Effect of Noisy Phase Reference on Coherent Detection of Offset-QPSK Signals

Imperfect carrier synchronization causes a performance loss for coherent phase-shift-keyed (PSK) communications. This detection loss is greater for quaternary signaling (QPSK) than for the binary case (BPSK). The use of an offset form of QPSK, also known as double-biphase modulation, is shown to yield a probability of bit error in detection that is equal to the average of the detection performances for BPSK and conventional QPSK. Because of frequency instabilities in communications systems, it is sometimes difficult to obtain carrier synchronization with sufficiently low jitter to preclude significant detection losses. The use of offset QPSK in lieu of conventional QPSK modulation is shown to lower by almost 3 dB the required SNR of the synchronizer phase reference for satisfying a specified value of allowable detection loss.     

A bit error probability analysis of a digital PLL based demodulatorof differentially encoded BPSK and QPSK modulation

Presents a bit error probability analysis of a digital phase-locked loop based demodulator, of differentially encoded BPSK and QPSK modulations. Differential decoding is a method of resolving a phase ambiguity, typical of fully modulated signals, that uses two consecutive demodulated symbols to estimate the information symbols. The effects of a noisy phase reference on demodulator performance are well documented for uncoded modulations (single symbol demodulation). The paper investigates performance for phase reference time variations between the two symbols. The time varying reference investigated is produced by a digital phase-locked loop. The noisy phase reference has negligible additional effect on the bit error probability for differentially encoded BPSK and QPSK     

Decision-directed burst-mode carrier synchronization techniques

A decision-directed, digitally implemented carrier synchronizer for channels with both frequency and phase uncertainty is presented. This combined algorithm and its derivatives are analyzed with respect to the achievable carrier acquisition time and the resulting bit error probability. For certain data rates (approximately 50 MSps or less), this algorithm can be implemented using CMOS gate array technology. As examples BPSK and QPSK modulation formats are studied herein and compared to their differentially coherent counterparts of DPSK and DQPSK     

Performance analysis of generalized-faded coherent PSK channels with equal-gain combining and carrier phase error

A new method is developed to analyze the performance of partially coherent PSK systems in wireless channels with equal-gain combining diversity receiver. Two performance criteria are considered: the average bit error probability and the probability distribution of the combiner SNR (SNR reliability). Tikhonov-distributed phase error processes are assumed and generalized fading channels including Rayleigh, Rician, and Nakagami-m are investigated. We evaluate the detection loss suffered by the carrier recovery for different SNR reliability levels when BPSK and QPSK systems are used in wireless channels. The analysis is based on a convergent infinite series for the distribution of the sum of random variables. The convergence rate of the proposed series is investigated and the analytical results are presented along with providing results obtained by simulation.     

Probability of error calculation of OFDM systems with frequencyoffset

Orthogonal frequency-division multiplexing (OFDM) is sensitive to the carrier frequency offset (CFO), which destroys orthogonality and causes intercarrier interference (ICI), Previously, two methods were available for the analysis of the resultant degradation in performance. Firstly, the statistical average of the ICI could be used as a performance measure. Secondly, the bit error rate (BER) caused by CFO could be approximated by assuming the ICI to be Gaussian. However, a more precise analysis of the performance (i.e., BER or SER) degradation is desirable. In this letter, we propose a precise numerical technique for calculating the effect of the CFO on the BER or symbol error in an OFDM system. The subcarriers can be modulated with binary phase shift keying (BPSK), quaternary phase shift keying (QPSK), or 16-ary quadrature amplitude modulation (16-QAM), used in many OFDM applications. The BPSK case is solved using a series due to Beaulieu (1990). For the QPSK and 16-QAM cases, we use an infinite series expression for the error function in order to express the average probability of error in terms of the two-dimensional characteristic function of the ICI     

载波相位误差对解调性能的影响分析

对MPSK、QAM信号载波相位误差对于解调性能的影响进行了定量分析,推导给出了载波估计方差较小时BPSK、QPSK信号载波相位误差对解调性能影响的表达式。根据定量分析结果,载波估计方差较小时对BPSK、QPSK信号载波估计方差与误码率的关系进行了仿真,仿真结果和理论分析结果是一致的。结果表明在Es/N0为2、载波估计方差小于1×10-2的情况下,载波相位误差对于解调性能的影响小于0.2 dB。     

Approximate results for the bit error probability of binary phaseshift keying with noisy phase reference

Approximate results for the bit error probability (BEP) of binary phase shift keying (BPSK) in the presence of a noisy carrier phase reference are presented. The results show correctly the behavior or the BEP as a function of SNR. The accuracy of the approximations is verified by simulations and numerical integration of the BEP formulas. The results are compared with existing bounds     

Simplified bit error rate evaluation of Nagakami‐m PSK systems with phase error recovery

An efficient analytical and simulation techniques were developed to analyze the bit error rate of PSK Nakagami‐m fading systems with imperfect carrier recovery. We evaluate the detection loss due to the carrier recovery for different rms phase error values when coherent BPSK and QPSK systems are used in wireless channels. Our results are useful in designing practical systems and will enable designers to determine the phase precision of PSK systems in wireless environments. Copyright © 2010 John Wiley & Sons, Ltd.     

On the performance of rate 1/2 convolutional codes with QPSK onRician fading channels

Consideration is given to the bit error probability performance of rate 1/2 convolutional codes in conjunction with quaternary phase shift keying (QPSK) modulation and maximum-likelihood Viterbi decoding on fully interleaved Rician fading channels. Applying the generating function union bounding approach, an asymptotically tight analytic upper bound on the bit error probability performance is developed under the assumption of using the Viterbi decoder with perfect fading amplitude measurement. Bit error probability performance of constraint length K=3-7 codes with QPSK is numerically evaluated using the developed bound. Tightness of the bound is examined by means of computer simulation. The influence of perfect amplitude measurement on the performance of the Viterbi decoder is observed. A performance comparison with rate 1/2 codes with binary phase shift keying (BPSK) is provided     

Effects of Jitter and Cycle Slipping of Phase Reference Upon Unique Word Missed Detection in QPSK Systems

The effects of phase jitter and cycle slipping of the recovered carrier upon unique word (UW) missed detection in QPSK systems are investigated. Schrempp et al. have already presented the relationship between the UW missed detection probability (UWMP) and the bit error probability, which is simple and useful as long as the phase reference is noiseless. However, when the authors recently made some theoretical and experimental assessments of UW missed detection, they found that the above disturbances of the recovered carrier significantly affected the UW missed detection performance. Specifically, the actual UWMP was often worse than that predicted hy Schrempp et al. In fact, a bottoming effect takes place in the UWMP versus UW length characteristic. In this paper, after obtaining the conditional symbol and bit error probabilities for the recovered carrier with some phase error, we discuss the nature of phase fluctuation and cycle slipping for the recovered carrier. Consequently, we derive general expressions for the UWMP in both CPSK and DCPSK transmissions. The UWMP's are numerically calculated, and are then compared to our experimental data.     

Integrated Balanced BPSK and QPSK Modulators for the Ka-Band

Microwave integrated circuit (MIC) balanced biphase-shift-keying (BPSK) and quadri-phase-shift-keying (QPSK) modulators have been achieved in the 27-GHz band. The modulators are fabricated using a combination of microstrip lines and slot lines, viz., tow-sided MIC. The diodes used are beam-lean Schottky-barrier diodes. Balanced BPSK modulation is performed by path-switching and mode transformation from the slot line to microstrip lines. The insertion loss is 2.2 dB at a carrier frequency of 27 GHz. The phase error and the amplitude deviation are less than 1° and 0.5 dB, respectively. The QPSK modulator consists of two BPSK modulators, a power divider, and a branch-line hybrid coupler. The configuration of the modulator is the parallel-connected type. The insertion loss is 6.3 dB at a carrier frequency of 27 GHz. The phase error is less than 2°, and the rise time and fall time of the modulated earner are less than 300 ps. The isolation between the carrier input port and the QPSK modulated earner output port is greater than 25 dB. These modulators can be extended to the millimeter-wave band.     

基于商业零中频芯片的BPSK/QPSK解调器设计

提出基于商业零中频芯片MAX2837的BPSK/QPSK解调器设计,详细分析了零中频芯片MAX2837的特性、AGC环路、载波同步及位同步环路的设计.工程实测结果表明:该系统在误比特率为10-5时,解调损耗约2.5 dB,完成系统设计要求;该系统集成度高、体积小、重量轻、成本低.     

Intersymbol interference effects on BPSK and QPSK carrier trackingloops

The tracking performance of three conventional carrier tracking loops in the presence of intersymbol interference (ISI) is analyzed. The closed-form expressions for the squaring losses of BPSK (binary phase-shift-keyed) low-SNR (signal-to-noise ratio), BPSK high-SNR, and QPSK (quaternary phase-shift-keyed) low-SNR loops are derived. ISI is shown to affect the BPSK high-SNR loop as much as the I-Q loop despite the nonlinear effect of the hard-limiter. For the QPSK carrier tracking loop, the degradation is shown to be greater due to the modulation of both components of the carrier. In this case, ISI, in addition to modifying the coefficients in the squaring loss, adds a new term not present in wideband channels. In all cases, a unity squaring loss could not be achieved because of the irreducible error due to pattern noise. This noise is only present in band-limited channels and is dependent on the data model used     

Signaling Performance Over a Piecewise Linear Limited Channel in the Presence of Interference and Gaussian Noise

Presented here are a model and the analysis for evaluating bit error probability of a BPSK signal transmitted through a band-limited piecewise linear (PWL) limited satellite channel subject to continuous wave (CW) interference as well as additive Gaussian noise. The CW interference is assumed to have a random phase over (0, 2pi) and a fixed frequency fjwhich may be either in or out of the signal band. The analysis is carried out by first formulating a conditional error probability on the uplink channel noise and the CW interference phase and then averaging over the appropriate random variables through conventional Gaussian quadrature formulas and the moment technique used in [2]. Numerical results for the error rate performance are compared to those of hard-limited channels. The results indicate that a PWL limited channel outperforms a hard-limited channel when the out-of-band CW interference power is close to or greater than the desired signal.     

Analytical Study on the Effect of Cochannel Interference on Partially Coherent Diversity Systems

In this paper, we study the effect of cochannel interference (CCI) on the performance of partially coherent BPSK and QPSK in uncorrelated L-branch equal-gain combining systems. We consider a generalized propagation model wherein the desired and interfering signals undergo Nakagami-m or Rician fading with different amounts of fading severity. Further, the interfering signals are assumed to be asynchronous symbol timing with the desired signal, so that the effect of cross-signal intersymbol interference (ISI) is taken into account. Using a convergent Fourier series method, we derive extensive analytical results for the average bit error probability and the SNR gain penalty caused by the interference signals for different signal to-interference ratio levels. The numerical results presented in this paper demonstrate the system performance under very realistic propagation and detection conditions including CCI, carrier phase error recovery, cross-signal ISI, generalized fading channels, and AWGN. Hence our results are expected to be of significant practical use for such scenarios.     

Study of behavior of digital modulations for beam steerable reflectarray antennas

This paper investigates the bit error rate (BER) performance of digital modulations in a system with a scanning reflectarray antenna. A reflectarray causes intersymbol interference (ISI) in a digitally modulated signal, its phase shifters' phase errors cause signal distortion, and its phase shifters' phase transient causes beam pattern degradation during direction switching. In this paper, composite signal models of the reflectarray are established for both static and transient states. Due to different feed-to-element distances and the element-to-observation distances, different delays exist in signal components. These delays cause ISI whose effect is analyzed and evaluated. Effects of phase shifters' phase errors and phase transient during beam switching are also analyzed and evaluated. Numerical calculations and simulations are performed. The analytical and simulation results for an example reflectarray at f/sub c/=26.5 GHz and bit rate of 1.325 Gbps show that the BER degradation due to ISI is proportional to the symbol rate and the loss ranges from about 1 dB to around 2 dB in E/sub b//N/sub o/, depending on original E/sub b//N/sub o/, for BPSK, QPSK, 8PSK, and 16QAM. The phase error effect is negligible for lower order modulations and is unacceptable for higher order modulations such as 64QAM and 256QAM. The degradation due to phase transient effect is about 2 dB for BPSK and QPSK.     

Error Probability Performance of Unbalanced QPSK Receivers

A simple technique for calculating the error probability performance and associated noisy reference loss of practical unbalanced QPSK receivers is presented. The approach is based on expanding the error probability conditioned on the loop phase error φ in a power series in φ and then, keeping only the first few terms of this series, averaging this conditional error probability over the probability density function of φ. Doing so results in an expression for the average error probability which is in the form of a leading term representing the ideal (perfect synchronization references) performance plus a term proportional to the mean-squared crosstalk. Thus, the additional error probability due to noisy synchronization references occurs as an additive term proportional to the mean-squared phase jittersigma_{phi}^{2}directly associated with the receiver's tracking loop. Similar arguments are advanced to give closed-form results for the noisy reference loss itself.     

An Exact Error Probability Analysis of OFDM Systems with Frequency Offset

In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for orthogonal frequency division multiplexing (OFDM) systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in additive white Gaussian noise (AWGN), frequency flat and frequency selective Rayleigh fading channels. The BER/ SER performances of BPSK and QPSK modulation schemes are analyzed for AWGN and frequency-flat Rayleigh fading channels while BPSK is considered for frequency-selective Rayleigh fading channels. Our results can easily be reduced to the respective analytical error rate expressions for the OFDM systems without CFO error. Furthermore, the simulation results are provided to verify the accuracy of the new error rate expressions.     

基于LDPC码的无线光通信副载波误码性能分析

为了研究信道编码技术对无线光通信副载波系统差错性能的影响,基于无线光通信链路噪声特性,建立了大气信道等效数学模型。采用低密度奇偶校验(LDPC)码作为信道编码方式引入无线光通信,在不同光强闪烁指数下对基于副载波相移键控调制无线光通信系统进行了差错性能仿真,比较分析了LDPC编码前后副载波调制系统的误比特率,并对二相相移键控及四相相移键控两种系统进行了对比。结果表明,副载波二相相移键控调制系统的差错性能优于四相相移键控系统,同时LDPC码在弱湍流信道具有优越的纠错能力,可以获得比未编码系统较高的编码增益,在无线光通信领域具有一定的应用价值。     

Physical‐layer network coding with limited feedback using orthogonal space–time block codes

This paper introduces limited feedback technique into physical‐layer network coding (PLNC) scheme, which is the most spectrally efficient protocol in two‐way relay channels, consisted of one relay and two end nodes (sources). Decode‐and‐forward (DF) and partial‐decode‐and‐forward (PDF) strategies are considered for PLNC, and all nodes are assumed to have two antennas to allow transmission by Alamouti's orthogonal space–time block code to provide diversity. In DF, by limited feedback, one of the sources is informed about instantaneous channel state information (CSI) to increase the bit error rate (BER) performance at relay. The closed‐form upper and lower bounds on the bit error probability are derived for binary phase‐shift keying (BPSK) and quadrature PSK (QPSK) modulations and approved via computer simulations. In PDF strategy, each source has to know CSI between relay and the other source for decoding, which causes extra protocol complexity. Moreover, for the system in which all nodes have two antennas, classical PDF strategy does not satisfy orthogonality at the end nodes. Therefore, in this paper, a modified‐PDF (MPDF) strategy with limited feedback is proposed. In MPDF, for decoding at the end nodes, differential phase information between channel fading coefficients having maximum amplitudes is fed back to the sources by relay. This approach enables single‐symbol decoding, besides full diversity, and sources do not need to know CSI between relay and the other source. It is shown via computer simulations that MPDF strategy provides significantly better BER performance than the classical PDF for BPSK and QPSK modulations.Copyright © 2012 John Wiley & Sons, Ltd.