A class of band-limited chip waveforms for DS-CDMA systems

In Direct Sequence Code Division Multiple Access （DS-CDMA） systems, the chip waveform affects the implementation, system bandwidth, envelope uniformity, eye pattern and Multiple user Access Interference （MAI）. In this paper, based on an elementary density function of a second order polynomial, a class of second order continuity pulses is proposed. From this class of pulses, we can find some members having faster decaying rate, bigger eye opening, more uniform envelope and stronger anti-MAI capability than the Nyquist waveform. The normalized-bandwidth-pulseshape-factor product, the decaying rate of the tail of the time waveform, the opening of the eye diagram, and the envelope uniformity of the second order continuity pulses are addressed in the paper that provide the basic information for the selection of the chip pulse for CDMA systems.     

Analysis and optimization of DS-CDMA systems with time-limited partial response chip waveforms

Conventional direct sequence code division multiple access systems (DS-CDMA) using offset quadrature phase shift key (OQPSK) usually employ a strictly bandlimited partial response square-root raised cosine pulse as the chip waveform. They have the disadvantage of large envelope fluctuation that will incur performance degradation due to the intermodulation and bandwidth enlargement caused by post nonlinear processing. To improve the performance of DS-CDMA systems, the chip waveform and receiver should be properly selected. This paper presents a systematic performance analysis of a matched filter receiver and zero-forcing filter (ZF) receiver for DS-CDMA using a time-limited partial response chip waveform. Nevertheless the systematic performance analysis is applicable to bandlimited chip pulse as well. For the zero-forcing filters, we propose to select the frequency responses that satisfy the first Nyquist criterion. With this class of filters, we can choose the roll-off factor to minimize the total power of multiple access interference and noise power. The zero-forcing filter with proper choice of roll-off factor, referred to as optimum ZF, yields a performance better than the matched filter counterpart. The bit error rate (BER) performance of the optimum ZF with superposed quadrature amplitude modulation signal as the time pulse waveform is evaluated. It is shown that the optimum ZF provides better BER performance than conventional OQPSK and minimum shift keying, and its envelope uniformity is much better than that of OQPSK.     

DS-CDMA chip waveform design for minimal interference underbandwidth, phase, and envelope constraints

This paper investigates the effect of chip waveform shaping on the error performance, bandwidth confinement, phase continuity, and envelope uniformity in direct-sequence code-division multiple-access communication systems employing offset quadrature modulation formats. An optimal design methodology is developed for the problem of minimizing the multiple-access interference power under various desirable signal constraints, including limited 99% and 99.9% power bandwidth occupancies, continuous signal phase, and near-constant envelope. The methodology is based on the use of prolate spheroidal wave functions to obtain a reduced-dimension discrete constrained optimization problem formulation. Numerous design examples are discussed to compare the performance achieved by the optimally-designed chip waveforms with other conventional schemes, such as offset quadrature phase-shift keying, minimum-shift keying (MSK), sinusoidal frequency-shift keying (SFSK), and time-domain raised-cosine pulses. In general, it is found that while the optimized chip pulses achieved substantial gains when no envelope constraints were imposed, these gains vanish when a low envelope fluctuation constraint was introduced. In particular, it is also shown that MSK is quasi-optimal with regard to the 99% bandwidth measure, while the raised-cosine pulse is equally good with both the 99% and 99.9% measures, but at the expense of some envelope variation. On the other hand, SFSK is quasi-optimal with regard to the 99.9% bandwidth occupancy, among the class of constant-to-low envelope variation pulses     

使用基于二阶多项式Nyquist波形降低同信道干扰的影响

本文讨论了在Nakagami衰落条件下,使用一类基于二阶多项式Nyquist波形的BPSK系统中的同信道干扰问题。我们发现在新提出的这类脉冲波形中总可以找到合适的成员,较升余弦Nyquist脉冲相比,具有更强的抗同信道干扰能力。     

Performance Limits in DS-CDMA Timing Acquisition

This paper addresses timing acquisition aspects in direct-sequence code division multiple access (DS-CDMA) systems. Various chip waveform shaping schemes are considered, including both one-chip long full-response pulses, and partial-response ones occupying several chip periods. Different figures of merits are considered in a comparative analysis that seeks to establish performance limits in terms of correct timing detection capability, false alarm rate, bandwidth occupancy, multiple-access interference (MAI), and inter-chip interference (ICI). A waveform design algorithm is formulated to optimize system performance in terms of signal-to-interference-ratio (SIR) subject to other signalling constraints, and a solution based on the use of prolate spheroidal wave functions (PSWF) is derived. Numerous waveform design examples are then constructed to illustrate acquisition detection capability versus system load for both faded and unfaded cases. A comparative assessment of the performance of conventional signalling waveforms against the optimized ones is also presented. In particular, the numerical results show that the half-sine pulse used in minimum shift keying (MSK) is quasi-optimal within the full-response category, while root-raised cosine (RRC) Nyquist filtering with 22% rolloff (used in third generation CDMA standards) is also close to optimal when considering many-chip-long pulses.     

A Unified Analysis of Quaternary DS-CDMA Systems with Arbitrary Chip Waveforms and Its Applications

This paper is to present a systematic performance analysis of asynchronous quaternary direct sequence code division multiple access (DS-CDMA) systems using random signature sequences with arbitrary chip waveforms. The simplified improved Gaussian approximation method for bit error rate computation is extended to include arbitrary time-limited (full response or partial response) or band-limited chip waveforms with arbitrary receiver filters. As a time-limited partial response chip waveform modulation format, the well-known power and spectral efficient superposed quadrature amplitude modulation with matched filter or zero-forcing filter is evaluated, and the results show that the optimum zero-forcing filter will yield a performance better than the matched filter counterpart. For band-limited chip waveforms, based on an elementary density function of a second-order polynomial, a class of second-order continuity pulses is proposed for analysis. It is found that all common band-limited pulses are only its special cases. As a member of the class, the widely used frequency domain raised cosine pulse has the worst anti-multiuser-access-interference capability, which has been pointed out in (H. H. Nguyen, Proceedings of IEEE Canadian Conference on Electrical & Computer Engineering, 2002, pp. 1271–1275).     

PCM-FDM: System Capability and Performance Improvement on Waveform Equalization and Synchronization

To obtain wider waveform equalization range and higher synchronization accuracy, we have introduced: 1) a multilevel pilot-pulse equalization system and 2)an in-band in-phase pilot synchronization system into multilevel VSB-conversion PCM-FDM equipment. This equipment is used to transmit digital signals on existing analog lines. 1) Multilevel pilot pulses with a smaller number of levels than the information pulses are inserted into the information pulse train. Due to the larger eye opening of the received pilot pulse, the automatic equalizer can converge and equalize the distortion more quickly and easily. For example, let 2-level pilot pulses be inserted into every 32 16-level information pulses. As long as the eye pattern of the pilot pulse is open, it is possible to allow up to 15 times more distortion in the transmission line. Thus the transmission span can be greatly extended. There are various other advantages in using this pilot pulse, such as dc drift suppression, in-service error rate monitoring, etc. 2) A carrier pilot and a sample timing pilot for phase synchronization are superimposed on the carrier frequency and 1/2 Nyquist rate, respectively, within the transmission signal spectra. Thus no excess bandwidth for pilots is necessary, and the phase error between pilot and signal is smaller. In this case, the phase jitter of regenerated carrier and timing clock caused by the neighboring signal spectra can decrease if the pilots are coupled in the same phase with the neighboring signal. For example, phase jitter of less than 0.5° (which was experimentally 1/10 phase error of the quadrature coupling) could be realized easily, even if the signal-to-pilot ratio is about 20 dB.     

A comparison of system performance using two different chip pulsesin multiple-chip-rate DS/CDMA systems

This paper describes a comparison of system performance using two different chip waveforms of spreading sequences in multiple-chip-rate (MCR) direct-sequence (DS)/code-division multiple-access (CDMA) systems. The chip pulses used in this study are closely related to the characteristics of output filter employed at transmitter. In general, the chip waveform is an important factor to determine the link performance. The raised cosine chip pulse with a roll-off factor of α will be adopted for IMT-2000 systems in order to reduce both the intersymbol effect and the spectral width of the modulated signal. However, due to the complexity of obtaining quantitative results on the performance of MCR-DS/CDMA systems, rectangular chip pulses are mainly utilized in performance analysis. Therefore, it is necessary to investigate the effect of the chip pulses used, i.e., a rectangular and a raised cosine chip pulses on system performance in order to evaluate MCR-DS/CDMA systems accurately. Thus, the effect of the chip pulses used on the performance in MCR-DS/CDMA systems is investigated in terms of the system capacity and blocking probability. It is shown that the system using a raised cosine chip pulse (i.e., RC system) supports at least 80% more capacity and 57% more traffic than that using a rectangular chip pulse (i.e., R system)     

On chip-matched filtering and discrete sufficient statistics forasynchronous band-limited CDMA systems

The problem of generating discrete sufficient statistics for signal processing in code-division multiple-access (CDMA) systems is considered in the context of underlying channel bandwidth restrictions. Discretization schemes are identified for (approximately) bandlimited CDMA systems, and a notion of approximate sufficiency is introduced. The role of chip-matched filtering in generating accurate discrete statistics is explored. The impact of approximate sufficiency on performance is studied in three cases: conventional matched filter (MF) detection, minimum mean-squared-error detection, and delay acquisition. It is shown that for waveforms limited to a chip interval, sampling the chip-MF output at the chip rate can lead to a significant degradation in performance. Then, with equal bandwidth and equal rate constraints, the performance with different chip waveforms is compared. In all three cases above, it is demonstrated that multichip waveforms that approximate Nyquist sine pulses achieve the best performance, with the commonly used rectangular chip pulse being severely inferior. However, the results also indicate that it is possible to approach the best performance with well-designed chip waveforms limited to a chip interval, as long as the chip-MF output is sampled above the Nyquist rate     

Minimization of detection of symbol-rate spectral lines by delayand multiply receivers

The detectability of the symbol rate of a digitally modulated signal by a delay and multiply receiver is investigated. Two signal pulse types are considered: Nyquist pulses and rectangular pulses. Since many digital transmission systems use rectangular pulse shapes, symbol rate-line detectability is considered for receivers optimized for rectangular pulses. For a receiver configuration that is reasonable for rectangular pulses, it is found that with a Nyquist pulse parameter α=0.25, the rate-line signal-to-noise ratio is down about 20 dB from that for a rectangular pulse signal     

On computing the minimum distance for faster than Nyquist signaling

The degradation suffered when pulses satisfying the Nyquist criterion are used to transmit binary data at a rate faster than the Nyquist rate over the ideal band-limited (brick-wall) channel is studied. The minimum distance between received signals is used as a performance criterion. It is well-known that when Nyquist pulses (i.e. pulses satisfying the Nyquist criterion) are sent at the Nyquist rate, the minimum distance between signal points is the same as the pulse energy. The main result is to show that the minimum distance between received signals is the same as the pulse energy for rates of transmission about 25% beyond the Nyquist rate, which is the best possible result. In fact, one can even identify the precise error event and signaling rate that causes the minimum distance to be no longer equal to the pulse energy. The mathematical formulation of the problem is analyzed     

Parametric construction of Nyquist-I pulses

A novel parametric approach for constructing families of intersymbol-interference (ISI)-free pulses is presented and examined. Some new pulses so constructed have smaller maximum distortion, a more open receiver eye, and a smaller probability of error in the presence of symbol-timing error than the Nyquist raised-cosine pulse for the same excess bandwidth. The parametric approach gives more degrees of freedom in the design of ISI-free pulses, and subsumes previous ISI-free pulses as special cases. A number of theorems that relate time-domain behaviors of a pulse to the pulse's frequency spectrum are proved. A previously known result relating pulse tail-time decay to discontinuity of the pulse-frequency spectrum is corrected and clarified.     

Approximation of Löwdin orthogonalization to a spectrally efficient orthogonal overlapping PPM design for UWB impulse radio

In this paper we consider the design of spectrally efficient time-limited pulses for ultra-wideband (UWB) systems using an overlapping pulse position modulation scheme. For this we investigate an orthogonalization method, which was developed in 1950 by Löwdin [1] and [2]. Our objective is to obtain a set of N orthogonal (Löwdin) pulses, which remain time-limited and spectrally efficient for UWB systems, from a set of N equidistant translates of a time-limited optimal spectral designed UWB pulse. We derive an approximate Löwdin orthogonalization (ALO) by using circulant approximations for the Gram matrix to obtain a practical filter implementation as a tapped-delay-line [7]. We show that the centered ALO and Löwdin pulses converge pointwise to the same square-root Nyquist pulse as N tends to infinity. The set of translates of the square-root Nyquist pulse forms an orthonormal basis for the shift-invariant-space generated by the initial spectral optimal pulse. The ALO transformation provides a closed-form approximation of the Löwdin transformation, which can be implemented in an analog fashion without the need of analog to digital conversions. Furthermore, we investigate the interplay between the optimization and the orthogonalization procedure by using methods from the theory of shift-invariant-spaces. Finally we relate our results to wavelet and frame theory.     

脉冲波形对其轴线能量传播特性影响的研究

在相同平面圆形辐射器条件下,对具有相同中心频率的几种典型脉冲,根据电磁场理论,给出了它们轴线能量传播特性的解析计算公式和数字模拟结果。研究表明:当脉冲的上升时间小于有效脉冲宽度的1/20时,在脉冲传播的慢衰减区,等腰梯形脉冲的传播特性优于目前普遍应用的正弦脉冲。     

22–29 GHz Ultra-Wideband CMOS Pulse Generator for Short-Range Radar Applications

The pseudo-millimeter-wave ultra-wideband (UWB) is attractive for applications in short-range automotive radar systems using 22 to 29 GHz in order to realize road safety and intelligent transportation. Although the CMOS is suitable for short- range radar since processing units can be implemented in the same chip as the UWB front-end building block, it is difficult to operate CMOS pulse generators at such a high frequency. To realize the pseudo-millimeter-wave band using CMOS, we have proposed a new pulse generator consisting of a series of delay cells and edge combiners with waveform shaping for short-range radar. As a result of measurement using 90-nm CMOS technology, 1 Gb/s/bit pulses with 71 mV peak-to-peak, 39.2 ps monopulse width and 552 ps envelope width are successfully generated with a power consumption of 1.4 mW at a supply voltage of 0.91 V. This result can be the basis for developing the key technology for one-chip short-range radar sensors.     

HP83480数字通信分析仪的硬件测量算法

参数测量主要指对波形特性，如上升时间、下降时间、过冲、周期、脉冲波形或眼图的幅度等。掩码测量将波形与预定掩码比较。眼参数测量是专用于眼图性质的测量，如眼高、眼宽、抖动、交叉高度和消光比等。     

Effect of transmitter Nyquist shaping on ICI reduction in OFDM systems with carrier frequency offset

The effect of several Nyquist pulse-shapings, including the Franks pulse, the raised-cosine pulse, the 'better than' raised-cosine pulse, the second-order continuous window, and the polynomial pulse on inter-carrier interference reduction in OFDM systems with carrier frequency offset is studied.     

Optimum Pulse Shapes for Pulse-Amplitude Modulation Data Transmission Using Vestigial Sideband Modulation

When designing pulse-amplitude modulation (PAM) systems for use over bandpass channels having restricted bandwidth, one may be led to use single-sideband (SSB) or vestigial sideband (VSB) transmission in order to maximize transmission rate. Carefully shaped pulses must be used to minimize degradation due to intersymbol interference (isi). In this paper VSB pulses are derived that have no inherent isi, and in addition have maximum immunity in a mean-squared-error (MSE) sense to timing and carrier phase errors. The results here generalize on those of Franks who treated the SSB case. The optimum VSB pulses are shown to be identical to those of Franks at the band edges, and to have vestigial roll-off characteristics of a similar discontinuous nature. It is also shown that one may allocate available bandwidth to the vestigial roll-off band band and Nyquist roll-off band in any way desired. The final performance for the optimum pulse depends only on the total bandwidth used. These results are shown to apply as well to a system employing a matched filter. The case of random timing and phase errors is also considered, and optimum pulses are again found. Several mathematical properties of the optimal pulses are given physical justification and geometric insight through error ellipses, and optimal signal shapes are plotted for various cases of special interest.     

DFB-LD在不同温度下的频响测量

利用脉冲注入法测量了分布反馈激光器(DFB-LD)芯片温度与激射波长的关系.基于此关系测量了不同芯片温度下分布反馈激光器的小信号响应曲线、传输眼图和误码率,并讨论了温度、偏置电流对响应曲线、传输眼图和误码率的影响.     

杂波中MIMO雷达恒模波形及接收机联合优化算法研究

为提高集中式MIMO雷达在强杂波中的目标检测性能,同时兼顾雷达发射机对于恒定包络波形的需求,以系统输出信杂噪比最大为优化准则,研究了MIMO雷达恒模多波形及接收机权值的联合优化问题.基于循环优化算法将联合优化问题分解为两个子优化步骤,并提出了基于半正定松弛及高斯随机化的恒模波形设计算法.结果表明所提算法能够在迭代过程中不断增加输出信杂噪比直至算法收敛.此外,其相比于能量约束下的最优波形性能损失很小,能够实现自适应杂波抑制并改善目标检测性能.