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Michael G. Larimore, Applied Signal Technology (U.S.A.)
Sally L. Wood, Santa Clara University (U.S.A.)
John R. Treichler, Applied Signal Technology (U.S.A.)
The length of a linear equalizer filter is highly dependent on the nature of the channel effects it must mitigate. Design rules are typically stated in terms of the channel's temporal characteristics, i.e. impulse response duration. Equalizer implementational complexity is a principal limiting factors for high bandwidth data communication applications, and consequently there is motivation for reexamining accepted design guidelines. Recently, it was demonstrated that for relatively benign conditions on the effective channel and transmitter pulse shaping, there exists a linear equalizer that perfectly mitigates intersymbol interference, and whose span matches that of the composite distortion. Our paper examines the implications of the minimal-length equalizer in light of convention design rules, and shows that a tangible loss in performance can be assigned to this complexity reduction. Actual line-of-sight microwave radio channels are used to demonstrate the nature of the performance loss.
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Patrick Grohan, LSS-CNRS (France)
Sylvie Marcos, LSS-CNRS (France)
The aim of this paper is to revisit the problem of nonlinear channel equalization. The equalization is here viewed as the estimation, from the observation of the channel output, of the state vector of the channel consisting of the last transmitted symbols. If the probability density function of the state vector given all the available observations, (the a posteriori density function) were known, an estimate of the state vector for any performance criterion could be determined. Alspach and Sorenson proposed an approximation by a weighted sum of Gaussian probability density functions that permits the explicit calculation of the a posteriori density from the Bayesian recursion relations. The application of these results to the minimum mean square error solution of the nonlinear channel equalization problem provides a new scheme which consists of the convex combination of the output of several extended Kalman filters operating in parallel.
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Said Tateesh, Surrey University. (U.K.)
Samuel Atungsiri, Surrey University. (U.K.)
Ahmet Kondoz, Orbital. (U.K.)
This paper investigates the benefits of link adaptation according to the propagation conditions using multi-rate vocoders and channel coders. A multi-rate source and channel coding (MRC) system trades-off the source codec bit rate against channel codec bit rate according to the prevailing channel conditions. MRC systems continuously reconfigure transmission resources to optimally combat channel degradations and hence, maintain a reasonable quality of service even in marginal channel conditions. The aim is to maintain a satisfactory level of speech quality over a wide range of channel conditions with minimum resources. This paper shows the benefit of MRC system particularly in crowded cells of high channel interference.
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Ahmad Bahai, Bell Labs, Lucent Technologies (U.S.A.)
Markus Rupp, Bell Labs, Lucent Technologies (U.S.A.)
Optimum detection in randomly time-varying channels requires an efficient adaptive receiver structure. The complexity of signal processing in the receiver is limited by the amount of processing power and power consumption of the receiver. Therefore, efficiency and convergence of adaptive matched filtering and equalization techniques are very important. We extend common results in tracking theory for system identification to the equalization case for systems with short impulse response. Unlike in system identification where a steady-state error energy is minimized, the optimization criterion here is the minimum of the BER. However, they are related by a monotone function and therefore minimizing the BER is equivalent to minimizing the steady-state-error energy. Optimum parameters for LMS as well as RLS algorithms are derived and simulation results indicate that under the conditions defined in the TDMA standards and small delay spread, the performance of the two methods is comparable.
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Mohammed Al-Janabi, University of Westminster (U.K.)
Izzet Kale, University of Westminster (U.K.)
Richard C.S. Morling, University of Westminster (U.K.)
Two novel effective-fourth-order (eighth-order) resonator based MASH bandpass S-D modulators are introduced at the behavioural level and subsequently examined by simulations utilising the ALTA SPW environment. The considered bandpass configurations have in their loop filter a cascade of standard second-order resonator structures in order to achieve appropriate noise shaping. The quantisation noise in each stage is suppressed by feeding the error of each section into the input of the following stage. It is demonstrated in this paper that the quadruple effective-first-order cascade configuration has significantly better performance as well as conforming more closely with theory in comparison with the effective-second-order effective-second-order cascade. The superior performance of the former can be attributed to the cumulative effect of the multi-bit outputs as well as the presence of more notch filters.
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Tetsuya Shimamura, Saitama University (Japan)
Colin F.N. Cowan, Queens University (U.K.)
For the purpose of equalisation of rapidly time variant multipath channels, the RLS algorithm might provide better performance than the LMS algorithm. However, the RLS algorithm requires complicated operation to adapt the equaliser coefficients. In this paper, we derive a novel adaptive algorithm, amplitude banded LMS(ABLMS), and develop it as the adaptation procedure for a linear transversal equaliser(LTE) and a decision feedback equaliser(DFE). Computer simulations demonstrate that with small increase of computational complexity, the ABLMS equalisers provide a significant improvement related to the conventional LMS DFE as well as LMS LTE.
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Walter Frank, University of BW München (Germany)
Ulrich Appel, University of BW München (Germany)
Nonlinear intersymbol interferences (ISI) often arise in voice-band communication channels at high transmission rates or in satellite channels due to nonlinearities in the power amplifiers. Proposed equalizers for the cancellation of these nonlinear interferences are mainly based on the Volterra series expansion, which is an elegant but very complex model. This paper presents a decision feedback equalizer (DFE) which is based on a new nonlinear filter structure. It is composed only of linear taped delay line filters and multipliers. Hence, the complexity of this still very general structure is comparable to linear filtering. Simulation of data transmission over a telephone channel show that the proposed DFE clearly outperforms the conventional DFE and is also superior to the Volterra DFE with a comparable complexity.
ic972501.pdf ic972501.pdf TOPWalter Chen, Texas Instruments, Inc. (U.S.A.)
The unshielded twisted pair can be used as a transmission media for local distribution networks. To maintain a high transmission throughput, an analog or a digital adaptive channel equalizer is usually required in the receiver to minimize the effect of inter-symbol interference. Under the observation that the high sampling rate high precision A/D and subsequent digital adaptive signal processing is an expensive approach, a direct equalization method, where the equalizer is implemented in the transmitter, is proposed for symmetrical twisted pair transmission channels. This direct equalization method can also be applied to the analog equalization approach for reduced system complexity.
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Michael Reuter, NCCOSC RDTE DIV (U.S.A.)
James Zeidler, NCCOSC RDTE DIV (U.S.A.)
An adaptive transversal equalizer based upon the least-mean-square (LMS) algorithm, operating in an environment with a temporally correlated interference, can exhibit better steady-state mean-square-error (MSE) performance than the corresponding Wiener filter. This phenomenon is a result of the non-linear nature of the LMS algorithm and is obscured by traditional analysis approaches that utilize the independence assumption. We use a transfer function approach to quantify the MSE performance of the LMS algorithm and demonstrate that the degree to which LMS may outperform the corresponding Wiener filter is dependent on system parameters such as signal-to-noise ratio and the step-size parameter.
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Gi Hun Lee, Sogang University (Korea)
Rae-Hong Park, Sogang University (Korea)
For quadrature amplitude modulation (QAM) systems, the joint blind equalization (JBE) algorithm, concatenation of two different equalization modes, has been widely used. After the eye is opened by the blind equalization mode, the decision-directed (DD) mode follows to improve the equalization performance with fast convergence. This paper proposes a shell partition-based CMA (SPCMA) which acts as the DD mode in the JBE. Computer simulation results for 16-QAM show the effectiveness of the proposed JBE.
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Oguz Tanrkulu, Imperial College (U.K.)
Buyurman Baykal, Imperial College (U.K.)
Anthony G. Constantinides, Imperial College (U.K.)
Jonathon A. Chambers, Imperial College (U.K.)
New Constant Modulus (CM) algorithms are presented that are based on soft constraint satisfaction. The stationary points of an algorithm in this family is studied for an AR($p$) channel and it is shown that Ding-type Undesirable Local Solutions (ULS) do not exist. This is due to the normalisation of the gradient vector and the soft nonlinearity used in these algorithms. Error Performance Surfaces (EPS) and convergence trajectories from arbitrary initialisations are presented for various channels that support the analytical findings.
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Tuan Nguyen, Auburn University (U.S.A.)
Zhi Ding, Auburn University (U.S.A.)
Blind adaptive beamforming is often used in communication systems to combat co-channel interference. Among a number of techniques, the constant modulus algorithm (CMA) has proven to be an effective tool for blind beamforming of uncorrelated signals. Unfortunately, CMA beamformers encounter problems for correlated signals and interferences. In this paper, we consider correlated co-channel input signals as a result of multipath. We present two adaptation methods based on CMA to capture distinct signal sources. One approach is to use an orthogonal projection constraint on the beamformer parameters. The other approach relies on the independence of source signals and exploit a Gram-Schmidt orthogonalization at beamformer outputs. The performance of our methods will be shown through computer simulations.
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Sally L. Wood, Santa Clara University (U.S.A.)
Michael G. Larimore, Applied Signal Technology (U.S.A.)
John R. Treichler, Applied Signal Technology (U.S.A.)
The gradient-descent-based Constant Modulus Algorithm (CMA) is commonly thought to converge much more slowly than its Least Mean Square (LMS) counterpart, particularly for quadrature-amplitude-modulated (QAM) signals. Experiments shown in this paper indicate that in fact there is no substantial difference in the convergence rates of the two methods in the important special case of constant envelope signals (e.g., FM and FSK). For both CMA and LMS algorithms the convergence for nontrivially frequency-modulated signals depends on the same eigenvalue disparity problem that affects all gradient-descent techniques.
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Won Gi Jeon, C.A.U. (Korea)
Yong Soo Cho, C.A.U. (Korea)
Kyung Hi Chang, ETRI (Korea)
In this paper, an equalization technique for OFDM and MC-CDMA systems in a time-varying multipath fading environment is described. A loss of subchannel orthogonality due to time-variation of multipath channels leads to interchannel interference (ICI) which increases the error floor in proportion to Doppler frequency. A simple frequency domain equalizer which can compensate the effect of time-variation in a multipath fading channel is proposed by taking into account only the ICI terms significantly affecting the error performance and by modifying the previous frequency-domain equalization techniques. The effectiveness of the proposed approach is demonstrated via computer simulation by applying it to OFDM system when the multipath fading channel is time-varying.
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