standards should be flexible in order to allow the use of as many types of diversity as possible to enhance the cellular spectrum efficiency     

Vehicle location in cellular mobile radio systems

A tutorial discussion of vehicle location as used to control cellular mobile radio systems is presented. Early concepts and misconceptions concerning vehicle location are described, and the relation between location "accuracy" and system performance optimization is discussed. Measurement parameters commonly used for vehicle location are described, and considerations relating to the algorithm used in the location process are presented.     

Advantages of CDMA and spread spectrum techniques over FDMA andTDMA in cellular mobile radio applications

A unified theoretical method for the calculation of the radio capacity of multiple-access schemes such as FDMA (frequency-division multiple access), TDMA (time-division multiple access), CDMA (code-division multiple access) and SSMA (spread-spectrum multiple access) in noncellular and cellular mobile radio systems is presented for AWGN (additive white Gaussian noise) channels. The theoretical equivalence of all the considered multiple-access schemes is found. In a fading multipath environment, which is typical for mobile radio applications, there are significant differences between these multiple-access schemes. These differences are discussed in an illustrative manner revealing several advantages of CDMA and SSMA over FDMA and TDMA. Novel transmission and reception schemes called coherent multiple transmission and coherent multiple reception are briefly presented     

A study of the antenna array configuration of an M-branch diversity combining mobile radio receiver

The theoretical analysis in this paper is based on the assumption that the angles of signal arrival on the mobile receiver are uniformly distributed. From the analysis and experimental studies, we find that if the antenna spacing between two adjacent antennas in a space diversity array is greater than 0.5λ the array configuration does not affect the cumulative distribution curves nor the shapes of the level-crossing-rate (LCR) curves, and only slightly affects the signal level at which the maximum LCR occurs. Hence a three-element array with a triangular shape or a four-element array with a rectangular shape can be considered a good arrangement, provided each side (antenna spacing) is greater than 0.5λ. Two slightly better arrangements than those we just mentioned for improving the signal fading are also proposed for three-branch and four-branch diversity signals, respectively.     

Power control and diversity in mobile radio cellular systems in thepresence of Ricean fading and log-normal shadowing

The performance of a cellular mobile radio system with frequency reuse is evaluated in terms of outage probability. Deterministic path loss, log-normal shadowing, and Ricean fading are accounted for, and the use of diversity and power control is considered in order to enhance system performance. Both hexagonal and lineal cells are considered. Particular attention is given to the sensitivity of the outage probability to the system parameters, especially those related to the propagation model (fading, shadowing, and path loss). It is seen that diversity and power control can improve the system behavior. The performance is sensitive to the fading parameter (i.e., the Rice factor) of the intended user, but is relatively independent of that of the interferers. Also, a significant dependence is observed on the shadowing parameter, whereas a limited dependence is seen on the outage threshold and the channel utilization. Finally, the presence of a dual path loss law degrades the performance, and the outage probability increases as the breakpoint distance gets larger     

Outage probability in cellular mobile radio due to Nakagami signaland interferers with arbitrary parameters

Outage probability provides a fundamental performance measure of the grade of service for cellular mobile radio systems. Determination of the outage probability in a Nakagami (1960) mobile environment is particularly important since Nakagami fading is, as shown by various empirical measurements, the most appropriate model in many practical applications. Effective techniques have been developed recently to determine outage probability in the presence of multiple Nakagami interferers by assuming that the fading parameters of both signal and co-channel interferences are integer-valued. However, the general problem with arbitrary Nakagami signal and interferers remains unsolved. A new technique is presented, which allows the Nakagami distributions for both signal and interferers to be arbitrary. Exact formulas for probability of outage with and without a constraint on minimum signal power are derived, and computer results are also presented to illustrate the theory