Uniformly Improving the CramÉr-Rao Bound and Maximum-Likelihood Estimation

An important aspect of estimation theory is characterizing the best achievable performance in a given estimation problem, as well as determining estimators that achieve the optimal performance. The traditional CramÉr–Rao type bounds provide benchmarks on the variance of any estimator of a deterministic parameter vector under suitable regularity conditions, while requiring a-priori specification of a desired bias gradient. In applications, it is often not clear how to choose the required bias. A direct measure of the estimation error that takes both the variance and the bias into account is the mean squared error (MSE), which is the sum of the variance and the squared-norm of the bias. Here, we develop bounds on the MSE in estimating a deterministic parameter vector$ bf x_0$over all bias vectors that are linear in$ bf x_0$, which includes the traditional unbiased estimation as a special case. In some settings, it is possible to minimize the MSE over all linear bias vectors. More generally, direct minimization is not possible since the optimal solution depends on the unknown$ bf x_0$. Nonetheless, we show that in many cases, we can find bias vectors that result in an MSE bound that is smaller than the CramÉr–Rao lower bound (CRLB) for all values of$ bf x_0$. Furthermore, we explicitly construct estimators that achieve these bounds in cases where an efficient estimator exists, by performing a simple linear transformation on the standard maximum likelihood (ML) estimator. This leads to estimators that result in a smaller MSE than the ML approach for all possible values of$ bf x_0$.     

基于导频辅助的低压电力线通信系统信道估计算法

针对低压电力线信道噪声强、衰减大的问题,基于OFDM技术的电力线通信系统采用时域扩充结构,提高导频数据的可靠性.确定了在OFDM时域扩充结构中应用LMMSE准则时最大多径时延的最优取值.在此基础上提出一种更适合时域扩充系统的信道估计优化算法,通过利用OFDM符号内所有导频参与信道估计从而在低信噪比条件下获得更低的误码率.仿真结果表明提出的改进算法与传统LMMSE算法相比具有更好的信道估计性能,在信噪比低于0dB时改进算法的性能优势更加明显.     

一种改进的直接判决信道估计算法研究

信道估计技术是正交频分复用(OFDM)系统中的关键技术。其中直接判决信道估计算法在减少均方误差(MSE)和误码率(BER)等方面具有优越性而备受关注。提出了一种基于循环线性最小均方误差(LMMSE)的直接判决信道估计算法,并且在高斯白噪声信道和多径瑞利信道下进行了仿真。实验结果表明,该算法与其他的算法相比,在减少MSE和BER等方面具有明显的优势。     

A Current Re-Use Mixer and a Push–Pull Buffer for Base Station Applications

A high dynamic range (DR) current reuse mixer and a linear push–pull buffer with an active area of 0.11mm$times$0.1mm were realized for base station applications in a 5-V complementary 0.4-$muhboxm$SiGe process. At 2GHz, a mixer test block with the proposed mixer achieves a nominal measured DR of$+$154 dB, while drawing 29 mA from a 3.3-V supply, whereas the push–pull buffer outputs an$ OP_1 dB$of$+$9dBm, while drawing 33 mA from a 5-V supply.     

A maximum-likelihood bound approaching minimum bit error rate linear multiuser detector for frequency-selective DS-CDMA systems

In this letter, a minimum bit error rate (MBER) linear multiuser detector (MUD) is considered for direct-sequence code-division multiple-access (DS-CDMA) communication systems, distorted by time-varying and frequency-selective multipath fading channels. Based on the approach for finding filter coefficients of the proposed MBER MUD, an efficient Newton method with a barrier parameter is developed. The BER performance of the MBER MUD is compared to other conventional detectors. The study finds that the proposed MBER MUD has more than 2 dB gain over the linear minimum mean-squared error (LMMSE) detector. Furthermore, in the high SNR region, the BER performance of the proposed MBER MUD approaches the performance of the maximum-likelihood (ML) detector.     

Iterative Channel Estimation Based on B-splines for Fast Flat Fading Channels

We propose novel low-complexity iterative channel estimators based on B-splines. Local splines are adopted for computational simplicity. Minimum mean square error (MMSE) local splines with integral sampling are derived. The MSE of the proposed estimators depends on signal-to-noise ratio, fading rate, sampling interval, spline order and the number of weighting coefficients; these dependencies are investigated. The linear and cubic local splines with as few as seven weighting coefficients are capable of achieving MSE and BER performance comparable to those of the Wiener filter and the spheroidal basis expansion. However, a significantly lower complexity is achieved using B-splines     

Soft-decision multistage multiuser interference cancellation

Successive interference cancellation (SIC) refers to a family of low-complexity multiuser detection methods for direct-sequence code-division multiple-access systems. The performance of multistage SIC depends on the decision function used in the interference cancellation iterations, e.g., hard, soft, or linear decision functions. Due to error propagation, multistage SIC with hard data bit decisions may perform more poorly than multistage SIC with linear or soft decision functions. We propose and analyze a family of generalized unit-clipper bit decision functions that better combine linear and hard decisions. Performance within 0.4 dB of the single-user bound can be obtained. We then make robust the above soft-decision SIC to time-delay errors as large as half a PN chip and evaluate its performance.     

Successive interference cancellation with SISO decoding and EMchannel estimation

We derive a low-complexity receiver scheme for joint multiuser decoding and parameter estimation of code division multiple access signals. The resulting receiver processes the users serially and iteratively and makes use of soft-in soft-out single-user decoders, of soft interference cancellation and of expectation-maximization parameter estimation as the main building blocks. Computer simulations show that the proposed receiver achieves near single-user performance at very high channel load (number of users per chip) and outperforms conventional schemes with similar complexity     

Phase-Conjugate External-Cavity Diode Laser

An external-cavity diode laser based on self-pumped phase-conjugate optical feedback is reported. An antireflection-coated diode laser is subjected to strong phase-conjugate feedback from a photorefractive Ce-doped$hboxBaTiO_3$crystal. This provides narrow laser linewidth and good stability. Inherent linewidth of 25 kHz and relative frequency stability of$1.5,times 10 ^-8$(at 100 s) are demonstrated. Due to phase-conjugate feedback, the laser is insensitive to mechanical drifts and misalignment of the feedback element.     

Analysis and optimization of pilot symbol-assisted Rake receivers for DS-CDMA systems

The effect of imperfect channel estimation (CE) on the performance of pilot-symbol-assisted modulation (PSAM) and MRC Rake reception over time- or frequency-selective fading channels with either a uniform power delay profile (UPDP) or a nonuniform power delay profile (NPDP) is investigated. For time-selective channels, a Wiener filter or linear minimum mean square error (LMMSE) filter for CE is considered, and a closed-form asymptotic expression for the mean square error (MSE) when the number of pilots used for CE approaches infinity is derived. In high signal-to-noise ratio (SNR), the MSE becomes independent of the channel Doppler spectrum. A characteristic function method is used to derive new closed-form expressions for the bit error rate (BER) of Rake receivers in UPDP and NPDP channels. The results are extended to two-dimensional (2-D) Rake receivers. The pilot-symbol spacing and pilot-to-data power ratio are optimized by minimizing the BER. For UPDP channels, elegant results are obtained in the asymptotic case. Furthermore, robust spacing design criteria are derived for the maximum Doppler frequency.     

Temperature-Dependent Gain Variation Reduction in$C$-Band Erbium-Doped Fiber Amplifier Using Phosphorus-Erbium-Doped Silica Fiber

We propose a new technique to reduce the temperature-dependent gain (TDG) tilt of erbium-doped fiber amplifier in the$C$-band by supplying a composite optical gain block, conventional aluminum-rich erbium-doped fiber (EDF) serially concatenated with a special EDF composed of phosphorus-doped silica host, which showed opposite TDG coefficients in the$C$-band. The TDG variation was suppressed to less than$pm$0.45 dB for the saturated gain of 16 dB in 1525–1565 nm, within the temperature range of$ -$40$^circ$C to$+$80$^circ$C.     

Iterative Equalization using Improved Block DFE for Synchronous CDMA Systems

Iterative equalization using optimal multiuser detector and optimal channel decoder in coded CDMA systems improves the bit error rate (BER) performance tremendously. However, given large number of users employed in the system over multipath channels causing significant multiple-access interference (MAI) and intersymbol interference (ISI), the optimal multiuser detector is thus prohibitively complex. Therefore, the sub-optimal detectors such as low-complexity linear and non-linear equalizers have to be considered. In this paper, a novel low-complexity block decision feedback equalizer (DFE) is proposed for the synchronous CDMA system. Based on the conventional block DFE, the new method is developed by computing the reliable extrinsic log-likelihood ratio (LLR) using two consecutive received samples rather than one received sample in the literature. At each iteration, the estimated symbols by the equalizer is then saved as a priori information for next iteration. Simulation results demonstrate that the proposed low-complexity block DFE algorithm offers good performance gain over the conventional block DFE.     

Efficient BER evaluation of linear multiuser detectors with imperfect channel estimation for CDMA fading channels

In this paper, we present a unified mathematical framework to analyze the bit-error rate (BER) performance of general linear coherent multiuser receivers with diversity reception and imperfect channel estimation for doubly selective Rician-fading asynchronous code-division multiple-access channels. BERs of linear receivers with channel state information and data-aided channel estimation are analyzed, and both exact and low-complexity approximate BER evaluation formulas are presented. Furthermore, by using a Markov chain steady-state analysis, a tight BER approximation for receivers with decision-directed channel estimation is proposed. Numerical and simulation results verify the accuracy of the proposed BER evaluation methods.     

Decision-feedback soft-input/soft-output multiuser detector foriterative decoding of coded CDMA

The optimal decoding scheme for a code-division multiple-access (CDMA) system that employs convolutional codes results in a prohibitive computational complexity. To reduce the computational complexity, an iterative receiver structure was proposed for decoding multiuser data in a convolutional coded CDMA system. At each iteration, extrinsic information is exchanged between a soft-input/soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders. However, a direct implementation of the full-complexity SISO multiuser detector also has the exponential computational complexity in terms of the number of users. This paper proposes a low-complexity SISO multiuser detector based on tentative hard decisions that are made and fed back from the channel decoders in the previous iteration. The computational complexity of the proposed detector is linear in terms of the number of users and can be adjusted according to the complexity/performance tradeoff. Simulation results show that even with this simple feedback scheme, the performance of the coded multiuser system approaches that of the single-user system for moderate to high signal-to-noise ratios (SNRs)     

Low Complexity Soft Decoder for Nordstrom-Robinson Code With Application to the Chinese DTTB Standard

Nordstrom-Robinson (NR) code followed by 4 quadrature-amplitude modulation (4QAM) mapping is one of the working modes in the Chinese digital television terrestrial broadcasting (DTTB) standard, where the outer code is a low-density parity-check (LDPC) code. Since LDPC decoders usually accept soft rather than hard inputs for better error performance, soft NR decoders are highly recommended. In this paper, several novel low-complexity soft NR decoders are proposed with excellent error performance. Simulation results show that the proposed algorithm based on the maximum, second and third maximum (MST) cross correlation values achieves very low complexity at the cost of performance loss only about 0.1 dB at bit error rate (BER) of $10^{-6}$ , under both additive white Gaussian noise (AWGN) and independent Rayleigh fading channels, compared to the ideal maximum a posteriori (MAP) decoder.      

Tracking of fast-fading channels in long-code CDMA

A new technique for blind tracking of fast-fading channels in long-code code division multiple access (CDMA) is proposed by exploiting multipath diversity. Based on a linear interpolation channel model, the proposed method blindly identifies a time-varying channel at arbitrary estimating points within a block up to a scale factor and increases bandwidth efficiency allowing only one pilot symbol within a block, which is much larger than channel coherence time. The proposed method can be implemented using an efficient state-space inversion technique for multiuser cases. The mean square error (MSE) performance of the proposed estimator is compared with the Cramer-Rao bound (CRB) for interpolated channel. Modeling error and bit error rate (BER) are also evaluated using Monte-Carlo simulations and compared with the block fading model and a decision-directed tracking technique.     

MUI-free receiver for a synchronous DS-CDMA system based on blockspreading in the presence of frequency-selective fading

We discuss a synchronous direct-sequence code division multiple-access (DS-CDMA) system based on block spreading in the presence of frequency-selective fading. Note that block spreading, which is also known as chip interleaving, refers to a spreading of a data block sequence, which is obtained by dividing a data symbol sequence into consecutive blocks. For such a system, we develop a simple new receiver that completely removes the multiuser interference (MUI) without using any channel information. The MUI-free operation is obtained by the use of a shift-orthogonal set of code sequences on which this receiver is based. Within the framework of the MUI-free receiver, we further present a subspace deterministic blind single-user channel estimation algorithm. As a benchmark for the MUI-free receiver and the corresponding subspace deterministic blind single-user channel estimation algorithm, we consider the linear multiuser equalizer and the corresponding subspace deterministic blind multiuser channel estimation algorithm developed by Liu and Xu (1996) for a standard synchronous DS-CDMA system in the presence of frequency-selective fading. We show that the complexity of the MUI-free receiver using the corresponding subspace deterministic blind single-user channel estimation algorithm is much smaller than the complexity of the linear multiuser equalizer using the corresponding subspace deterministic blind multiuser channel estimation algorithm. We further show that the performance of the MUI-free receiver is comparable with the performance of the linear multiuser equalizer. This is for the case in which the channels are known as well as for the case in which the channels are estimated with the corresponding subspace deterministic blind channel estimation algorithm     

On the Design of Bit-Interleaved Turbo-Coded Modulation With Low Error Floors

In this paper, we introduce an algorithm to optimize the performance in the error-floor region of bit-interleaved turbo-coded modulation (BITCM) on the additive white Gaussian noise channel. The key ingredient is an exact turbo code weight distribution algorithm producing a list of all codewords in the underlying turbo code of weight less than a given threshold. In BITCM, the information sequence is turbo-encoded, bit-interleaved, and mapped to signal points in a signal constellation. Using the union-bounding technique, we show that a well-designed bit interleaver is crucial to have a low error floor. Furthermore, the error-rate performance in the waterfall region depends on the bit interleaver, since the level of protection from channel noise on the bit level depends on the bit position and the neighboring bit values within the same symbol in the transmitted sequence. We observe a tradeoff between error-rate performance in the waterfall and error-floor regions, as illustrated by an extensive case study of a high-rate BITCM scheme. This tradeoff is typical in iterative decoding of turbo-like codes. The reported case study shows that it is possible to design bit interleavers with our proposed algorithm with equal or better performance in the waterfall region and superior performance in the error-floor region, compared with randomly generated bit interleavers. In particular, we were able to design BITCM schemes with maximum-likelihood decoding frame-error rates of$10^-12$and$10^-17$at 2.6 and 3.8 dB away from unconstrained channel capacity, at spectral efficiencies of 3.10 and 6.20 b/s/Hz using square 16 and 256-quadrature amplitude modulation signal constellations, respectively.     

A 15-Gb/s 2.4-V Optical Receiver Using a Ge-on-SOI Photodiode and a CMOS IC

We report the fastest (15 Gb/s) and lowest voltage (2.4V) all-silicon-based optical receiver to date. The receiver consists of a lateral, interdigitated, germanium-on-silicon-on-insulator (Ge-on-SOI) photodiode wire-bonded to a 0.13-$mu$m complementary metal–oxide–semiconductor (CMOS) receiver integrated circuit (IC). The photodiode has an external quantum efficiency of 52% at$lambda=850$nm and a dark current of 10 nA at$-$2 V. The small-signal transimpedance of the receiver is 91-dB$Omega$and the bandwidth is 6.6 GHz. At a bit-error rate of$10^-12$and$lambda=850$nm; the receiver exhibits sensitivities of$-$11.0,$-$9.6, and$-$7.4 dBm at 12.5, 14, and 15 Gb/s, respectively. The receiver operates error-free at rates up to 10 Gb/s with an IC supply voltage as low as 1.5 V and with a photodiode bias as low as 0.5 V. The power consumption is 3 to 7 mW/Gb/s. The Ge-on-SOI photodiode is well suited for integration with CMOS processing, raising the possibility of producing high-performance, low-voltage, monolithically integrated receivers based on this technology in the future.     

A low-complexity SISO multiuser detector for iterative decoding of asynchronous CDMA systems with convolutional codes

The optimal decoding scheme for asynchronous code-division multiple-access (CDMA) systems that employ convolutional codes results in a prohibitive computational complexity. To reduce the computational complexity, an iterative receiver structure was proposed for decoding multiuser data in a convolutional coded CDMA system. At each iteration, extrinsic information is exchanged between a soft-input soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders. A direct implementation of the optimal SISO multiuser detector, however, has exponential computational complexity in terms of the number of users which is still prohibitive for channels with a medium to large number of users. This paper presents a low-complexity SISO multiuser detector using the decision-feedback scheme, of which tentative hard decisions are made and fed back to the SISO multiuser from the previous decoding output. In the proposed scheme, the log-likelihood ratios (LLR) as well as the tentative hard decisions of code bits are fed back from the SISO decoders. The hard decisions are used to constrain the trellis of the SISO multiuser detector and the LLRs are used to provide a priori information on the code bits. The detector provides good performance/complexity tradeoffs. The computational complexity of the detector can be set to be as low as linear in the number of users. Simulations show that the performance of the low-complexity SISO multiuser detector approaches that of the single-user system for moderate to high signal-to-noise ratios even for a large number of users.