Recurrent neural networks (RNNs) are well known for their capability to minimize suitable cost functions without the need for a training phase. This is possible because they can be Lyapunov stable. Although the global stability analysis has attracted a lot of interest, local stability is desirable for specific applications. In this brief, we investigate the local asymptotical stability of two classes of discrete-time, continuous-state, complex-valued RNNs with parallel update and inner state feedback. We show that many already known results are special cases of the results obtained here. We also generalize some known results from the real-valued case to the complex-valued one. Finally, we investigate the stability in the presence of time-variant activation functions. Complex-valued activation functions in this brief are separable with respect to the real and imaginary parts.

For a special class of convolutional codes, iterative threshold decoding (ITD) has been shown by simulations to achieve the same error rate performance as belief propagation (BP). In order to get a better understanding of these iterative decoding algorithms, we describe ITD and BP as discrete-time dynamical systems. Based on the theory of dynamical systems, we compare the dynamical behavior of ITD and BP. For the special case of a linear dynamical system, the behavior can be completely characterized. In this case we show that the fixed points of both ITD and BP are globally stable but they do not coincide. The analysis is extended to the case of a continuous-time dynamical system, which represents an important step for modeling analog iterative decoders.

In this paper, we introduce a low decoding complexity space-time modulation scheme that achieves full transmit diversity without the need of channel knowledge at the transmitter (Tx) nor at the receiver (Rx). The scheme is based on differential encoding of a low-complex quasi-orthogonal space-time block code (STBC). The idea of the differential encoding is based on mapping the original system to an equivalent system which is composed of two orthogonal subsystems. The differential encoding and decoding approach is described and the receiver metric is derived. The described technique is valid for any number of transmit antennas M for which a square orthogonal code of size M/2 exists, and is valid for any number of receive antennas. The proposed scheme is favourable in that it has single complex symbol decoding complexity while achieving a performance close to other differential quasi orthogonal codes of higher complexity and a remarkable performance advantage compared to differential orthogonal schemes especially at high data rates.

Motivated from results for the point-to-point block MIMO fading channels without channel knowledge, we propose an AF scheme for the non-coherent two-way relaying channel with the half-duplex constraint. The communication takes place in two phases, multicast and broadcast. In the multicast phase the terminals send the signals simultaneously. In the broadcast phase, the relays resend the signal received in the broadcast phase. The code construction is based on subspace packings in the Grassmann manifolds. We show, that although no channel knowledge is assumed at either the terminals or at the relays, the terminals are able to subtract the self-interference part of the received signal. The performance analysis shows that the noncoherent two-way relaying outperforms non-coherent one-way relaying and delivers the promise of increased spectral efficiency.

Rate bounds for the non-coherent two-way relaying channel under the high SNR assumption are derived. No channel knowledge is assumed at neither the terminals nor at the relays. An upper and lower bound on the achievable rates are derived and shown that they differ only by a constant in the high SNR regime. As corollary from the analysis, the degrees of freedom of the non-coherent two-way channel are derived. Additionally, it is shown that the degrees of freedom can be achieved by an AF scheme.

In this paper, two types of multiple binary zero correlation zone (ZCZ) sequence sets are constructed: 1. Each set is a binary(2n+1Zcz,2n,Zcz)-ZCZ sequence set, which is one of the best cases in the known constructions. 2. Among all the sets, the sequences still possess good cross-correlation property within the zone of lengthZ≤Zcz. In particular, the first type sequence sets have a common zero correlation zone of lengthZ, which solves the previous research problem. These multiple binary ZCZ sequence sets are suitable for multiuser environments.

We propose a distributed differential space-time coding scheme for two-way relaying over unknown block Rayleigh fading channels. The accent is on a two-time slots scheme, where in the first stage both terminals transmit their signals to the relays and in the second stage the relays broadcast to the terminals. Although we do not assume channel knowledge neither at the relays nor at the terminals, we show that it is possible for the terminals to subtract their contribution from the broadcasted signal and decide on the desired signal from the other terminal. The performance analysis reveals that the two-time slots differential scheme offers advantage over the traditional four-time slots differential scheme.

Noncoherently detected frequency shift keying can be used in fast fading environments where it is difficult to track the channel. In this paper we present two methods to improve the performance of iteratively detected OFDM-MFSK. OFDM-MFSK is a combination of orthogonal frequency division multiplexing (OFDM) and noncoherent M-ary frequency shift keying (MFSK) that was developed as a robust transmission method for fast time varying channels. The first method increases the number of bits per label and therefore leads to an increased data rate, but also to an ambiguous mapping which has to be resolved by the channel decoder. In the second method, a precoder is inserted between the channel coder and the mapper, leading to a system of three serially concatenated codes. To analyze the iterative behavior of the receiver, we will use three dimensional EXIT charts, which allow us to predict the performance. The intention of both methods is to adapt the channel code to the modulation scheme in order to improve the performance of the iterative receiver.

In this letter, a new class of almost quadriphase sequences with a single zero element of period N, where N=1( mod 4) a prime, is presented. The new sequences have ideal autocorrelation property.

Two noncoherent space-frequency block coding schemes for MIMO OFDM are proposed and corresponding ML detection rules are derived. Both schemes have high flexibility and merely a linear growth in complexity with the number of OFDM subcarriers. One scheme shows a decrease in the diversity order with increasing number of subcarriers. It performs still better than the original code from (H. Boleskei et al., 2005), which is used as a basis for blocks, if the channel delay greatly exceeds the delay the code is designed for. The second scheme is a unitary blockwise design and it achieves full diversity order. It has the same performance as the original code if there is a channel delay design-mismatch.

A non-coherent distributed space-time coding scheme for wireless relay networks is presented. The scheme is the counterpart of non-coherent coding based on Grassmann codes, for cooperative wireless networks with relays. It is shown that special classes of Grassmann codes obtained from unitary codes such as Alamouti or Sp(n) codes, can be used as noncoherent distributed space-time codes. The scheme is extended to construct non-coherent distributed space-time codes of large block lengths in a recursive procedure.

This paper presents a method for construction of high-dimensional Grassmann space-time codes for non-coherent block fading MIMO channels, aiming at codes with large block lengths compared to the number of transmit antennas. The construction method is recursive, starting from a low-dimensional coherent or non-coherent code. The performance analysis of the constructed codes supports the theoretical prediction of performance improvement when increasing the code block length. Additionally, the code structure could potentially offer a possibility for complexity reduction of the decoding procedure.

As we have known, in OFDM a carrier frequency offset (CFO) can give rise to amplitude reduction and phase rotation of the desired signals, and induce inter-carrier interference (ICI). Accordingly, signal-to-interference-and-noise ratio (SINR) instead of signal-to-noise ratio (SNR) should be considered at the receiver. In this paper, on the basis of the proposed vector-valued transmission model, SINR will be investigated for un- coded OFDMA systems in the presence of CFOs. It will be shown that in frequency selective fading channels, the average SINR is dependent on the values of CFOs as well as the channel characteristics.

We consider the design of a block equalizer for an intersymbol interference channel, given that the channel impulse response is not perfectly known at the receiver. In contrast to other schemes, our receiver is designed for imperfect channel state information and incorporates the statistics of the channel estimation error. In particular, we suggest an error model for data transmission that takes the influence from the data symbols on the estimation noise into account. We derive the optimum detection rule for the considered error model according to the maximum likelihood criterion and verify that the covariance matrix of the estimation noise depends on the actual transmitted data symbols. Motivated by this result, we propose a realizable receiver structure adopting the turbo principle that exploits the data-dependency of the covariance matrix of the estimation noise. The proposed scheme outperforms conventional receivers that neglect the exact statistics of the estimation noise. The core of our receiver is a soft-input soft-output block equalizer based on constrained minimum variance filter design. We assess the performance of the proposed turbo equalization scheme for block Rayleigh fading channels, applying both one-shot training-based channel estimation and iterative data-aided channel estimation

We show that orthogonal space-time block codes may be identified with packings on the Grassmann manifold. We describe a general criterion for packings on the Grassmann manifold that yield coherent space-time constellations with the same code properties that make orthogonal space-time block codes so favorable. As an example, we point out that the rate 3/4 orthogonal space-time block code motivates a packing on the Grassmann manifold that allows for a simplified maximum likelihood detection rule using the newly introduced framework. As a side product, this packing defines a noncoherent space-time constellation that may be regarded as a generalization of certain existing noncoherent space-time codes.

We address the problem of how to use a priori information of data symbols to improve signal-to-noise ratio (SNR) estimation. Digital transmission with binary phase-shift keying (BPSK) over additive white Gaussian noise (AWGN) channels serves as a background. At the receive side, both pilot and data symbols are used to estimate the SNR. In addition, we assume that a priori information of the data symbols is available. Our proposed estimator is then derived as an approximate solution of the maximum-likelihood (ML) approach. A significant improvement in the low-SNR regime over the corresponding estimator without a priori information is shown. Hence, an estimator that uses a priori information of data symbols is suitable to be embedded in iterative decoding schemes like, e.g., turbo decoding or turbo equalization. In addition, the Cramer-Rao lower bound (CRLB) for SNR estimators using a priori information of data symbols is derived

We derive two theorems that enable us to determine the bit error rate performance of orthogonal space-time block codes in an analytical way if the channel impulse response is measured by pilot based maximum likelihood estimation at the receiver. The first one gives an exact solution, but requires numerical integration. The second one provides an approximation that is improving with increasing number of antennas. The analysis is based on a real-valued transmission model which allows for a representation of orthogonal space-time block codes as linear spreading matrices. That means, encoding and decoding the space-time block code is carried out by a single matrix multiplication at the transmitter and the receiver, respectively.

We propose a soft-input soft-output block equalizer based on constrained minimum variance filters. In contrast to other schemes, our receiver is designed for imperfect channel state information and incorporates the statistics of the channel estimation error. Thereby, we distinguish between data independent and data dependent evaluation of the covariance matrix of the estimation error. We show that the performance of our block equalizer is significantly improved when considering the influence of the actual data symbols on the estimation error. The additional complexity compared to the case when ignoring the data dependency of the estimation error increases quadratically with the block length. We assess the performance of our equalizer for block Rayleigh fading channels via Monte Carlo simulation, employing turbo equalization and one-shot training-based channel estimation

We present closed-form expressions for the symbol error probability (SEP) of diversity combining receivers operating under Rayleigh fading. Only an imperfect, training-based estimate of the individual, possibly correlated fading branches shall be available at the receiver. While most of the previous papers on this topic have dealt with PSK schemes only, we address the more complicated problem of finding SEP expressions for general multi-amplitude ASK and QAM constellations. Both one-and two-dimensional constellations are considered and virtually no restrictions are made regarding the covariance matrices of channel and noise

The paper deals with space-time-coded transmissions sence of channel estimation errors. A simple on model is described which gives insight into the tions between space-time block coding schemes and l concept of spreading. On the basis of this model, lgebraic space-time (DAST) block codes are taken as an or maximum ratio combing and equal gain combining n, that in case of channel estimation errors suboptimum at the receiving side might outperform optimum ones. atical equivalence between DAST and multicarrier ion multiplexing as a by-product of the modelling is ssed.

We present a model of linear space-time block coded multiple input multiple output wireless systems for quasi-static frequency nonselective fading channels. The code is described by its set of spreading matrices. We give a condition on the spreading matrices in order not to degrade the mutual information compared to the uncoded case. The knowledge of the channel impulse response and the spreading matrices at the receiver defines the relationship between the received and transmitted symbol vectors via a positive semidefinite matrix R (k). We present a new criterion for optimizing linear space-time block codes based on the fact that all the entries of R (k) are sums of quadratic forms and that the intersubchannel interference is represented by the off-diagonal entries. This criterion aims at minimizing the peak value of the intersubchannel interference.

We address the problem of interference cancellation for MC-CDM when the channel is uncertain, i.e., not perfectly known. In contrast to the decision-directed schemes that iteratively improve a channel estimate, we study a simpler receiver that tries to allow for the uncertainty of a solely pilot-based estimate. For this, we first derive the optimal receiver for both OFDM and MC-CDM, which merges the two processing stages of channel estimation and data detection, and show that this receiver may be partitioned into a pilot-based channel estimator and a detector that incorporates the estimator's error covariance matrix. Such a decomposition suggests an error model on the basis of deriving a block decision feedback equalizer (BDFE) which utilizes the estimator's error covariance as a reliability information. Simulation results demonstrate the performance of the error-aware BDFE.

We consider receiver design for doubly-selective, rapidly time-varying channels with the goal of maximizing the signal to noise ratio at the sampling instant. Three types of receivers are studied: the optimum adaptive matched filter that requires accurate channel tracking, a statistical matched filter design, and a receiver concept that approximates the adaptive matched filter by coherently combining the outputs of a limited number of channel eigenfunction filters.

We derive a lower bound for the capacity of a communication channel comprising a memoryless nonlinearity such as a saturating amplifier, and distortion by additive white gaussian noise. The channel input is a bandlimited bandpass process, channel input and output are assumed to be zero-mean and stationary. The bound's integral expression is evaluated and plotted for the case of a transmit signal with constant power spectral density.

We consider the uplink transmission of a coded MC-CDMA system in the presence of carrier frequency offsets. Based on a vector transmission model the impacts of these frequency offsets are analyzed and a downlink carrier frequency offset estimation and compensation scheme is proposed for use in the uplink. At the base station a linear minimum mean square error multiuser detector is employed to suppress the multiuser interference caused by the frequency estimation errors as well as by multipath propagation.

In recent years, there has been a growing interest in applying turbo algorithms to enhance performance in communication systems. Among them, iterative equalization and decoding, turbo equalization, has proven to be a powerful technique to mitigate intersymbol interference. In this paper, we propose a soft interference canceler with memory, suitable for general complex symbol alphabets, as part of a turbo equalization scheme and investigate its convergence behavior using the extrinsic information transfer (EXIT) chart tool. Although the true behavior of the trajectory of the iterative process cannot be perfectly predicted, we obtain useful information to reduce computational complexity of the turbo scheme.

The performance of orthogonal frequency division multiplexing (OFDM) deteriorates in a rapidly time-varying environment due to the loss of orthogonality, resulting in inter-channel interference (ICI). Moreover, the quality of model-based channel estimation may degrade if the estimator has been designed for a time-invariant scenario. In this paper, we consider OFDM and pilot-aided channel estimation via Wiener filtering and derive the filter for a time-variant WSSUS model. In addition, the analysis allows to compute the performance loss for an improper estimation filter which suffers from the problem of model mismatch.

Pilot symbol assisted modulation (PSAM) eases the task of estimating the channel gain and phase in frequency-flat Rayleigh fading. Inaccurate channel estimates may lead to an increased error probability in a subsequent data detection stage. For PSAM and flat Rayleigh fading, the effects of channel estimation errors on the error probability have been analyzed in A. Aghamohammadi and H. Meyr [Nov. 1990]. We pursue the analysis given in A. Aghamohammadi and H. Meyr [Nov. 1990] and derive the maximum a-posteriori (MAP) detector which minimizes the symbol error probability by processing the data and pilot receive symbol(s) simultaneously. This detector is compared to the conventional 2 step receiver which performs channel estimation followed by data detection. Moreover, a basic approach to calculate the symbol error probability is given and we study and illustrate the decision regions of the two detectors.

A discrete-time matrix transmission model is introduced for wideband multiuser multiple-input multiple-output (MIMO) transmission systems. The model is more general than existing ones in the sense that it incorporates correlated interference and noise by means of prewhitening. It allows a flexible treatment of users that may or may not be included in a joint detection process. On the basis of the matrix transmission model, conventional multiuser detection techniques are easily adapted for the multiuser MIMO case. It is shown that for certain types of interference, a linear matrix transmission model exists only for a real-valued notation. Moreover, the real-valued notation provides the possibility to include space-time block codes in the linear transmission model. In order to endorse the introduction of this particular matrix model, we show that the discrete-time transmission matrix immediately determines the capacity of the MIMO transmission system. Some simulation results based on optimum and suboptimum detection techniques indicate that the loss of performance due to the exclusion of users from joint detection is quite small.

Multicarrier spread spectrum transmission methods based on orthogonal frequency division multiplexing employ a linear transform to spread energy of transmitted symbols over statistically independent Rayleigh fading subcarriers, in order to enable a diversity gain at the receiver. We jointly treat the mapping from bits into transmit symbols and the spreading transform as a code in Euclidean space. We describe criteria to identify good and bad spreading transforms, in terms of the asymptotic bit-error probability (BEP) at high signal-to-noise ratio. Upper and lower bounds on the BEP are derived. It is shown that the BEP performance of the commonly used Hadamard transform is asymptotically bad. Alternative orthogonal transforms with better asymptotic performance are proposed. Simulation results are given for the example of 2-phase-shift keying, block length 8.

Abstract Multiuser/multisubchannel detection schemes based on a recurrent neural network (RNN) structure are a promising alternative to conventional detection schemes, both in terms of performance and complexity. This paper gives an overview of different approaches that make use of the results of RNN research for multiuser/multisubchannel detection. The detectors' results are compared with the results of conventional detection schemes in simulations of the uplink of a DS‐CDMA packet transmission system. Copyright © 2002 John Wiley & Sons, Ltd.

We investigate amplitude distributions of transmit signals for multi-carrier spread spectrum (MCSS) transmission methods based on orthogonal frequency division multiplexing (OFDM), also called multi-carrier code division multiplexing (MC-CDM). In particular we compare Fourier spreading with the commonly used Walsh-Hadamard spreading. As a basis for the comparison we describe a general model. Both up- and downlink of multiple access transmission schemes employing either multi-carrier code division multiple access (MC-CDMA) or multi-carrier frequency division multiple access (MC-FDMA) are compared.

Channel capacities of various channel models are investigated. We consider two frequency selective channels, the indoor radio channel, simulated with ray tracing, and the two path channel. Additionally Rayleigh-, Rice- and Nakagami-m-distributed stochastic channel models and the discrete-time additive Gaussian noise channel with binomial distributed input alphabet are treated.

We describe a power and bandwidth efficient transmission scheme for Rayleigh fading channels and a suitable low complexity combined equalization and decoding system. The transmission system is based on an orthonormal transform (fast Hadamard transform) combined with trellis-coded modulation (TCM). The receiver uses an iterative block decision feedback equalizer and a Viterbi algorithm to decode the TCM. It is shown that the equalizer transforms the Rayleigh fading channel asymptotically into a set of parallel AWGN subchannels. Therefore, the decoder of each subchannel "sees" an AWGN channel. Hence, coding gains comparable to the coding gains in an AWGN environment can be achieved. The results are considerably better than the performance of TCM codes designed for the Rayleigh fading channel with the same power and bandwidth efficiency. The conclusions of channel capacity considerations support the potential of the proposed transmission and reception scheme. The theoretical findings are furthermore supported by simulation results.