ABSTRACT This paper is dedicated to the study of the multiple‐input multiple‐output generalized frequency division multiplexing with index modulation (MIMO‐GFDM‐IM) wireless communication system. This system garners significant interest for future communications technologies due to its notable features, such as high spectral efficiency, energy efficiency, and robustness against multipath propagation channels. Preceding the study of the system, the model of signals and systems for MIMO‐GFDM is developed based on the MIMO orthogonal frequency division multiplexing model and detection strategies for the system are presented. A new proposal for MIMO‐GFDM detection, based on two filtering phases, is presented, resulting in an attractive tradeoff between detection performance and computational complexity. The presented system model is then extended to include index modulation as an information carrier, resulting in the MIMO‐GFDM‐IM system. Different proposals for detectors based on processing the complete channel matrix and also for detectors of reduced complexity are evaluated, from the perspective of detection performance and computational complexity.

In this paper, a hybrid precoder and a hybrid combiner are proposed. The analog beamformer of the hybrid precoder aims at the system sum-rate maximization. In contrast, the baseband beamformer of the hybrid precoder applies a low-dimensional baseband precoder to mitigate the inter-user/symbol interference and runs the proposed power allocation algorithm. The design of the power allocation matrix allocates the available transmit power such that the instantaneous bit error rate (BER) is reduced. On the other hand, the proposed hybrid combiner works cooperatively with the analog beamformer of the hybrid precoder to further increase the sum rate. Extensive simulation results evidence the positive effects of the proposed method in terms of BER and sum-rate performance compared to other processing techniques from the literature.

The present work focuses on obtaining better Bit Error Rate performance (BER), in precoded Single User-Multiple Input, Multiple Output-Orthogonal Frequency Division Multiplexing, SU-MIMO-OFDM systems in downlink through the use of Index Coding IC and a novel optimization procedure to select the Index Coding Matrix (ICM). A discrete model of the MIMO-OFDM system is presented which is efficient in signal generation and subsequent signal detection and identifies parameters that can be optimized, i.e, the optimal choice of the ICM, in order to improve the BER performance of the system.

Millimetre‐wave (mmWave) communications have been regarded as a key technology for the next‐generation cellular systems since the huge available bandwidth can potentially provide the rates of multiple gigabits per second. Conventional precoding and combining techniques are impractical at mmWave scenarios due to manufacturing costs and power consumption. Hybrid alternatives have been considered as a promising technology to provide a compromise between hardware complexity and system performance. This study examines, using a semi‐analytic approach, the downlink performance of massive MU‐MIMO mmWave systems in terms of the bit error rate (BER). Also, a general expression is derived to estimate an upper bound/approximation to the BER performance via the Monte Carlo method, which can be used for any hybrid precoder/combiner, modulation and different data detectors. Numerical results evidence that the approximate BER expressions provide values very close to the ones obtained through simulation using only two statistical moments related to parameters of the system, mean and variance.

This paper proposes a combination of the Single Carrier (SC) block transmission and the Code Division Multiple Access (CDMA) technique. Performance comparisons with the traditional SC DS- CDMA block transmission system are presented. A key feature of the proposed transmission technique is that, unlike SC DS-CDMA transmissions, the original code orthogonality between users is preserved despite propagation through multipath frequency selective channels, thus ideally allowing the decoupling of the signals at the receiver side. Besides this advantage, and mostly due to it, the performance results indicate a clear superiority of the proposed system over the traditional SC DS-CDMA. The simulation results consider frequency domain MMSE (Minimum Mean Squared Error) equalization and assume perfect knowledge of the transmission channels.

This letter proposes a novel sparsity-aware adaptive filtering scheme and algorithms based on an alternating optimization strategy with shrinkage. The proposed scheme employs a two-stage structure that consists of an alternating optimization of a diagonally-structured matrix that speeds up the convergence and an adaptive filter with a shrinkage function that forces the coefficients with small magnitudes to zero. We devise alternating optimization least-mean square (LMS) algorithms for the proposed scheme and analyze its mean-square error. Simulations for a system identification application show that the proposed scheme and algorithms outperform in convergence and tracking existing sparsity-aware algorithms.

In this paper an inverse QR decomposition based recursive least-squares algorithm for linearly constrained minimum variance filtering is proposed. The proposed algorithm is numerically stable in finite precision environments and is suitable for implementation in systolic arrays or DSP vector architectures. Its performance is illustrated by simulations of a blind receiver for a multicarrier CDMA communication system and compared with previously proposed inverse QR decomposition recursive least-squares algorithms. Highlights? We propose a Constrained Inverse QR decomposition based RLS (CIQRD-RLS) filtering algorithm. ? Proposed algorithm implemented by an update process followed by a downdate process. ? Several update and downdate QR decomposition algorithms are available in the literature. ? Proposed algorithm exhibits good numerical stability and steady-state performance.

The use of a feedback link in wireless orthogonal frequency division multiplexing (OFDM) systems is analysed. Although open-loop scenarios have been rigorously investigated in the literature, closed-loop scenarios, in which there is a feedback link from a strong to a weak user, have not been thoroughly studied. The study mainly focus on the recently proposed dynamic pilot symbol arrangement strategy. It was shown in a recent paper that for coherent OFDM transmission, this strategy is capable of delivering substantial gains in the performance. Pilot symbols are used to sample channel behaviour so that data symbols can be decoded correctly. However, these pilots do not need to be arranged so as to estimate the channel in the best possible way. In this work, the authors propose a pilot symbol arrangement strategy that minimises the bit error rate, we analyse the solution in detail and propose a low complexity search that maintains most of the quality of an exhaustive search. This low complexity search makes the pilot symbol method viable for medium to large-scale OFDM systems. The authors also analyse the use of a Wiener filter for channel estimation combined with the dynamic pilot symbol strategy and show that it delivers good gains in comparison to a simple maximum likelihood channel estimate.

We propose blind adaptive multi-input multi-output (MIMO) linear receivers for DS-CDMA systems using multiple transmit antennas and space-time block codes (STBC) in multipath channels. A space-time code-constrained constant modulus (CCM) design criterion based on constrained optimization techniques is considered and recursive least squares (RLS) adaptive algorithms are developed for estimating the parameters of the linear receivers. A blind space-time channel estimation method for MIMO DS-CDMA systems with STBC based on a subspace approach is also proposed along with an efficient RLS algorithm. Simulations for a downlink scenario assess the proposed algorithms in several situations against existing methods.

In this paper we proposed a linearly constrained minimum variance receiver for a space-time coded multicarrier (MC) CDMA system in frequency selective fading channels. It is shown that in the proposed receiver the channel can be blindly estimated as the eigenvector that corresponds to the maximum eigenvalue of an autocorrelation matrix, and then, efficient algorithms for subspace tracking can be used. Computer simulations shows that the proposed channel estimation algorithm achieves performance comparable to traditional algorithms with less computational cost.

This paper presents novel adaptive reduced-rank filtering algorithms based on joint iterative optimization of adaptive filters. The novel scheme consists of a joint iterative optimization of a bank of full-rank adaptive filters that constitute the projection matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe least squares (LS) expressions for the design of the projection matrix and the reduced-rank filter and recursive least squares (RLS) adaptive algorithms for its computationally efficient implementation. Simulations for a space-time interference suppression in a CDMA system application show that the proposed scheme outperforms in convergence and tracking the state-of-the-art reduced-rank schemes at about the same complexity.

This work proposes a low-complexity blind adaptive reduced-rank method (BARC) for symbol estimation using an adaptive decimation and interpolation scheme based on diversity-combining and the constant modulus criterion for interference suppression. The proposed approach employs an iterative procedure to jointly optimize the interpolation, decimation and estimation tasks for blind reduced-rank parameter estimation. We describe joint iterative estimators based on the constrained constant modulus (CCM) criterion, introduce alternative decimation structures, including the optimal decimation scheme, and develop low-complexity stochastic gradient adaptive algorithms for the proposed structure. Simulations for a CDMA interference suppression application show an excellent performance and substantial gains over prior art.

This paper presents a novel adaptive reduced-rank multi-input-multi-output (MIMO) linear equalization structure based on joint iterative optimization of adaptive filters. The proposed reduced-rank linear equalization structure consists of a joint iterative optimization of two equalization stages, namely, a projection matrix that performs dimensionality reduction and a reduced-rank linear equalization filter that retrieves the desired transmitted symbol. The novel linear reduced-rank structure is responsible for cancelling the inter- antenna interference caused by the associated data streams and exploiting the available degrees of freedom at the antenna-array receiver. We describe least squares (LS) expressions for the design of the projection matrix and the reduced-rank filter along with computationally efficient recursive least squares (RLS) adaptive estimation algorithms. Simulations for a MIMO linear equalization application show that the proposed scheme outperforms the state-of-the-art reduced-rank and the conventional estimation algorithms at about the same complexity.

In this paper we use an alternative implementation of the RLS based linearly constrained minimum variance (LCMV) receiver for multicarrier (MC) CDMA systems. As a result of this implementation a new blind channel estimation algorithm is proposed. It is shown through computer simulations that the resulting receiver filter achieves nearly the same performance than previously proposed methods, while reduces the computational complexity.

This paper presents a novel adaptive reduced- rank multi-input-multi-output (MIMO) decision feedback equalization structure based on joint iterative optimization of adaptive estimators. The novel reduced-rank equalization structure consists of a joint iterative optimization of two equalization stages, namely, a projection matrix that performs dimensionality reduction and a reduced-rank estimator that retrieves the desired transmitted symbol. The proposed reduced- rank structure is followed by a decision feedback scheme that is responsible for cancelling the inter-antenna interference caused by the associated data streams. We describe least squares (LS) expressions for the design of the projection matrix and the reduced-rank estimator along with computationally efficient recursive least squares (RLS) adaptive estimation algorithms. Simulations for a MIMO equalization application show that the proposed scheme outperforms the state-of-the-art reduced-rank and the conventional estimation algorithms at about the same complexity.

In this paper we propose iterative turbo minimum mean squared error (MMSE) successive parallel arbitrated decision feedback (DF) receivers for direct sequence code division multiple access (DS-CDMA) systems. We describe the MMSE design criterion for DF multiuser detectors along with successive, parallel and iterative interference cancellation structures. A novel efficient turbo DF structure that employs soft-decision successive cancellation with parallel arbitrated branches and a near-optimal low complexity user ordering algorithm are presented. The proposed iterative turbo DF receiver structure and the ordering algorithm are then combined with iterative cascaded DF stages for mitigating the deleterious effects of error propagation for uncoded systems. Simulations for an uplink scenario show substantial gains for the proposed iterative turbo DF detectors over the best known methods.

A space–time adaptive reduced-rank processor for interference mitigation in DS-CDMA systems is proposed based on interpolated finite impulse response filters with time-varying interpolators. The proposed space–time processor allows a significant reduction in the number of estimation elements, thereby increasing the convergence and tracking performance of the estimation algorithms. In order to compute the parameters of the proposed space–time processor, a least squares design is presented and computationally efficient recursive least-squares (RLS) algorithms are developed for estimating the parameters of both reduced-rank receiver and interpolator. A linear and successive interference cancellation space–time receivers based on the proposed reduced-rank processor for mitigating multi-access and intersymbol interference in an uplink scenario are proposed. An analysis of the convergence properties of the proposed space–time processor is carried out and analytical expressions are derived for predicting the mean squared error performance of the proposed RLS algorithm. Simulation results show that the proposed reduced-rank space–time processor and RLS algorithms outperform existing techniques at lower complexity.

Blind adaptive and iterative interference cancellation (IC) receiver structures for direct sequence code division multiple access systems in multipath channels are proposed. A code-constrained constant modulus design criterion based on constrained optimisation techniques and adaptive algorithms for receiver and channel parameter estimation are described for successive IC (SIC) and parallel IC (PIC) detectors and a new hybrid IC (HIC) scheme in scenarios subject to multipath fading. The proposed HIC structure combines the strengths of linear, SIC and PIC receivers and is shown to outperform the conventional linear, SIC and PIC structures. A novel iterative detection approach that generates different cancellation orders and selects the most likely symbol estimate on the basis of the instantaneous minimum constant modulus criterion is also proposed and combined with the new HIC structure to further enhance performance. Simulation results for an uplink scenario assess the algorithms, the proposed blind adaptive IC detectors against existing receivers and evaluate the effects of error propagationof the new cancellation techniques.

This paper presents a new approach to efficient acoustic echo cancellation (AEC) based on reduced-rank adaptive filtering equipped with selective-decimation and adaptive interpolation. We propose a novel structure of an AEC scheme that jointly optimizes an interpolation filter, a decimation unit, and a reduced-rank filter. With a practical choice of parameters in AEC, the total computational complexity of the proposed reduced-rank scheme with the normalized least mean square (NLMS) algorithm is approximately half of that of the full-rank NLMS algorithm. We discuss the convergence properties of the proposed scheme and present a convergence condition. First, we examine the performance of the proposed scheme in a single-talk situation with an error-minimization criterion adopted in the decimation selection. Second, we investigate the potential of the proposed scheme in a double-talk situation by employing an ideal decimation selection. In addition to mean squared error (MSE) and power spectrum analysis of the echo estimation error, subjective assessments based on absolute category rating are performed, and the results demonstrate that the proposed structure provides significant improvements compared to the full-rank NLMS algorithm.

In this paper we propose minimum mean squared error (MMSE) iterative successive parallel arbitrated decision feedback (DF) receivers for direct sequence code division multiple access (DS-CDMA) systems. We describe the MMSE design criterion for DF multiuser detectors along with successive, parallel and iterative interference cancellation structures. A novel efficient DF structure that employs successive cancellation with parallel arbitrated branches and a near-optimal low complexity user ordering algorithm are presented. The proposed DF receiver structure and the ordering algorithm are then combined with iterative cascaded DF stages for mitigating the deleterious effects of error propagation for convolutionally encoded systems with both Viterbi and turbo decoding as well as for uncoded schemes. We mathematically study the relations between the MMSE achieved by the analyzed DF structures, including the novel scheme, with imperfect and perfect feedback. Simulation results for an uplink scenario assess the new iterative DF detectors against linear receivers and evaluate the effects of error propagation of the new cancellation methods against existing ones.

A space-time adaptive decision feedback (DF) receiver using recurrent neural networks (RNNs) is proposed for joint equalization and interference suppression in direct-sequence code-division multiple-access (DS-CDMA) systems equipped with antenna arrays. The proposed receiver structure employs dynamically driven RNNs in the feedforward section for equalization and multiaccess interference (MAI) suppression and a finite impulse response (FIR) linear filter in the feedback section for performing interference cancellation. A data selective gradient algorithm, based upon the set-membership (SM) design framework, is proposed for the estimation of the coefficients of RNN structures and is applied to the estimation of the parameters of the proposed neural receiver structure. Simulation results show that the proposed techniques achieve significant performance gains over existing schemes.

In this paper we present a blind interference suppression technique for DS-CDMA systems based on a reduced-rank decomposition of a code-constrained constant modulus design criterion. We describe a least-squares (LS) type design criterion for blind linear detectors using the constrained optimization of the constant modulus cost function subject to code constraints. Based on this design approach and using the Lanczos algorithm, a multistage decomposition in the Krylov subspace is devised for blind reduced-rank parameter estimation. A computationally efficient blind reduced-rank LS type algorithm is also developed and compared with existing methods. Numerical results show that the proposed full-rank and reduced-rank techniques outperform existing methods for the linear suppression of multi-access and intersymbol interference in DS-CDMA systems.

This work proposes a low-complexity reduced-rank method for general parameter estimation using an adaptive decimation and interpolation scheme based on diversity-combining. The new approach employs an iterative procedure to jointly optimize the interpolation, decimation and estimation tasks for reduced-rank parameter estimation. We describe joint iterative minimum mean-squared error (MMSE) design filters, propose alternative decimation structures, including the optimal decimation scheme, and develop low-complexity adaptive algorithms for the proposed structure. Simulations for a block equalization application in doubly-selective channels show the remarkable potential of the proposed scheme.

An adaptive low-complexity space-time reduced-rank processor is proposed for interference suppression in asynchronous DS-CDMA systems based on a diversity-combined decimation and interpolation method. The novel design approach for the processor employs an iterative procedure to jointly optimize the interpolation, decimation and estimation tasks for reduced-rank parameter estimation. We describe joint iterative least squares (LS) design parameter estimators, propose alternative decimation structures, including the optimal decimation scheme, and develop low complexity adaptive recursive least squares (RLS) algorithms for the proposed structure. Linear space-time receivers with antenna arrays based on the proposed reduced-rank processor are presented and investigated for mitigating multi-access interference (MAI) and intersymbol interference (ISI) in an asynchronous DS-CDMA system uplink scenario.

This paper revisits the subspace-based channel estimation problem in zero-padded systems and proposes an alternative formulation that leads to a solution to which power techniques are readily applicable. Additionally, a lower-complexity post-DFT implementation that also allows the use of power techniques is derived. Both solutions are shown to be equivalent. Furthermore, links to previous related work are established. Mean square error and bit error rate performance analysis of the estimators through computer simulations reveals that for moderate signal to noise ratio, power techniques with powers as low as m = 3 achieves performance similar to the conventional SVD-based estimator.

In this work, we propose a new blind channel estimator based on correlation-matching techniques for zero padded OFDM systems. The correlation matching approach consists in matching the observation covariance matrix, which is parameterized by the unknown channel vector, with its estimates based on the received observations. The channel estimate, within a complex scalar ambiguity, can be obtained blindly as the solution of a minimization problem. Consistency of the estimator is addressed. Mean square error performance of the proposed estimator and the resulting bit-error rate (BER) performance after zero-forcing equalization are analyzed through computer simulations. The results show the robustness of the proposed technique.

This letter proposes a novel adaptive reduced-rank filtering scheme based on joint iterative optimization of adaptive filters. The novel scheme consists of a joint iterative optimization of a bank of full-rank adaptive filters that forms the projection matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe minimum mean-squared error (MMSE) expressions for the design of the projection matrix and the reduced-rank filter and low-complexity normalized least-mean squares (NLMS) adaptive algorithms for its efficient implementation. Simulations for an interference suppression application show that the proposed scheme outperforms in convergence and tracking the state-of-the-art reduced-rank schemes at significantly lower complexity.

This work presents low complexity blind constrained data-reusing adaptive filtering algorithms based on the minimum variance and constant modulus cost functions. Constrained minimum variance (CMV) and constrained constant modulus (CCM) affine projection type algorithms are developed and investigated in a CDMA interference suppression scenario. Computer simulations are used to analyze the proposed techniques and compare them with existing stochastic gradient (SG) and recursive least-squares (RLS) type techniques. The results show that the new algorithms outperform previously reported SG techniques with small additional computational requirements and achieve a performance very close to RLS algorithms at greatly reduced complexity

A space-time adaptive reduced-rank processor for interference suppression in DS-CDMA systems is proposed based on interpolated FIR filters. The interpolated minimum mean squared error (MMSE) solution is described for a novel scheme where the interpolator is rendered adaptive and adaptive algorithms are developed for estimating the parameters of both reduced-rank receiver and interpolator. Linear and successive interference cancellation (SIC) space-time receivers with the proposed structure are investigated for mitigating multi-access interference (MAI) and intersymbol interference (ISI) in an uplink scenario. An analysis of the convergence properties of the proposed structure is carried out and simulations for typical scenarios are performed, showing the superiority of the method against previously reported ones

In this paper we examine blind adaptive and iterative decision feedback (DF) receivers for direct sequence code division multiple access (DS-CDMA) systems in frequency selective channels. Code-constrained minimum variance (CMV) and constant modulus (CCM) design criteria for DF receivers based on constrained optimization techniques are investigated for scenarios subject to multipath. Computationally efficient blind adaptive recursive least squares (RLS) algorithms are developed for estimating the parameters of DF detectors along with successive, parallel and iterative DF structures. A new successive parallel arbitrated DF scheme is presented and combined with iterative techniques for use with cascaded DF stages for mitigating the deleterious effects of error propagation. Simulations for an uplink scenario assess the new blind algorithms, DF structures and the effects of error propagation of the new techniques

In this letter, we propose a broadly applicable reduced-rank filtering approach with adaptive interpolated finite impulse response (FIR) filters in which the interpolator is rendered adaptive. We describe the interpolated minimum mean squared error (MMSE) solution and propose normalized least mean squares (NLMS) and affine-projection (AP) algorithms for both the filter and the interpolator. The resulting filtering structures are considered for equalization and echo cancellation applications. Simulation results showing significant improvements are presented for different scenarios.

Blind adaptive reduced-rank receivers based on interpolated finite impulse response (FIR) filters with adaptive interpolators for direct sequence code division multiple access (DS-CDMA) systems are proposed and examined in multipath channels. The interpolated constrained minimum variance (CMV) solutions for both receiver and interpolator are described for mitigating multiple access interference (MAI) and multiple-path propagation effects in a downlink scenario. Computationally efficient blind adaptive algorithms for both receiver and interpolator based upon the minimum variance (MV) performance criterion are then developed with appropriate constraints to mitigate MAI, intersymbol interference (ISI) and jointly estimate the channel.

We propose reduced-rank receivers based on adaptive interpolated finite impulse response (FIR) filters and adaptive interpolators for direct sequence code division multiple access (DS-CDMA) systems, and examine the novel structures in multipath fading channels. We describe the interpolated minimum mean squared error (MMSE) and the interpolated least squares (LS) for both receiver and interpolator to mitigate multiple access interference (MAI) and multiple-path propagation effects in a downlink scenario. Based on the interpolated MMSE and LS solutions, we present normalised least mean squares (NLMS) and recursive least squares (RLS) algorithms for both receiver and interpolator filters. Simulation experiments show that the proposed structures achieve a superior convergence performance to previously reported reduced-rank techniques and to the full-rank receiver.

In this work we propose the blind adaptive decision feedback (DF) receivers for direct sequence code division multiple access (DS-CDMA) systems in frequency selective channels. Closed-form expressions for the design of blind DF DS-CDMA receivers are presented. Blind adaptive stochastic gradient (SG) and recursive least-squares (RLS) type algorithms are developed for use with the constrained minimum variance (CMV) and constrained constant modulus (CCM) receivers along with successive and parallel DF structures. Numerical results show significant performance gains for the proposed blind DF receivers.

We investigate the use of adaptive minimum bit error rate (MBER) gradient-Newton algorithms in the design of linear multiuser receivers (MUD) for DS-CDMA systems. The proposed algorithms approximate the bit error rate (BER) from training data using linear multiuser detection structures. We carry out a comparative analysis of linear MUDs employing minimum mean squared error (MMSE), previously reported MBER and the proposed MBER algorithms. Computer simulation experiments show that the MBER gradient-Newton approaches outperform other analysed algorithms and can operate with shorter training sequences.

We investigate the use of an approximate minimum bit error rate (MBER) approach to multiuser detection using recurrent neural networks (RNN). We examine a stochastic gradient adaptive algorithm for approximating the MBER from training data using RNN structures. A comparative analysis of linear and neural multiuser receivers (MUD), employing minimum mean squared error (MMSE) and approximate MBER (AMBER) adaptive algorithms is carried out. Computer simulation experiments show that the neural MUD operating with a criterion similar to the AMBER algorithm outperforms neural receivers using the MMSE criterion via gradient-type algorithms and linear receivers with MMSE and MBER techniques.

In this letter we investigate the performance of a per-survivor phase estimation algorithm for detection of trellis-coded modulation (TCM) signals in the presence of phase jitter and frequency error. Phase and frequency estimates are derived based on a second-order phase-locked loop (PLL)-like algorithm. A simplified transient and steady-state analysis of the algorithm recursive equations is derived. A heuristic blind phase acquisition scheme is proposed and shown to achieve good results. Computer simulations are used to compare the algorithm's performance to other methods described in the literature.

This paper presents a fast algorithm that performs a selective counting of the third-order intermodulation products generated when several carriers of various types are transmitted through a common nonlinear device. In deriving the algorithm, the carrier configuration and the frequency distribution of intermodulation products are both described by polynomials which are related to each other. The frequency distributions of third-order intermodulation products of the various kinds are then obtained with the aid of an FFT algorithm and a numerical method for solving a set of linear equations. When compared to a direct counting procedure, the proposed algorithm has presented a drastic reduction on the required Computational effort. This advantage is particularly important when the number of carriers sharing the nonlinearity is large. In an example with 1366 carriers of three different types sharing the nonlinearity, the CPU time was reduced from 7 h 46 min. down to 52 s.

The performance of sum/difference and reference/difference code tracking loops in direct-sequence spread-spectrum communication systems are fully analyzed and compared for nonwhite interference situations. In particular, symmetric dual-tone interference is considered and the worst case tone spacing and relative tone energies are determined. Parameterized curves of tracking-error variance and mean-time to lose lock are presented as a function of signal-to-interference ratio, dual tone spacing, and early-late gate delay difference.

Optimal design of a precorrelation filtering system for use in noncoberent direct-sequence code-tracking loops in the presence of colored noise is described, utilizing a linearized theory of loop operation. The design produces a bias-free loop with an odd S-curve, for which the rms tracking error is minimized. As a byproduct, one arm of the tracking loop provides an optimized signal for data-detection purposes. Widely applicable performance calculations, including rms tracking jitter, mean time to lose lock, and average detection signal-to-noise ratio, are given and illustrated, based on nonlinear models of loop operation.

When several voice-activated SCPC/FM carriers are transmitted through a nonlinear satellite repeater, a large number of intermodulation products appear at the output. An analysis of the baseband effect of these products is presented, taking into account the random on-off pattern followed by each carrier, the random nature of the level of each modulating speech signal, and a precise definition of the carrier power spectral density which is conditioned on the fact that the carrier is on, assuming that this is the circumstance under which we want to examine interference effects on any particular carrier. The analysis shows that computing intermodulation baseband noise, simply by introducing a penalty factor into the noise that would result by treating intermodulation as if it were thermal noise, may lead to very conservative estimates of intermodulation effects. The paper is restricted to the situation in which all carriers have equal amplitudes, but the general analysis is still valid when this is not so. The extension is straightforward except for the difficulties in counting the number of products of each type.