Bit error rate performance of π/4-DQPSK in a frequency-selectivefast Rayleigh fading channel

The bit error rate (BER) performance of π/4-differential quadrature phase shift keying (DQPSK) modems in cellular mobile communication systems is derived and analyzed. The system is modeled as a frequency-selective fast Rayleigh fading channel corrupted by additive white Gaussian noise (AWGN) and co-channel interference (CCI). The probability density function of the phase difference between two consecutive symbols of M-ary differential phase shift keying (DPSK) signals is first derived. In M-ary DPSK systems, the information is completely contained in this phase difference. For π/4-DQPSK, the BER is derived in a closed form and calculated directly. Numerical results show that for the 24 kBd (48 kb/s) π/4-DQPSK operated at a carrier frequency of 850 MHz and C/I<20 dB, the BER will be dominated by CCI if the vehicular speed is below 100 mi/h. In this derivation, frequency-selective fading is modeled by two independent Rayleigh signal paths. Only one co-channel is assumed in this derivation. The results obtained are also shown to be valid for discriminator detection of M-ary DPSK signals     

Nonredundant error correction analysis and evaluation ofdifferentially detected π/4-shift DQPSK systems in a combined CCI andAWGN environment

The application of the nonredundant error correction (NEC) technique to the North American and Japanese digital cellular modulation standard, π/4-shift differential quadrature phase shift keying (DQPSK), in a combined additive white Gaussian noise (AWGN) and cochannel interference (CCI) environment is proposed, analyzed, and theoretically evaluated. The performance for NEC receivers with single, double, and triple error correction capability is theoretically analyzed and evaluated. For the CCI, the general model, which includes M statistical independent interferers also employing the π/4-shift DQPSK modulation format, is adopted. The theoretical symbol error probability versus carrier-to-noise ratio have been obtained with M and the carrier-to-interference ratio (C/I) as parameters. The results indicate significant performance improvements over conventional differentially detected systems. Some of the results have been verified by computer simulation. The gains offered by the NEC receivers increase as C/I decreases and/or M increases. Significant error floor reductions have been observed     

On the error rates of differentially detected narrowbandπ/4-DQPSK in Rayleigh fading and Gaussian noise

Closed-form formulas for the probability density function (PDF) and cumulative distribution function (CDF) of the differential phase of a phase-modulated carrier in Rayleigh-fading and correlated noise is derived and applied to evaluate the bit-error-rate (BER) of π/4-DQPSK and conventional DQPSK (differential quaternary phase-shift keyed) systems. Under very narrow IF band-limitation and at high SNR, the π/4-DQPSK outperforms the conventional DQPSK because the former has less spectral splatter during phase transitions between symbol. The performances of these two systems approach one another as the bandwidth parameter BT increases     

Digital frequency estimation in burst mode QPSK transmission

In burst digital transmission using PSK (phase shift keying) modulation with coherent detection, the recovery of the carrier reference phase and the symbol clock is a key aspect. If all users have a common clock synchronization, symbol timing needs not to be recovered in each burst. A digital processor for carrier recovery without preambles, in the presence of frequency offset, is considered. As an example, a 2 Mb/s QPSK transmission system is considered in which E _b/N_o=10 dB, and the burst and estimation interval length L=15. Using the algorithm described and averaging eight successive estimated frequency offsets, in order to eliminate anomalous errors, the BER (bit error rate) degradation is equal to 0.14 dB when Δf=20 kHz     

On the performance of DQPSK communication systems impaired bytiming error, mixer imbalance, and frequency nonselective slow Rayleighfading

In this paper, the error performance of the differential detection scheme is assessed for differentially encoded quaternary-phase-shift-keying (DQPSK) and π/4-shifted-DQPSK signals, It is assumed that the receiver suffers from mixer imbalance and timing error impairments. Expressions for the system bit-error rate (BER) are obtained when the channel is free of fading and when the channel suffers from frequency nonselective (flat) slow Rayleigh fading in the face of additive white Gaussian noise. To arrive at the desired expressions, the probability density function (pdf) of the phase angle between a pair of Gaussian random vectors is used to obtain the probability of bit error conditioned on the channel fading and timing error. The resulting expressions are then averaged over the nonnegligible timing error and the channel fading to arrive at the desired expressions for the system BER. Finally, with the aid of numerical analysis and in the presence of the aforementioned impairments, a number of conclusions are drawn and the performance of differential receivers for DQPSK and π/4-shifted-DQPSK modulation schemes are compared. It is shown here that the performance of a DQPSK receiver in the absence of fading and timing error is substantially impaired by mixer imbalance for BERs less than 10^-4. In the presence of fading, the performance is noticeably degraded due to mixer imbalance when a nonzero timing error is present     

An improved π/4-QPSK with nonredundant error correction forsatellite mobile broadcasting

An improved π/4-quadrature phase-shift keying (QPSK) receiver that incorporates a simple nonredundant error correction (NEC) structure is proposed for satellite and land-mobile digital broadcasting. The bit-error rate (BER) performance of the π/4-QPSK with NEC is analyzed and evaluated in a fast Rician fading and additive white Gaussian noise. (AWGN) environment using computer simulation. It is demonstrated that with simple electronics the performance of a noncoherently detected π/4-QPSK signal in both AWGN and fast Rician fading can be improved. When the K-factor (a ratio of average power of multipath signal to direct path power) of the Rician channel decreases, the improvement increases. An improvement of 1.2 dB could be obtained at a BER of 10^-4 in the AWGN channel. This performance gain is achieved without requiring any signal redundancy and additional bandwidth. Three types of noncoherent detection schemes of π/4QPSK with NEC structure, such as intermediate frequency band differential detection, baseband differential detection, and FM discriminator, are discussed. It is concluded that the π/4-QPSK with NEC is an attractive scheme for power-limited satellite land-mobile broadcasting systems     

Multiple differential detection of continuous phase modulationsignals

A sequence estimation algorithm for the differential detection of the continuous phase modulation (CPM) signals, yielding significant gains in BER performance and with considerable resistivity to fading, is introduced. These advantages, along with the reduced hardware complexity, low cost, and fast synchronization which characterize the differential detector, make the proposed receiver useful for land mobile radio and mobile-satellite communications. The new receiver is based on multiple differential detection. The multiple differential detection strategy provides the decoder with more information regarding the transmitted data and applies a noise decorrelation process on the received signal, useful to the sequence estimation. The algorithm is derived in a general form, and can be applied on any CPM scheme, with any degree of complexity. The authors have evaluated the receiver for two of the most popular CPM schemes, the tamed frequency modulation (TFM) and Gaussian minimum-shift keying (GMSK) (with B₁ T=0.25), in the presence of additive white Gaussian noise (AWGN) and Rician fading. The BER performance evaluation results indicated significant gains and considerable reduction of error floors. In AWGN improvements close to 9 dB have been verified     

Performance of π/4 SQAM in a hard-limited channel in thepresence of AWGN

A strategy that reduces the spectral spreading when an ideal hard-limiter is used as a first approximation to a fully saturated power amplifier is presented. This strategy combines superposed quadrature amplitude modulation (SQAM) filtering with the π/4-shift quadrature phase-shift keying (QPSK) digital transmission format adopted for the first generation of US digital cellular systems. Simulation results showed that this π/4 SQAM filtering strategy increased capacity by 35% in comparison to hard-limited π/4 QPSK. Using computer-aided design, a receive filter that would limit the degradation of E _b/N₀ to less than 1.4 dB at a bit error rate of P_e=10^-4 was selected     

On the design of FIR digital differentiators which are maximallylinear at the frequency π/p, p ∈ {positiveintegers}

Digital differentiators (DDs) which are maximally linear at the spot frequency ω=π/p, p ∈ {positive integers} are proposed for operation over a narrow band of frequencies. The suggested DDs, besides giving zero phase error over the entire band of frequencies (-π⩽ω⩽π), can achieve very high accuracy in the magnitude response, over a given frequency range, with attractively low order of structure. For example, for p=3, magnitude accuracy better than 99.999% can be achieved over the passband 0.26π⩽ω⩽0.41π with an order of structure of 21. Mathematical formulas for the weighting coefficients required in the design have also been given     

π/4-QPSK modems for satellite sound/data broadcast systems

The use of π/4 quadrature phase-shift keying(QPSK) modems for satellite sound broadcast systems (SSBS) broadcasting to mobile or portable receivers is proposed. Three different differential detectors (including the FM-discriminator followed by integrate-sample-and-dump filter) and a novel coherent detector are discussed. The degradation caused by the frequency offset between the local oscillator and the unmodulated carrier in the baseband differential detector is studied. The performance of both coherently and differentially detected π/4-QPSK in a Gaussian channel is also studied. It is shown that with a frequency offset of more than 3% of the symbol rate, the performance degradation is more than 1 dB at 10^-4. The out-of-band power of the nonlinearly amplified bandlimited π/4-QPSK signals is reduced from -13 dB to -37 dB if a 2-dB output back-off amplifier is used instead of a hardlimiter. The performance of the π/4-QPSK is equivalent to that of QPSK, although the π/4-QPSK has the advantage of less spectrum restoration after nonlinear amplification. The coherent demodulator and differential decoder avoid the three-level detection and achieve the same bit-error-rate (BER) performance as DEQPSK with a simple circuit     

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     

Bit error rate of binary and quaternary DPSK signals with multipledifferential feedback detection

A differentially coherent detection scheme with improved bit error rate (BER) performance is presented for differentially encoded binary and quaternary phase shift keying (PSK) modulation. The improvement is based on using L symbol detectors with delays of 1, 2, . . ., L symbol periods and on feeding back detected PSK symbols. Exact formulas for the bit error probability are derived for the case that correct symbols are fed back. The effect of symbol errors in the feedback path on the BER is determined by computer simulations     

Double series representation of bounded signals

Series representations of the form f(t)~Σ_n=-∞^∞Σ _k=-∞^∞a_n,kν(t-n)_e ^2πkts/ for bounded signals f(t) are studied, as are conditions on the unit function ν(t), such that coefficients a_n,k reveal the energy content of f(t) in the time interval n-(1/2)⩽t⩽n+(1/2) and frequency interval 2π(k-(1/2))⩽ω⩽2π(k+(1/2)). These conditions turn out to be orthogonality and integrability. Based on these conditions a number of properties of the expansion are derived, including summability of the double series and energy and power estimations. Some examples of the expansion are presented     

Spectral efficiency of optical FDM systems impaired by phase noise

The required frequency spacings between channels in an optical frequency division multiplexing (FDM) network are considered. The minimum permissible spacings consistent with meeting bit error rate (BER) objectives are derived. The assumed transmission uses on-off keying (OOK), at a data rate 1/T (in bits per second), via external modulation of a laser source having linewidth β (in hertz). The assumed receiver consists of an optical channel selection filter followed by a p-i-n photodiode and a postdetection integrate-and-dump circuit. The analysis estimates the adjacent channel interference (ACI)-induced floor on BER for the middle of three FDM channels, as a function of frequency spacing and linewidth-to-bit rate ratio (βT). For BER=10^-9 and βT ranging from 0.32 to 5.12, the required channel spacing ranges from 5.2 to 27.5 bit rates. The multiplying factors associated with using (wide-deviation) frequency shift keying (FSK), coherent (heterodyne) detection, and infinitely many FDM channels, respectively, are estimated to be 2.0, at most 3.0, and at most 1.37     

Continuous phase quadrature phase shift keyed signaling techniquewith coding

A continuous phase quadrature phase shift keyed (CPQPSK) modulation technique is presented. This method utilizes a conventional QPSK modulator and a phase trajectory converter to approximate M=4, h=1/4 continuous phase signal and allows low cost, low complexity, and high rate (>1 Gbit/s) CPM modem implementation for bandwidth efficient transmission through nonlinear satellite channels. Using a communications analysis computer program it has been found that CPQPSK has 99 percent out-of-band power of 0.8R (MSK has 99 percent out-of-band power of 1.2 R where R is defined as bit rate), continuous phase trajectories, and nearly constant envelope amplitude. Simulation of realistic hardware designs indicate that the CPQPSK will require an Eb/No of 14 dB to achieve a bit error rate (BER) of 10^-6. Forward error correcting techniques using block codes with an overhead of 10 percent indicate that the Eb/No requirements can be reduced to 11.2 dB for 10^-6 BER     

Error probability of M-ary FSK with differential phasedetection in satellite mobile channel

Formulas are derived for the error probability of M-ary frequency shift keying (FSK) with differential phase detection in a satellite mobile channel. The received signal in this channel is composed of a specular signal, a diffuse signal, and white Gaussian noise; hence, the composite signal is fading and has a Rician envelope. The error probability is shown to depend on the following system parameters: (1) the signal-to-noise ratio; (2) the ratio of powers in the specular and diffuse signal components; (3) the normalized frequency deviation; (4) the normalized Doppler frequency; (5) the maximum normalized Doppler frequency; (6) the correlation function of the diffuse component, which depends on the normalized Doppler frequency and the type of the antenna; (7) the number of symbols; and (8) the normalized time delay between the specular and diffuse component (t _d/T) where 1/T is the symbol rate. Except for T_d/T, all normalized parameters are the ratios of the parameter value and symbol rate. The Doppler frequency depends on the velocity of the vehicle and the carrier frequency. The error probability is computed as a function of the various parameters. The bit error probability is plotted as a function of signal-to-noise ratio per bit and other system parameters     

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     

Simulation of bit error performance of FSK, BPSK, and π/4 DQPSKin flat fading indoor radio channels using a measurement-based channelmodel

The results of a simulation study that provides insight into the simulation methodology and bit error rate (BER) performance of frequency-shift keying (FSK), binary phase-shift keying (BPSK), and π/4 differential phase-shift keying (π/4 DQPSK) in flat fading channels inside open plan buildings are presented. A detailed measurement-based propagation channel model, SIRCIM (simulation of indoor radio channel impulse response models), which generates over 1000 closely spaced baseband equivalent complex impulse responses for a mobile radio operating at 1.3 GHz and traveling over a 1-m path, is used. The small-scale channel model, the communication system models used in the analysis and the methods used to predict BER are described. The channel simulator and the systems models have been thoroughly tested, and results from average instantaneous BER simulations are shown. The BER performances of the modulation techniques are presented. It is found that BPSK offers between a 2.8-dB and 3.0-dB improvement over π/4 DQPSK, although the latter offers a 3-dB increase in capacity for a given spectrum allocation     

Closest coset decoding of |u|u+v| codes

The general concept of closest coset decoding (CCD) is presented, and a soft-decoding technique for block codes that is based on partitioning a code into a subcode and its cosets is described. The computational complexity of the CCD algorithm is significantly less than that required if a maximum-likelihood detector (MLD) is used. A set-partitioning procedure and details of the CCD algorithm for soft decoding of |u|u+v| codes are presented. Upper bounds on the bit-error-rate (BER) performance of the proposed algorithm are combined, and numerical results and computer simulation tests for the BER performance of second-order Reed-Muller codes of length 16 and 32 are presented. The algorithm is a suboptimum decoding scheme and, in the range of signal-to-noise-power-density ratios of interest, its BER performance is only a few tenths of a dB inferior to the performance of the MLD for the codes examined