Experimental rain attenuation statistics estimated from radarmeasurements useful to design satellite communication systems for mobileterminals

Based on experimental data, we have reported a reliable method to scale the cumulative time T_F,T(A) that rain attenuation A (dB) is exceeded in a fixed satellite system to the time T_M,T(A) that it is exceeded in a satellite system for mobile terminals. Zigzag routes and ring-roads simulated city patterns; straight routes simulated freeways. In all cases, T_M,T(A) can be expressed as T_M,T(A)=ξT_F,T (A) with a probability scaling factor ξ independent of A. The simulations have been made at 19.77 GHz with satellite elevation angle &thetas; of 30.6°, 45°, 60°, 80°, and 90°. For the horizontal structure of rain, we have used a very large number of rain-rate maps of rain storms randomly observed in 1989-1992 by a meteorological radar placed at Spine d'Adda (northern Italy). The vehicle speed was modeled as a log-normal random variable. We found: (a) in zigzag routes, T_M,T(A)F,T(A), i.e., ξ<1, with results depending on vehicle speed modeling and starting conditions; (b) in a ring-road, there is no difference between fixed and mobile systems (ξ=1); and (c) in straight freeways, T_M,T(A)≪T_F,T (A)(ξ≪1); T_M,T(A) can change significantly in different straight lines and in opposite directions (anisotropy and asymmetry) for medium-large attenuation. When compared to zigzag routes or ring-roads, the performance in straight freeways is the most optimistic. For &thetas;>30.6° and for the same pattern, ξ is fairly independent of &thetas;. Since the radar rain maps are a reliable estimate of the horizontal structure of rain, the findings, which can be considered frequency-independent, stand as a very good prediction of the results obtainable by experiments     

The dynamics of group codes: state spaces, trellis diagrams, andcanonical encoders

A group code C over a group G is a set of sequences of group elements that itself forms a group under a component-wise group operation. A group code has a well-defined state space Σ_k at each time k. Each code sequence passes through a well-defined state sequence. The set of all state sequences is also a group code, the state code of C. The state code defines an essentially unique minimal realization of C. The trellis diagram of C is defined by the state code of C and by labels associated with each state transition. The set of all label sequences forms a group code, the label code of C, which is isomorphic to the state code of C. If C is complete and strongly controllable, then a minimal encoder in controller canonical (feedbackfree) form may be constructed from certain sets of shortest possible code sequences, called granules. The size of the state space Σ_k is equal to the size of the state space of this canonical encoder, which is given by a decomposition of the input groups of C at each time k. If C is time-invariant and ν-controllable, then |Σ_k|=Π_1⩽j⩽v|F_j/F _j-1|^j, where F₀ ⊆···⊆ Fν is a normal series, the input chain of C. A group code C has a well-defined trellis section corresponding to any finite interval, regardless of whether it is complete. For a linear time-invariant convolutional code over a field G, these results reduce to known results; however, they depend only on elementary group properties, not on the multiplicative structure of G. Moreover, time-invariance is not required. These results hold for arbitrary groups, and apply to block codes, lattices, time-varying convolutional codes, trellis codes, geometrically uniform codes and discrete-time linear systems     

On the capacity of two-dimensional run-length constrained channels

Two-dimensional binary patterns that satisfy one-dimensional (d, k) run-length constraints both horizontally and vertically are considered. For a given d and k, the capacity C_d,k is defined as C_d,k=lim_m,n→∞log₂N_m,n ^d,k/mn, where N_m,n^d,k denotes the number of m×n rectangular patterns that satisfy the two-dimensional (d,k) run-length constraint. Bounds on C_d,k are given and it is proven for every d⩾1 and every k>d that C_d,k=0 if and only if k=d+1. Encoding algorithms are also discussed     

Three space-economical algorithms for calculatingminimum-redundancy prefix codes

The minimum-redundancy prefix code problem is to determine, for a given list W=[ω₁,..., ω_n] of n positive symbol weights, a list L=[l₁,...,l_n] of n corresponding integer codeword lengths such that Σ_i=1 ⁿ 2^-li⩽1 and Σ_i=1ⁿ ω_il_i is minimized. Let us consider the case where W is already sorted. In this case, the output list L can be represented by a list M=[m₁,..., m_H], where m_l, for l=1,...,H, denotes the multiplicity of the codeword length l in L and H is the length of the greatest codeword. Fortunately, H is proved to be O(min(log(1/p₁),n)), where p₁ is the smallest symbol probability, given by ω₁/Σ _i=1ⁿ ω_i. We present the Fast LazyHuff (F-LazyHuff), the Economical LazyHuff (E-LazyHuff), and the Best LazyHuff (B-LazyHuff) algorithms. F-LazyHuff runs in O(n) time but requires O(min(H², n)) additional space. On the other hand, E-LazyHuff runs in O(n+nlog(n/H)) time, requiring only O(H) additional space. Finally, B-LazyHuff asymptotically overcomes, the previous algorithms, requiring only O(n) time and O(H) additional space. Moreover, our three algorithms have the advantage of not writing over the input buffer during code calculation, a feature that is very useful in some applications     

Plasma etching optimization of oxide/nitride/oxide interpolydielectric breakdown time in flash memory devices

The breakdown time of flash memory oxide/nitride/oxide (ONO) layer t_bd under positive constant current stressing has been found to be closely related to the cumulative extent of (over)etch of the tungsten silicide, control polysilicon, and ONO layers, i.e., Σ(ΛOE). An empirical first-order relation between t_bd and Σ(ΛOE) has been derived to facilitate the plasma etch recipe optimization. This has led to a four-fold increase in the average t_bd across a 200-mm wafer to 208 s. More importantly, the spread in t_bd has been tightened to ~5%, which is down from ~54%     

Continuous-time identification of SISO systems using Laguerrefunctions

This paper looks at the problem of estimating the coefficients of a continuous-time transfer function given samples of its input and output data. We first prove that any nth-order continuous-time transfer function can be written as a fraction of the form Σ_k=0 ⁿb¯_kL_k(s)/Σ_k=0 ⁿa¯_kL_k(s), where L_k(s) denotes the continuous-time Laguerre basis functions. Based on this model, we derive an asymptotically consistent parameter estimation scheme that consists of the following two steps: (1) filter both the input and output data by L_k(s), and (2) estimate {a¯_k, b¯_k} and relate them to the coefficients of the transfer function. For practical implementation, we require the discrete-time approximation of L_k(s) since only sampled data is available. We propose a scheme that is based on higher order Pade approximations, and we prove that this scheme produces discrete-time filters that are approximately orthogonal and, consequently, a well-conditioned numerical problem. Some other features of this new algorithm include the possibility to implement it as either an off-line or a quasi-on-line algorithm and the incorporation of constraints on the transfer function coefficients. A simple example is given to illustrate the properties of the proposed algorithm     

The length of a typical Huffman codeword

If p_i(i=1,···, N) is the probability of the ith letter of a memoryless source, the length l_i of the corresponding binary Huffman codeword can be very different from the value -log p_i. For a typical letter, however, l_i≈-logp_i. More precisely, P_m ^-=Σ/sub j∈{i|l<-logpj-m}/p_j<2^-m and P_m ⁺=Σ/sub j∈{i|li>-logpi+m/}p_j<2^-c(m-2)+2, where c≈2.27     

On a new cylindrical harmonic representation for spherical waves

An exact series representation is presented for integrals whose integrands are products of cosine and spherical wave functions, where the argument of the cosine term can be any integral multiple n of the azimuth angle φ. This series expansion is shown to have the following form: I(n)=e^-jkR0/R₀ δ_no-jk Σ_m=1^∞ C(m,n)(k ²ρρ0)/m! h_m⁽²⁾(kR₀)/(kR₀)^m . It is demonstrated that in the special cases n=0 and n=1, this series representation corresponds to existing expressions for the cylindrical wire kernel and the uniform current circular loop vector potential, respectively. A new series representation for spherical waves in terms of cylindrical harmonics is then derived using this general series representation. Finally, a closed-form far-field approximation is developed and is shown to reduce to existing expressions for the cylindrical wire kernel and the uniform current loop vector potential as special cases     

Dynamic algorithm transformations (DAT)-a systematic approach tolow-power reconfigurable signal processing

In this paper, dynamic algorithm transformations (DATs) for designing low-power reconfigurable signal-processing systems are presented. These transformations minimize energy dissipation while maintaining a specified level of mean squared error or signal-to-noise ratio. This is achieved by modeling the nonstationarities in the input as temporal/spatial transitions between states in the input state-space. The reconfigurable hardware fabric is characterized by its configuration state-space. The configurable parameters are taken to be the filter taps, coefficient and data precisions, and supply voltage V_dd. An energy-optimal reconfiguration strategy is derived as a mapping from the input to the configuration state-space. In this strategy, taps are powered down starting with the tap with the smallest value [w_k²/Σ_m(w_k)] (where w_k and Σ_m(w_k) are, respectively, the adders, redundant-to-binary conversion, tree adders, coefficient and energy dissipation of the kth tap). Optimal values for precision and supply voltage V_dd are subsequently computed from the roundoff error and critical path delay requirements, respectively. The DAT-based adaptive filter is employed as a near-end crosstalk (NEXT) canceller in a 155.52-Mb/s asynchronous transfer mode-local area network transceiver over category-3 wiring. Simulation results indicate that the energy savings range from -2% to 87% as the cable length varies from 110 to 40 m, respectively, with an average saving of 69%. An average saving of 62% is achieved for the case where the supply voltage V_dd is kept fixed     

A 3.2-GHz second-order delta-sigma modulator implemented in InP HBTtechnology

This paper presents a second-order delta-sigma (ΔΣ) modulator fabricated in a 70 GHz (f_T), 90 GHz (f_max) AlInAs-GaInAs heterojunction bipolar transistor (HBT) process on InP substrates. The modulator is a continuous time, fully differential circuit operated from ±5 volt supplies and dissipates 1 W. At a sample rate of 3.2 GHz and a signal bandwidth of 50 MHz (OSR=32100 MSPS Nyquist rate) the modulator demonstrates a Spur Free Dynamic Range (SFDR) of 71 dB (12-b dynamic range). The modulator achieves the ideal signal-to-noise ratio (SNR) of 55 dB for a second-order modulator at an oversampling ratio (OSR) of 32. The design of a digital decimation filter for this modulator is complete and the filter is currently in fabrication in the same technology. This work demonstrates the first ΔΣ modulator in III-V technology with ideal performance and provides the foundation for extending the use of ΔΣ modulator analog-to-digital converters (ADC's) to radio frequencies (RF)     

Evaluation of the quantization error in denominator-separable 2-Drecursive filters

The evaluation of the quantization error in two-dimensional (2-D) digital filters involves the computation of the infinite square sum J=Σ^∞_m=φΣ ^∞_n=φy² (m, n). A simple method is presented for evaluating J based on partial fraction expansion and using the residue method provided the Z-transform Y(Z₁, Z₂) of the sequence y(m, n) having quadrant support is a causal bounded input, bounded output (BIBO) stable denominator-separable rational function. The value of J is expressed as a sum of simple integrals which can easily be evaluated. The simple integrals are tabulated for ready reference. The proposed method is suitable for analytical as well as numerical computation and can easily be programmed     

玻璃钢激光烧蚀碳化致微波传输衰减的数值模拟

当激光辐照玻璃钢烧蚀碳化至一定程度时,产生的树脂碳产物对微波传输产生衰减作用。针对该现象,开展了数值建模研究,将激光辐照-微波传输衰减效应分解为激光辐照、材料热响应、提取模型表征量、微波传输衰减分析等过程。通过玻璃钢材料的激光耦合特性和表面温度测试,对建立的玻璃钢层合板激光辐照温度场计算模型进行了验证;通过材料体温度分布的时间演进分析,提取了网格单元温度超过阈值温度的持续时间加权和S_{t, Tc}、网格单元温度超过阈值温度的持续时间与温度乘积的加权和S_{Tt, Tc}两个模型表征量,采用单个实验数据标定系数、整体数据点匹配分析方法,对微波传输衰减实验与数值模拟结果进行了分析。分析结果表明,S_{t, Tc}比S_{Tt, Tc}更适于表征玻璃钢烧蚀碳化致微波传输衰减效应,温度阈值为873 ℃时计算结果与实验结果最匹配,其R2为0.9956。这说明,通过计算激光辐照玻璃钢温度响应并提取微波传输衰减效应表征量S_{t, Tc},可实现对玻璃钢激光烧蚀碳化致微波传输衰减效应的模拟和预测。     

Architecture, design, and test of continuous-time tunableintermediate-frequency bandpass delta-sigma modulators

This paper examines the architecture, design, and test of continuous-time tunable intermediate-frequency (IF) fourth-order bandpass delta-sigma (BP ΔΣ) modulators. Bandpass modulators sampling at high IFs (~100 MHz) allow direct sampling of the RF signal-reducing analog hardware and make it easier to realize completely software programmable receivers. This paper presents circuit design of and test results from continuous-time fourth-order BP ΔΣ modulators fabricated in AlInAs/GaInAs heterojunction bipolar technology with a peak unity current gain cutoff frequency (f_T) of 80 GHz and a maximum frequency of oscillation (f_MAX) of about 130 GHz. Operating from ±5-V power supplies, a fabricated 180-MHz IF fourth-order ΔΣ modulator sampling at 4 GS/s demonstrates stable behavior and achieves 75.8 dB of signal-to-(noise+distortion)-ratio (SNDR) over a 1-MHz bandwidth. Narrowband performance (~1 MHz) performance of these modulators is limited by thermal/device noise while broadband performance (~60 MHz), is limited by quantization noise. The high sampling frequency (4 GS/s) in this converter is dictated by broadband (60 MHz) performance requirements     

Fast evaluation of an integral occurring in digital filteringapplications

A fast evaluation procedure for the integral I_m,n,p=1/2πj∯_|z|=1H_m,n(z)H _m,n(z^-1)z^p-1dz for arbitrary nonnegative integer-valued m, n, and p, is presented, where H_m,n (z)=Σ_k=0^mb_m,kz^-k /Σ_l=0ⁿa_n,lz^-1,a _n,0≠0 is the transfer function of an arbitrary digital filter. Evaluation of this integral frequently appears in control, communication, and digital filtering. A notable result is the one-term recursion on p, for arbitrary but fixed nonnegative integers m and n. The computational complexity is analyzed, and two illustrative examples demonstrate some of the advantages of this approach     

On ternary complementary sequences

A pair of real-valued sequences A=(a₁,a₂,...,a_N) and B=(b₁,b ₂,...,b_N) is called complementary if the sum R(·) of their autocorrelation functions R_A(·) and R_B(·) satisfies R(τ)=R_A(τ)+R _B(τ)=Σ_i=1^N$ -^τa_ia_i+τ+Σ_j=1 ^N-τb_jb_j+τ=0, ∀τ≠0. In this paper we introduce a new family of complementary pairs of sequences over the alphabet α₃=+{1,-1,0}. The inclusion of zero in the alphabet, which may correspond to a pause in transmission, leads both to a better understanding of the conventional binary case, where the alphabet is α₂={+1,-1}, and to new nontrivial constructions over the ternary alphabet α₃. For every length N, we derive restrictions on the location of the zero elements and on the form of the member sequences of the pair. We also derive a bound on the minimum number of zeros necessary for the existence of a complementary pair of length N over α₃. The bound is tight, as it is met by some of the proposed constructions, for infinitely many lengths     

The nonexistence of some five-dimensional quaternary linear codes

Let n₄(k, d) be the smallest integer n, such that a quaternary linear [n, k, d; 4]-code exists. It is proved that n₄ (5, 20)=30, n₄(5, 42)⩾59, n₄(5, 45)⩾63, n₄(5, 64)⩾88, n₄(5, 80)=109, n₄(5, 140)⩾189, n₄(5, 143)⩾193, n₄ (5, 168)⩾226, n₄(5, 180)⩾242, n₄(5, 183)⩾246, n₄(5, 187)=251     

Capacity of the Gaussian arbitrarily varying channel

The Gaussian arbitrarily varying channel with input constraint Γ and state constraint Λ admits input sequences x=(x₁,---,X_n) of real numbers with Σx_i²⩽nΓ and state sequences s=(S₁,---,s_n ) of real numbers with Σs_i²⩽nΛ; the output sequence x+s+V, where V=(V₁,---,V_n) is a sequence of independent and identically distributed Gaussian random variables with mean 0 and variance σ². It is proved that the capacity of this arbitrarily varying channel for deterministic codes and the average probability of error criterion equals 1/2 log (1+Γ/(Λ+σ²)) if Λ<Γ and is 0 otherwise     

Theoretical analysis of word-level switching activity in thepresence of glitching and correlation

This paper presents a novel analytical approach to compute the switching activity in digital circuits at the word level in the presence of glitching and correlation. The proposed approach makes use of signal statistics such as mean, variance, and autocorrelation. It is shown that the switching activity α_f at the output node f of any arbitrary circuit in the presence of glitching and correlation is computed as α_f=Σ_i=1^S-1α(f _i,i+1)=Σ_i=1^{S- 1}p(f_i+1)(1-p(f_i))(1-ρ(f_i,i+1 )) (1) where ρ(f_i,i+1)=ρ(f_i,i+1)=(E[f_i(Sn)f _i+1(Sn)]- p(f_i)p(f_i+1))/(√(p(f _i)-p(f_i)²)(p(f_i+1)- p(f_i+1²))) (2). S number of time slots in a cycle; ρ(f_i,+1) time-slot autocorrelation coefficient; E[x]=expected value of x; p_x=probability of the signal x being “one”. The switching activity analysis of a signal at the word level is computed by summing the activities of all the individual bits constituting the signal. It is also shown that if the correlation coefficient of the higher order bits of a normally distributed signal x is ρ(x_c), then the bit P₀ where the correlation begins and the correlation coefficient is related hy ρ(x_c)=erfc{(2(P₀-1)-1)/(√2σ_x )} where erfc(x)=complementary error function; σ_x=variance of x. The proposed approach can estimate the switching activity in less than a second which is orders of magnitude faster than simulation-based approaches. Simulation results show that the errors using the proposed approach are about 6.1% on an average and that the approach is well suited even for highly correlated speech and music signals     

FIR perfect signal reconstruction from multiple convolutions:minimum deconvolver orders

Given p co-prime finite impulse response (FIR) filters h_i ∈R(m_h), it well known that there exist q _i∈R(m_q) such that Σ_ih_i*q_i=δ. Importantly, this enables signal recovery from its convolutions with p⩾2 co-prime FIR filters by FIR filtering. We show that such q_i exist almost surely if and only if m_q⩾[(m_h-1)/(p-1)], where [x] is the smallest integer greater than or equal to x. The results also provide conditions for full rank of certain key matrices arising in the blind multichannel deconvolution problem