Binary PRCPM with differential phase detection and maximal ratiocombining diversity in fading channels

We derive a formula for the bit-error probability (BEP) of binary partial-response continuous-phase modulation (PRCPM) with N-bit differential phase detection (DPD) in a Rician fading channel subject to L-branch maximum ratio combining (MRC) diversity. We compute the BEP for minimum-shift keying (MSK), Gaussian MSK (GMSK), and 2 RC (2-b-duration raised cosine) frequency signals as a function of the energy-to-noise ratio per bit E_b/N₀ and other system and channel parameters [N=1 and 2 and L=1, 2, and 3, Rician factor K=-∞, 0, 6, 10, and ∝ dB, Doppler frequency shift f_DT=0, 0.01, and 0.02, Gaussian premodulation filter bandwidth B_gT=∞, 0.5, 0.25, and the presence or absence of a Doppler frequency tracking loop (DFTL) in the receiver]. In all cases, the BEP is significantly reduced by diversity     

Narrowband M-ary DPSK-DPD with L-diversity maximum ratio combining in Rician fading channels

In this paper the bit error probability (BEP) of narrowband M-ary differential phase shift keying with differential phase detection (MDPSK-DPD) and maximum ratio combining (MRC) in Rician fading channels is computed. Two systems shall be investigated. In the first system the transmitted pulse is a Nyquist pulse with bandwidth B = R(1 + β), where R is the symbol rate and 0 ≤ β ≤ 1 is the roll-off and the receiver is matched to the transmitter. In the second system the shaping pulse is a rectangle of duration T = 1/R modified by narrowband Butterworth filters in the transmitter and receiver. The fading channel is both time selective with Doppler frequency shifts of f_DT = 0, 0·01, 0·02 and frequency selective with time delays of t_d/T = 0, 0·1, 0·2. The number of diversity channels is L = 1, 2, 3 and the Rician factor is K = 0, 1, 6 dB, 10, ∞, thus the whole range between Rayleigh and Gaussian channels is covered. © 1997 John Wiley & Sons, Ltd.     

The effect of pulse shaping and transmitter filter on theperformance of FSK-DPD and CPM-DPD in satellite mobile channel

This paper investigates how a bandlimiting transmitter filter and the shape of the frequency pulse effect the bit-error probability of frequency shift keying with differential phase detection in satellite mobile channel. Numerical results are presented for the case when the transmitter and receiver filters are Butterworth filters of order N_T=4 and N_R=3, respectively, and the frequency shaping pulse is rectangular or raised cosine. It is shown that in all cases of practical interest, continuous phase modulation (with raised cosine pulse shaping) gives a lower bit-error probability and requires less bandwidth than frequency-shift keying (with rectangular pulse shaping) when all other parameters (number of symbols, Rician factor of the channel, order of filters, etc.) are the same     

Bit error probability for MDPSK and NCFSK over arbitrary Ricianfading channels

In this paper, we analyze the bit error probability (BEP) of binary and quaternary differential phase shift keying (2/4 DPSK) and noncoherent frequency shift keying (NCFSK) with postdetection diversity combining in arbitrary Rician fading channels. The model is quite general in that it accommodates fading correlation and noise correlation between different diversity branches as well as between adjacent symbol intervals. We show that the relevant decision statistic can be expressed in a noncentral Gaussian quadratic form, and its moment generating function (MGF) is derived. Using the MGF and the saddle point technique, we give an efficient numerical quadrature scheme to compute the BEP. The most significant contribution of the paper, however, lies in the derivation of a closed-form cumulative distribution function (cdf) for the decision statistic. As a result, a closed-form BEP expression in the form of an infinite series of elementary functions is developed, which is general and unifies previous published BEP results for 2/4 DPSK and NCFSK for multichannel reception in Rician fading. Specialization to some important cases are discussed and, as a byproduct, a new and general finite-series expression for the BEP in arbitrarily correlated Rayleigh fading is obtained. The theory is applied to study 2/4 DPSK and NCFSK performance for independent and correlated Rician fading channels; and some interesting findings are presented     

Error rate analysis of differentially encoded and detected 16APSKunder Rician fading

Mobile radio systems require highly bandwidth efficient digital modulation schemes because of the limited resources of the available radio spectrum. A theoretical analysis of bit error rate (BER) is presented for the differential detection of differentially encoded 16-level amplitude/phase shift keying (16DAPSK) under Rician fading in the presence of Rayleigh faded co-channel interference (CCI) and additive white Gaussian noise (AWGN). Differential detection comprises eight-level differential phase detection (DPD) and two-level amplitude ratio detection (ARD). Exact expressions for probability distributions of differential phase noise and amplitude ratio are derived for the BER calculation. The calculated BER performance of 16DAPSK is presented for various values of Rician fading K factor, Doppler spread of diffused component, and Doppler shift of the specular component, and is compared with that of 4-16DPSK. It is shown that 16DAPSK is superior to 16DPSK and requires 1.7 (1.6) dB less E_b/N₀ (SIR) at BER=10^-3 in Rician channels with K=5 dB     

Error Performance of DQPSK with EGC Diversity Reception over Fading Channels

This paper derives the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with postdetection equal gain combining (EGC) diversity reception over independent and arbitrarily correlated fading channels. First, using the associated Legendre functions, the average BEP of DQPSK is analyzed over independent Rayleigh, Nakagami-m, and Rician fading channels. Finite-series closed-form expressions for the average BEP of DQPSK over L-branch independent Rayleigh and Nakagami-m fading channels (for integer Lm) are presented. Besides, a finite-series closed-form expression is given for the average BEP of differential binary phase shift keying (DBPSK) with EGC over independent Rician fading channels. Second, an alternative approach is propounded to study the performance of DQPSK over arbitrarily correlated Nakagami-m and Rician fading channels. Relatively simple BEP expressions in terms of a finite sum of a finite-range integral are proposed. Moreover, the penalty in signal to noise ratio (SNR) due to arbitrarily correlated channel fading is also investigated. Finally, the accuracy of the results is verified by computer simulation.     

Differential phase shift keying in two-path Rayleigh channel withadjacent channel interference

A formula is derived for the error probability of M-ary differential phase-shift keying with differential phase detection in a two-path Rayleigh fading channel taking into account adjacent channel interference (ACI), cochannel interference (CCI), intersymbol interference (ISI), and Doppler frequency shift. Square-root Nyquist filters are used with roll-off, β, the transmitter and receiver as in the proposed US digital mobile radio system. The presence of the second path has a profound effect on increasing the bit error probability (BEP) because it causes ISI. In the absence of ISI, ACI has a smaller effect on BEP than CCI. In the presence of ISI their effect is essentially the same. For a given bit energy-to-noise ratio, the binary system has the lowest BEP; however, the bit rate is also the lowest for a given bandwidth. When the main interference is ACI or CCI, a quaternary system has a lower BEP than the octal system. When the main interference is ISI, this is reversed     

Differential Space-Time Modulation Using DAPSK Over Rician Fading Channels

This paper studies differential space-time modulation using diversity-encoded differential amplitude and phase shift keying (DAPSK) for the multiple-input multiple-output (MIMO) system over independent but not identically distributed (inid) time-correlated Rician fading channels. An asymptotic maximum likelihood (AML) receiver is developed for differentially detecting diversity-encoded DAPSK symbol signals by operating on two consecutive received symbol blocks sequentially. Based on Beaulieu’s convergent series, the bit error probability (BEP) upper bound is analyzed for the AML receiver over inid time-correlated Rician fading channels. Particularly, an approximate BEP upper bound of the AML receiver is also derived for inid time-invariant Rayleigh fading channels with large received signal-to-noise power ratios. By virtue of this approximate bound, a design criterion is developed to determine the appropriate diversity encoding coefficients for the proposed DAPSK MIMO system. Numerical and simulation results show that the AML receiver for diversity-encoded DAPSK is nearly optimum when the average received signal-to-noise power ratios are high and the channel is heavily correlated fading and can provide better error performance than conventional noncoherent MIMO systems when the effect of non-ideal transmit power amplification is taken into account.     

Multicarrier 16QAM transmission with diversity reception

A 96 multicarrier 16QAM transmitter and a diversity receiver for 3.072 Mbit/s data transmission are described. Pilot symbol aided (PSA) coherent detection is applied. A laboratory experiment demonstrates that an irreducible bit error rate (BER) of 10^-3 can be achieved at the RMS delay spread τ_rms=6.3 μs under frequency selective Rayleigh fading when two branch maximal ratio combining (MRC) diversity is used     

Performance of four-dimensional digital communication system infading channels

The authors derive a formula for the bit-error probability (BEP) of a four-dimensional signal and coherent but simple detector in fading channels with Rician or Nakagami probability density function for the received signal envelope. They compute the BEP in both cases and show its dependence on the energy-to-noise ratio per bit, E_b/N_o and channel parameters, K and m, respectively     

Combined effects of phase sweeping transmitter diversity andchannel coding

A novel transmitter diversity scheme that generates forced fading to improve the performance of channel coding is proposed and investigated. Since the required phase sweeping frequency is much smaller than the transmission bit rate, bandwidth expansion is negligible. A sinusoidal phase sweeping function ΔΘ sin(2πf_Ht) is employed in laboratory experiments using 32 kbit/s quarternary differential phase shift keying (QDPSK) with differential detection and BCH(23,12) code. It is shown that ΔΘ=200° and f_H=67 Hz can be used when m (interleaving depth)=10 b. Hence, excessively long interleaving is not required by the use of transmitter diversity. Under very slow Rayleigh fading (f_D=1 Hz), a measured improvement of 4.8 dB is obtained at a word error rate of 10^-2 without receiver diversity. Applications include paging systems that require very simple receivers     

Analysis of differentially coherent linear receivers over Rician-faded CDMA channels

RicianAccurate performance analysis for linear receivers over frequency- and time-selective asynchronous code-division multiple-access Rician-fading channels is very useful and a general approach to this topic is very desirable. In this paper, by using a decision variable-based moment generating function approach, we provide a unified bit-error probability (BEP) analysis framework for different linear detectors with binary or quaternary differential phase-shift keying and postdetection combining over Rician-fading channels, taking into account the effects of the spreading code correlation, the system and fading-channel parameters, diversity combining, and branch correlation. To reduce the complexity of the exact BEP evaluation, we furthermore provide an approximate multivariate Gaussian assumption (MGA)-based method which entails a low complexity for BEP evaluation. Ideal and approximate linear minimum mean-squared error diversity receivers for correlated Rician-fading channels are proposed. Numerical results show that the phases of the line-of-sight (LOS) components of the desired user significantly affect the receiver performance over correlated multipath Rician channels, and this may be exploited to improve performance. Also, when the LOS components are affected by a significant Doppler shift, automatic frequency control is very useful in improving the receiver performance.     

Performance of Single and Multichannel Coherent Reception under Rician Fading

In the present work, simple closed-form series solutions for the average error rate of several coherent modulation schemes such as, binary phase shift keying (BPSK), binary frequency shift keying (BFSK), differential binary phase shift keying (DBPSK), quadrature phase shift keying (QPSK), offset-QPSK, minimum shift keying (MSK), and square M-ary quadrature amplitude modulation (M-QAM), operating over frequency non-selective slow Rician fading channel and corrupted by additive white Gaussian noise (AWGN) are derived. Further, to improve the link quality, receiver antenna space diversity is considered, where multiple independent and identically distributed (i.i.d.) as well as uncorrelated signal replicas are combined before successive demodulation. The proposed linear predetection combiner follows optimum maximal ratio combining (MRC) algorithm. Starting from a novel unified expression of conditional error probability the error rates are analysed using probability density function (pdf) based approach. The derived end expressions, consisting of rapidly converging infinite series summations of Gauss hypergeometric function, are accurate, free from any numerical integration and general enough, as it encompasses as special situations, some cases of non-diversity, non-fading AWGN and Rayleigh fading. Symbol or, bit error probabilities (SEP/BEP) are graphically displayed against signal to noise ratio (SNR) per bit per channel for all the digital modulation schemes stated above with different values of diversity order L and varying values of the channel specular-to-scatter ratio or, the Rician parameter K, as found from the measured statistics of mobile and indoor wireless channels. In addition, to examine the dependence of error rate performance of M-QAM on the constellation size M, numerical results are plotted for various values of M. Selected simulation results are also provided to verify the analytical deductions. The series solutions presented in current text realize a trade-off between precision and complexity and offers valuable insight into the performance evaluation over a fading channel in a unified manner.     

Performance of multi-bit differential SQAM in mobile radio channel

A new multi-bit DSQAM (differential superposed quadrature amplitude modulation) for use in bandwidth and power limited digital mobile radio is proposed. A DSQAM signal is generated by a differentially encoded SQAM processor, and is detected by a multi-bit differential receiver combined with a soft decision Viterbi decoder. The simulated BER result shows that, in an AWGN channel, a 5 bit DSQAM modem achieves a 7.2 dB E_b/N₀ improvement over a conventional 1 bit differential receiver. In Rician fading channels, DSQAM demonstrates a high degree of robustness suffering only a minor loss of signal     

A digital coherent receiver suitable for land-mobile satellitecommunications

Describes an advanced coherent demodulation technique suitable for land-mobile satellite communications. The proposed technique features a combined narrow/wide band dual open loop (DOL) carrier phase estimator, which effectively enables the coherent receiver to track fast phase fluctuations caused by fading, without degradation in phase slip characteristics. Additionally, an open loop phase estimator has inherent quick recovery performance. Its bit error rate (BER) performance is shown to be superior to that for existing detection schemes, achieving a 10^-2 BER at 6.3 dB E_b/N₀ (0.9 dB greater than the theoretical E_b/N₀ condition for perfect carrier phase tracking) for QPSK over a Rician fading channel with the 10 dB Rician factor and the 1/16 baud rate fading pitch. The paper also describes a quick bit timing recovery scheme, with interpolation, featuring an open loop structure. Further, it presents an experimental digital modem developed through the use of digital signal processors     

A new carrier recovery circuit for land mobile satellitecommunication

A DCF (dual carrier filter) reverse-modulation-type carrier recovery circuit is proposed to achieve a low carrier skipping rate and satisfactory phase tracking performance for coherent detection of PSK (phase shift keying) signals in fast Rician fading channels. The proposed scheme employs both narrow and wide bandwidth carrier filters simultaneously for the reverse-modulation-type carrier recovery circuit. It is clarified by computer simulation that the Pe performance of a QPSK (quadriphase shift keying) modem employing the proposed scheme shows an improvement of 1.5 dB in required E_s/N_O at Pe=10⁴ (after Viterbi decoding (R=7/8, K=7), C/M (direct-to-multipath signal power ratio)=10 dB, interleaving size=64×64), compared with conventional coherent detection employing the reverse modulation tank-limiter scheme or the Costas loop scheme     

Performance of asynchronous DS-CDMA using a maximal ratio combiningdiversity over a Rician fading channel

The final closed-form expression for bit error probability (BEP) is presented for a DS-CDMA system using a maximal ratio combining (MRC) diversity over a Rician fading channel. The accuracy of the BEP estimate evaluated by this expression is verified by comparison with a semi-analytic simulation result. The effect that diversity order has on the BEP is also considered for typical multipath delay profiles with different Rician ratios     

Error probability for coherent and differential PSK over arbitraryRician fading channels with multiple cochannel interferers

This paper discusses the performance of communication systems using binary coherent and differential phase-shift keyed (PSK) modulation, in correlated Rician fading channels with diversity reception. The presence of multiple Rician-faded cochannel users, which may have arbitrary and nonidentical parameters, is modeled exactly. Exact bit error probability (BEP) expressions are derived via the moment generating functions (MGFs) of the relevant decision statistics, which are obtained through coherent detection with maximum ratio combining for coherent PSK modulation, and differential detection with equal gain combining (EGC) for differential modulation. Evaluating the exact expressions requires a complexity that is exponential in the number of interferers. To avoid this potentially time-consuming operation, we derive two low-complexity approximate methods each for coherent and differential modulation formats, which are more accurate than the traditional Gaussian approximation approach. Two new and interesting results of this analysis are: (1) unlike in the case of Rayleigh fading channels, increasing correlation between diversity branches may lead to better performance in Rician fading channels and (2) the phase distribution of the line-of-sight or static fading components of the desired user has a significant influence on the BEP performance in correlated diversity channels     

Adjacent-Channel and Quadrature-Channel Interference in Minimum Shift Keying

In this paper we present formulas for the computation of error probability in the presence of quadrature-channel or adjacentchannel interference in addition to intersymbol interference in a minimum shift keying system. The filters in the receiver and transmitter are arbitrary but with a finite number of poles. The effect of phase jitter in the main channel, phase and symbol timing misalignment in the interfering channels, and sampling time jitter is taken into account. The probability of error is averaged over the phase and symbol timing misalignment. Numerical results are presented for Butterworth filters in the receiver and transmitter with two, three, and four poles. Curves of error probability as a function of various variables (signal-to-noise ratio, bandwidth of receiver and transmitter filters, number of poles, channel frequency separation, phase jitter, sampling time, and symbol timing and phase misalignment) are presented. The method of this paper can readily be applied to other filters; hence, it can be used in the design and prediction of the performance of digital communication systems.     

Asymptotic analysis of multi‐branch EGC and SC over equally correlated Rician channels

Closed‐form asymptotic expressions for bit error rate and outage probability are derived for multi‐branch equal gain combining and selection combining receiver diversity over equally correlated Rician channels. Numerical results indicate that these analytical solutions can provide accurate estimation of bit error rate and outage probability in large signal‐to‐noise ratio regimes. The analytical results reveal some important insights into the performance characteristics of equal gain combining and selection combining diversity operating over equally correlated Rician fading channels. Copyright © 2013 John Wiley & Sons, Ltd.