Frequency-Selective Fading Effects in Digital Mobile Radio with Diversity Combining

we analyze the effects of frequency-selective fading in a cellular mobile radio system that uses 1) phase-shift keying (PSK) with cosine rolloff pulses, and 2) space diversity with maximal-radio combining. The distorting phenomena with which we deal are multipath fading (which produces the frequency selectivity), shadow fading, and cochannel interference. The relevant quality measure is defined to be the bit error rate averaged over the multipath fading, denoted by (BER). The relevant system performance characteristic is defined to be the probability distribution for (BER), taken over the ensemble of shadow fadings and locations of the desired and interfering mobiles. To obtain numerical results, we use a combination of analysis and Monte Carlo simulation, invoke widely accepted models for the multipath and shadow fadings, and assume a cellular system with seven channel sets and centrally located base stations. The outcome is a set of performance curves that reveal the influences of various system and channel parameters. These include: the number of modulation levels (two or four), the diversity order, the shape of the multipath delay spectrum, and the standard deviation (or delay spread, τ0) of the multipath delay spectrum. Practical factors accounted for in these assessments include fading- and interference-related timing recovery errors and combiner imperfections. Our results highlight the importance of the ratiotau_{0}/T, whereTis the digital symbol period. They show that the delay spectrum shape is of no importance fortau_{0}/T leq 0.2, but can have a profound influence fortau_{0}/T geq 0.3. We also find that using 4-PSK leads to better detection performance, in certain cases, than using 2-PSK.     

Coded M-DPSK with built-in time diversity for fading channels

Good coded modulation for fading channels requires built-in time diversity. Under a constraint on the interleaving delay, the authors construct and compare three categories of coded M-DPSK (M-ary differential phase-shift keying) schemes with 4⩽M⩽16 for fading channels: two-dimensional trellis-coded, multidimensional trellis-coded, and block-coded. General rules for designing these schemes and their matched bit or symbol interleavers are given. A universal two-state interleaver is shown. These schemes have been extensively evaluated, using computer simulations, for a narrow-band cellular radio channel at different vehicle speeds, with and without twofold antenna diversity     

Multiple-symbol differential detection with interference suppression

A multiple-symbol differential detector is formulated for M-ary differential phase-shift keying modulation where the channel state information is unknown to the receiver. The maximum-likelihood decision statistic is derived for the detector, and its performance is demonstrated by analysis and simulation. Under the Gaussian assumption for the aggregate interference plus noise, an exact expression for the symbol pairwise error probability is developed for M-ary differential phase-shift keying modulation over a diversity, slow-fading Rayleigh channel in the presence of an interference source. A simpler expression of the pairwise error probability is developed for the asymptotic case of large signal-to-noise ratio and small signal-to-interference ratio. It is shown that with an increasing observation interval, the performance of the differential detector over an unknown channel approaches that of optimum combining with known channel.     

Error probability bounds for M-PSK and M-DPSK and selective fadingdiversity channels

A method is described for obtaining tight closed-form bounds on the probability of error for M-ary phase-shift keying (M-PSK) and M-ary differential phase-shift keying (M-DPSK) on fading diversity channels. The channels exhibit doubly selective fading and have specular components. In addition, the random impulse responses of the diversity channels may be correlated; and the probability distributions for the fading on different diversity channels need not be the same. Error probability expressions are given for binary DPSK, 8-DPSK, and 16-DPSK modulation as examples of the application of the general method described     

The Distribution of Error Probability for Rayleigh Fading and Gaussian Noise

The distribution function of the probability of error in the presence of Rayleigh fading and Gaussian noise is determined for the basic binary modulation schemes of coherent frequencyshift keying (CFSK), noncoherent frequency-shift keying (NCFSK), differential phase-shift keying (DPSK), and coherent phase-shift keying (CPSK). General expressions for the distribution function of error probability are also derived when linear maximal-ratio diversity combining is employed. Results are given for various values of average error probability and various orders of diversity.     

On the SNR penalty of MPSK with hybrid selection/maximal ratio combining over i.i.d. Rayleigh fading channels

Closed-form expressions that lower and upper bound the penalty of hybrid selection/maximal ratio combining relative to maximal ratio combining (MRC) for M-ary phase-shift keying (MPSK) modulation are proved. The bounds offer simple-to-evaluate explicit expressions, and are typically within 0.6 dB for hybrid systems with diversity order up to eight that use at least two branches, yet are independent of signal-to-noise ratio (SNR). Contrary to conclusions conjectured in a previously published paper, it is proved that the SNR penalty is not a constant, independent of SNR. It is also shown that previous estimates of the performance losses of selection diversity relative to MRC underestimate or lower bound the losses for MPSK modulation systems, and that the true loss can be significantly larger than previously believed. An upper bound to this loss is also obtained.     

Average error probability of digital cellular radio systems using MRC diversity in the presence of multiple interferers

The performance of digital cellular radio systems employing maximal ratio combining diversity is analyzed in a flat-fading channel with cochannel interference and additive white Gaussian noise. It is assumed that the desired signal may experience Rice fading (due to the presence of a line-of-sight component), while the interferers are Rayleigh-faded and may have similar or dissimilar average powers. Exact expressions are derived for the average symbol-error probability of M-ary phase-shift keying modulation in the presence of multiple independent Rayleigh-faded interferers.     

New results on selection diversity

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     

Analysis of a two-branch maximal ratio and selection diversitysystem with unequal SNRs and correlated inputs for a Rayleigh fadingchannel

An analytical expression for the probability density function of the signal-to-noise ratio (SNR) at the output of a two-branch maximal ratio and selection diversity system is given. The two branches are assumed to be Rayleigh fading, correlated, as well as of unequal average SNRs. Measurements of the cumulative distribution functions after selection and maximal ratio combining were made in Rayleigh fading channels and compared with the analytical results. Also presented are the exact analytical average probabilities of symbol error for coherent binary phase-shift keying and coherent quaternary phase-shift keying before and after two-branch maximal ratio combining for a slow and flat fading correlated Rayleigh channel     

Simulation of digital transmission over mobile channels at 300 kb/s

Studies of digital transmission over typical urban and suburban mobile channels using simulations that employ a local area model for the time varying mobile channel impulse response are discussed. The digital transmission techniques of coherently detected and differentially coherent detected versions of quadrature phase-shift keying (QPSK), Gaussian minimum shift keying (GMSK), and coherently detected binary phase-shift keying (BPSK) over example mobile channels are presented. Two measures of performance are considered; the mean bit error ratio (and irreducible bit error ratio), which is used to compare the robustness of the various modulation methods to delay spread, and the outage probability, which provides a measure of the overall transmission quality as would be perceived by a user. Emphasis is placed on results obtained for GMSK, which is the modulation scheme to be employed in the Pan-European digital cellular mobile system. The effects of RMS delay spread on the mean bit error ratio, mean irreducible bit error ratio, and probability of outage are considered for different channel types     

Error rates of DPSK systems with MIMO EGC diversity reception over Rayleigh fading channels

This paper analyzes the average bit error probability (BEP) of the differential binary and quaternary phase-shift keying (DBPSK and DQPSK respectively) with multiple-input multiple-output (MIMO) systems employing postdetection equal gain combining (MIMO EGC) diversity reception over Rayleigh fading channels. Finite closed-form expressions for the average BEP of DBPSK and DQPSK are presented. Two approaches are introduced to analyze the error rate of DQPSK. The proposed structure for the differential phase-shift keying (DPSK) with MIMO EGC provides a reduced-complexity and low-cost receiver for MIMO systems compared to the coherent phase-shift keying system (PSK) with MIMO employing maximal ratio combining (MIMO MRC) diversity reception. Finally, a useful procedure for computing the associated Legendre functions of the second kind with half-odd-integer order and arbitrarily degree is presented.     

Spread-spectrum path diversity in a shadowed Rician fadingland-mobile satellite channel

The effects of two types of path diversity techniques, namely selection diversity and maximal ratio combining, on the bit error probability are investigated for direct-sequence spread-spectrum (DS/SS) transmission in a land mobile satellite channel using coherent binary phase-shift keying (BPSK) modulation. It is assumed that the channel consists of a log-normally shadowed line-of-sight signal plus Rayleigh distributed multipath signals. The bit error probability is evaluated for light, average, and heavy shadowing. The performance is also measured in terms of the outage probability     

Diversity Analysis of Smart Relaying

It has been known that relaying can provide spatial diversity while satisfying the size-limited constraint of the users' devices in wireless communications systems. For a practically attractive decode-and-forward (DF) relaying system with maximal-ratio combining at the destination, spatial diversity is lost, except when the source–relay link is reliable. To deal with the problem and inspired by the work of Wang , this paper considers and analyzes an adaptive transmission scheme, which is referred to as smart relaying, when only the average relay–destination (R–D) signal-to-noise ratio (SNR) is available at the relay. In the system under consideration, the source continuously transmits the information to the destination. The relay adaptively scales its transmitted power to changes in the channel condition but never exceeds the total power that the conventional relaying used. Performance analysis proves that a diversity order of 2 is always obtained for binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK). A diversity order of 2 is also observed for higher order rectangular quadratic-amplitude modulation (QAM) constellations through numerical results. The result on diversity order does not depend on how perfect the R–D feedback channel and how exact the quantization of the power scaling are. All the corresponding results of Wang are subsumed in our analysis.      

Performance of diversity schemes for OFDM systems with frequency offset, phase noise, and channel estimation errors

We provide expressions for the bit error rate of various transmit and receive diversity schemes for orthogonal frequency division multiplexing (OFDM) systems in the presence of frequency offset, phase noise, and channel estimation errors. The derivations are also applicable for a general multiplicative distortion of the received signal. Our results show that with perfect channel estimates, practical values of the phase noise do not significantly degrade the performance of the various diversity methods for binary phase-shift keying modulation. In contrast, the transmit diversity schemes for OFDM are much more sensitive to channel estimation errors than maximal ratio combining receive diversity.     

Linear diversity analyses for M-PSK in Rician fading channels

Symbol and bit error rates of M-ary differentially encoded/differentially decoded phase-shift keying (MDPSK) and coherent M-ary phase-shift keying (M-PSK) over slow, flat, Rician fading channels are derived when linear diversity combining is applied to combat degradation due to fading. These closed-form solutions are general enough to cover several cases of nondiversity, additive white Gaussian noise (the nonfading mode), Rayleigh fading, mixtures of Rayleigh and Rician fading (the mixed mode), and Rician fading. The results presented here can also be applied to predict the error-rate performance when recent transmit diversity techniques are employed. The solutions for the nonuniform fading profile are included as well. Error probabilities are graphically displayed for both modulation schemes.     

Phase-Tunable Low-Loss, S-, C-, and L-Band DPSK and DQPSK Demodulator

Differential phase-shift keying (DPSK) and differential quadrature phase-shift keying (DQPSK) are touted as performers and reliable advanced modulation formats for next-generation optical transmission systems. One key device enabling such systems is the delay interferometer, converting the signal phase information into intensity modulation to be detected by the photodiodes. We developed an all-fiber delay-line interferometer for DPSK and DQPSK demodulation in the S-, C-, and L-band with low insertion loss, low-birefringence, and greater than 30 dB of extinction ratio over 100 nm and 20 dB from 1460 to 1640 nm in a single device. The device also features insensitivity to mechanical vibration, very low port imbalance (0.1 dB), and very low time delay between all outputs (0.1 ps). The device is highly reliable with a demonstrated failure-in-time rate of less than 100.     

Experimental demonstration of the maximum likelihood-based chromatic dispersion estimator for coherent receivers

We perform an experimental investigation of a maximum likelihood-based (ML-based) algorithm for bulk chromatic dispersion estimation for digital coherent receivers operating in uncompensated optical networks. We demonstrate the robustness of the method at low optical signal-to-noise ratio (OSNR) and against differential group delay (DGD) in an experiment involving 112 Gbit/s polarization-division multiplexed (PDM) 16-ary quadrature amplitude modulation (16 QAM) and quaternary phase-shift keying (QPSK).     

M-ary amplitude shift keying OFDM system

Coherent M-ary amplitude-shift keying (MASK) is proposed for use in orthogonal frequency-division multiplexing (OFDM) systems. The frequency separation between subcarriers is only 1/2T instead of 1/T. With a slightly wider bandwidth, an /spl radic/M-ary ASK OFDM can achieve the same bit-error rate (BER) of M-ary quadrature amplitude modulation (QAM) OFDM and a better BER than that of M-ary phase-shift keying (MPSK) OFDM. The /spl radic/M-ary ASK OFDM has the same peak-to-average-power ratio as that of the M-ary QAM OFDM. The MASK OFDM can be implemented digitally and efficiently by fast cosine transform and demodulated by inverse fast cosine transform. Comparisons show that implementation complexity is reduced for additive white Gaussian noise channels with the use of the new scheme.     

Robust channel estimation for OFDM systems with rapid dispersivefading channels

Orthogonal frequency-division multiplexing (OFDM) modulation is a promising technique for achieving the high bit rates required for a wireless multimedia service. Without channel estimation and tracking, OFDM systems have to use differential phase-shift keying (DPSK), which has a 3-dB signal-to-noise ratio (SNR) loss compared with coherent phase-shift keying (PSK). To improve the performance of OFDM systems by using coherent PSK, we investigate robust channel estimation for OFDM systems. We derive a minimum mean-square-error (MMSE) channel estimator, which makes full use of the time- and frequency-domain correlations of the frequency response of time-varying dispersive fading channels. Since the channel statistics are usually unknown, we also analyze the mismatch of the estimator-to-channel statistics and propose a robust channel estimator that is insensitive to the channel statistics. The robust channel estimator can significantly improve the performance of OFDM systems in a rapid dispersive fading channel     

Noncoherent diversity reception over Nakagami-fading channels

A method for computing the average bit-error probability of binary differential phase-shift keying (DPSK) and frequency shift-keying (FSK) signals transmitted over Nakagami asymptotically slow fading channels with postdetection diversity reception is presented to extend previously published results. The previously published results apply only for maximum ratio combining, i.e., with predetection combining, where phase coherency is necessary. The results for postdetection combining are derived with the explicit expressions for the most practical cases of independent channels and particular cases of correlated channels