This paper presents a comprehensive survey of semantic protocols, protocol learning, and AI-enabled semantic protocols within the context of Open RAN and 6G networks. We systematically review the significant progress achieved in these domains, highlighting key methods such as transformer-based semantic encoders, reinforcement learning–driven protocol adaptation, and federated learning frameworks for distributed training. Across surveyed studies, notable achievements include bandwidth savings of 35-70%, improved robustness under noisy conditions, and enhanced interoperability in multi-vendor environments. By consolidating findings, we identify major challenges such as the lack of standardized semantic KPIs, computational overhead at the edge, interoperability issues, and emerging security vulnerabilities. Furthermore, we categorize open research opportunities into theoretical, methodological, technical, and implementation directions, providing a clear roadmap for future development. This survey ultimately positions semantic communication and AI-enabled protocols as pivotal enablers for meaning-centric, adaptive, and efficient next-generation O-RAN/6G networks.

As communication systems evolve toward 6G, semantic communication is emerging as a transformative paradigm that prioritizes the accurate transmission of meaning rather than just bits. While artificial intelligence enables this shift by facilitating intelligent interpretation and context-aware processing, it also introduces significant challenges related to transparency, reliability, and user trust. XAI has thus become essential in making AI-enabled semantic communication systems more interpretable, auditable, and accountable. To the best of our knowledge, this is the first survey that systematically analyzes how explainability can be embedded across all stages of the semantic communication pipeline, integrating architectural design, metrics, security considerations, and human-in-the-loop mechanisms. Additionally, the survey identifies pressing research challenges, including the lack of standardization, real-time applicability, and vulnerabilities introduced by opaque AI models. By drawing attention to these issues and outlining future research directions, this survey aims to guide the development of responsible and trustworthy semantic communication systems for next-generation wireless networks.

The Cloud-Edge collaborative computing enables the deployment of latency-sensitive and data-intensive applications closer to end users. However, it introduces significant challenges for microservice placement, due to resource heterogeneity, limited edge capacity, and the need to satisfy storage requirements using aggregated resources across multiple nodes. To address these issues, we proposeDiktopos, a topology-aware, two-stage scheduling framework that jointly optimizes microservice placement and distributed storage volume allocation in cloud-edge networks. The joint optimization problem is decomposed into two subproblems: (i) microservice placement and (ii) distributed volume allocation, with the objective of minimizing computation, communication, energy, and storage costs. At its core, Diktopos employs a low-complexity, rank-based heuristic that ensures scalable and accurate placement across heterogeneous edge nodes. Simulation results show that our method achieves near-optimal placement decisions (within 1.67% of the optimal solution), and converges up to 5× faster than state-of-the-art approaches in large-scale deployments. Real-world experiments in Kubernetes environments demonstrate up to 53% latency reduction compared to the default scheduler, and up to 23% improvement over other baselines, confirming Diktopos' effectiveness in dynamic, resource-constrained edge scenarios.

Open Radio Access Network (O-RAN) enables modular and intelligent control of radio resources through open interfaces and programmable RAN components. As networks evolve toward sixth-generation (6G) systems, the proliferation of autonomous xApps and rApps introduces a critical challenge: Coordinating concurrent AI-driven control actions under tight near-real-time constraints while avoiding instability and conflicting decisions. This paper focuses on two tightly coupled enablers for AI-native O-RAN orchestration: Conflict-aware control and intent-driven automation. We propose an AI-native orchestration framework centered on a CME integrated into the Near-RT RIC, and a complementary LLM-based intent orchestration module deployed in the Non-RT RIC. The CME is designed to autonomously arbitrate conflicting xApp actions by learning adaptive mitigation policies from structured conflict signals, system context, and performance feedback, rather than relying on static priorities or predefined conflict classes. The LLM module translates high-level operator intents into policy constraints and control objectives that guide conflict resolution and xApp behavior. Overall, this work advances AI-native O-RAN orchestration by grounding conflict-aware control and LLM-assisted intent translation in practical measurements, and by outlining a clear path toward scalable, adaptive, and resilient control mechanisms required for future 6G RIC deployments.

In this paper, we present a programmable data plane design that implements IEEE 802.1Qcr’s Asynchronous Traffic Shaper (ATS) purely in software using Extended Berkeley Packet Filter (eBPF), eliminating specialized hardware requirements for industrial Time-Sensitive Networking (TSN) deployments. Unlike hardware-bound TSN solutions, our approach dynamically decouples and reprograms functions like filtering, metering, and queuing through in-kernel eBPF hooks, enabling adaptive priority management for concurrent streams within shared priority queues. The design explicitly models the ATS scheduler to parameterize per-stream eligibility times in TSN bridges while maintaining deterministic operation. This software-defined method provides a vendor-agnostic path for integrating ATS capabilities into existing industrial networks, particularly for Industry 5.0’s distributed control scenarios requiring flexible traffic multiplexing. The results confirm correct enforcement of ATS scheduling semantics under heterogeneous workloads.

The rise of real-time networking demands has driven the IEEE Time-Sensitive Networking (TSN) task group to develop new standards that ensure high bandwidth and lowlatency Ethernet communication. TSN is an essential component of next-generation 6G networks. It offers features that ensure deterministic data transmission and alleviate network congestion. These features are crucial in time-sensitive applications and systems, whereby both precision and reliability are paramount. While early TSN implementations relied heavily on synchronous communication, newer standards, such as IEEE 802.1Qcr, have introduced asynchronous mechanisms via Urgency-Based Scheduler (UBS). UBS employs advanced queuing and traffic shaping strategies, to guarantee minimal delay for real-time applications. Within the scope of 6G, this study evaluates the queuing and shaping strategies applied to multiple flows within the UBS framework. Moreover, we assess their impact on frame transmission rates at the shaper level, highlighting the optimal use case for each strategy.

The rapid development of reconfigurable intelligent surfaces (RISs) has sparked transformative advancements in wireless communication systems. These intelligent metasurfaces, adept at dynamically manipulating electromagnetic (EM) waves, hold vast potential for enhancing network capacity, coverage, and efficiency. However, to fully unleash the capabilities of RIS-aided communication systems, effective optimization is crucial. This article provides a recent development of RIS-assisted communication from the viewpoint of physically-consistent EM models. We delve into the realm of physically-consistent EM models, highlighting their pivotal role in achieving robust and efficient RIS designs. Furthermore, this paper offers a survey of the different optimization models utilized for RIS-assisted wireless communication systems, which consider various EM and physical aspects of RIS. We explore solution approaches aimed at optimizing different objectives like sum-rate/spectral efficiency and energy efficiency, spanning traditional optimization models to machine learning-based methods. Additionally, we discuss some open research issues in this field.

This article focuses on the stability of uncertain fractional order (FO) polynomials involving integer and FO natural exponential functions. These functions arise from the flexibility property and time delays in the control loop of the system of rigid–flexible coupling space structures. The coefficients of the polynomial are assumed to be complex numbers which are linear functions of uncertain real parameters. An analytical method is presented to check the robust bounded-input bounded-output stability of the control system. Furthermore, a method is developed to determine up to how much the amplitude of the uncertain parameters can grow such that the controller preserves the stability of the system. In the end, an improved optimal FO phase-lead controller is designed for the residual vibration suppression of the FO model of a rigid–flexible coupling space structure. Then, the merit of the presented theoretical results is demonstrated by applying them to the designed control loop.

This paper aims at the proportional-integral (PI) control of the cone vibration of the electrodynamic loudspeakers system recently described using a linear fractional order model. After introducing the fractional order model of the circuit of these loudspeakers, firstly, a new method is developed to design a fractional order PI controller to place the poles of the system in a desired area of the complex plane which is called D-stabilizing. The design parameters of the method depend directly on the speed of the system output response, the cone vibration. Moreover, the offered fractional order controller avoids any non-minimum phase zero, which causes undesired undershoots in the output, for the closed-loop control system. Secondly, considering uncertainties in the coefficients of the model, a methodology is presented to determine up to how much the uncertainties can increase such that the controller is still able to maintain both D-stability and the absence of non-minimum phase zeros for the control system. Finally, the merit of the presented results and the superiority of the designed fractional order controller over its conventional integer order counterpart are illustrated through numerical simulations.

Abstract Deep learning (DL) is attracting considerable attention in the design of communication systems. This paper derives a deep unfolded conjugate gradient (CG) architecture for large‐scale multiple‐input multiple‐output detection. The proposed technique combines the advantages of a model‐driven approach in readily incorporating domain knowledge and deep learning in effective parameters learning. The parameters are trained via backpropagation over a data flow graph inspired from the iterative conjugate gradient method. We derive the closed‐form expressions for the gradients for parameters training and discuss early results on the performance in a statistically identical and independent distributed channel where the training overhead is considerably low. It is worth noting that the loss function is based on the residual error that is not an explicit function of the desired signal, which makes the proposed algorithm blind. As an initial framework, we will point to the inherent issues and future directions.

Centralized Massive Multiple Input Multiple Output (MIMO) uplink detection techniques for baseband processing possess severe bottleneck in terms of interconnect bandwidth and computational complexity. This problem has been addressed in the current work by adapting the centralized Newton method for decentralized MIMO uplink detection leveraging several Base Station antenna clusters. The proposed decentralized Newton (DN) method achieves error-rate performance close to centralized Zero Forcing detector as compared to other decentralized techniques. Two hardware topologies, namely the ring and the star topologies, are proposed to assess and discuss the trade-off among interconnect bandwidth and throughput, in comparison with contemporary decentralized MIMO uplink detection techniques. As such the following findings are elaborated. On BS antenna cluster scaling for different MIMO system configurations, the ring topology provides high throughput at constant interconnect bandwidth, while the star topology provides lower latency with a deterministic variation in the hardware resource consumption. Due to strategic optimizations on the hardware implementation, additional user equipment can be allotted at a fractional increase in Field Programmable Gate Array resource consumption, improved energy efficiency, and increased transaction of bits per Joule. The ring topology can process additional subcarrier at a fractional increase in latency and improved system throughput.

The Surrogate Analysis (SA) is known to detect nonlinear signals, non-stationary signals and ARMA systems driven by non-Gaussian processes. This paper adds to address the detection of non-random phase signal, of which the linear phase signal is the best-known example. This is a new interpretation of the SA. In order to highlights the benefits of the interpretation, a new theoretical signals is constructed. The signal has a perfect Gaussian distribution and is not affected by periodic extension and is a linear phase signal. The SA will be shown able to detect this signal in a noise with exactly the same power spectrum. It will be clear that the SA is able to detect phase linearity even when the data is normally distributed. An application of the detection by SA is given regarding very noisy and short time electrocardiogram (ECG) signal and compared to higher order statistics and normality tests for this purpose.

Solving Complex Problem that is coupled with intensive workloads; necessities the access to a massively parallel computational power. Up to date, Graphic Processing Units (GPUs) are the only architecture that could handle the most complex computationally intensive workloads. In the light of this rapid-growing advancement in computational technologies, this paper will propose a high-performance parallel radix-23FFT suitable for such GPU and CPU systems. The proposed algorithm could reduce the computational complexity by a factor that tends to reach prif implemented in parallel (pr is the number of cores/threads) plus the combination phase to complete the required FFT.

In this paper we consider an efficient method to resolve the underlying large matrix inversion problem inherent in the antennas' mutual coupling based reciprocity calibration. Such calibration enables the downlink pre-coding using the uplink channel estimates in a time-division-duplex (TDD) massive MIMO systems. Based on least squares estimators, a large matrix inversion is required. Herein, we derive an efficient method based on successively updating a matrix inverse by exploiting the Gram matrix structure. The simulation results reveal that our proposed method performs as well as the direct matrix inversion (based on Cholesky decomposition) whereas the approximation techniques based on Gauss Seidel (GS) and Neumann series expansions (NSE) require a large number of iterations. The proposed method is computationally efficient and lend itself for an efficient parallel and pipelined architecture implementation.

In this paper, we study the energy efficiency of secure communication in an underlay cognitive radio network (CRN). We first formulate an optimization problem to maximize the secrecy energy efficiency (SEE) while meeting the quality-of-service (QoS) requirement for the primary user and the transmit power constraint at each base station. Since the problem is non-convex and very difficult to solve, we then convert the original fractional form into a subtractive one, and adopt the difference of two-convex functions (D.C.) approximation method to obtain an equivalent convex problem. Furthermore, a two-layer iterative algorithm is presented to solve the problem and obtain the optimal beamforming (BF) weight vectors. Finally, numerical results are provided to demonstrate the superiority of the proposed scheme.

This paper is concerned with the energy efficiency of secure transmission in an underlay cognitive relay network (CRN), where a secondary source communicates with a secondary destination via a multi-antenna relay in the presence of an eavesdropper. We first establish an optimization problem to maximize the secrecy energy efficiency (SEE) under the constraints of data rate and transmit power of the cognitive transmission as well as the interference limitation to the primary user. Then, we recast the original non-convex problem in fractional form into an equivalent subtractive one with an additional rank-one constraint. Moreover, we incorporate the rank-one constraint into the objective function as the penalty term and apply the difference of two-convex functions (D.C.) approach to obtain an equivalent convex problem. Finally, we present an iterative algorithm to obtain the optimal solution for the SEE maximization problem in the CRN. Numerical results are provided to demonstrate the effectiveness of the proposed scheme.

Fast Fourier Transform (FFT) is an important part of many applications, such as in wireless communication based on OFDM (Orthogonal Frequency Division Multiplexing). With Cloud Radio Access Networks, implementing FFTs on multiprocessor clusters is a challenging task. For instance, supporting the Long Term Evolution (LTE) protocol requires processing 100 independent FFTs (with sizes ranging from 128 to 2048 points) in 66.7 μs. In this work, seven native FFT candidate implementations are compared. The considered implementation environments are: OpenMP (Open Multi-Processing) on 1 core, MPI (Message Passing Interface) on 1 core, 2 cores, and 3 cores, Hybrid OpenMP+MPI on 1 core and 3 cores, and MPI on an heterogeneous platform composed of Xeon-Phi and 3 cores. The reported experimental results show that the latter method meets the latency requirements of LTE. It is shown that the OpenMP and MPI paradigms running only on MICs (Many Integrated Cores) cannot benefit fully from the computing capability of many-core architectures. The heterogeneous combination of Xeon+MICs provides a better performance.

The availability of channel state information (CSI) at the transmitter plays a central role to provide high system performance in massive multiple-input multiple-output (MIMO) systems. In a frequency division duplexing (FDD) system, acquiring this information requires a prohibitive amount of feedback and a significant feedback energy, since it increases with the number of transmit antenna. In this paper, we address the issue of significant energy consumed to feedback all CSI to the base station (BS). To this end, we propose a novel feedback routing scheme based on transmit antenna selection for massive MIMO systems. The proposed scheme aims to jointly reduce the energy needed to feedback the CSI to the BS and the complexity of the transmit antenna selection. We formulate the problem of finding the feedback routing that minimizes the energy consumption as a least cost Hamiltonian path problem. To solve the formulated problem, we propose both an integer linear programming formulation to find the optimal solution and a heuristic dynamic programming algorithm to find a suboptimal solution with reasonable computational complexity. Computer simulations show that our scheme offers enormous reduction in feedback energy while ensuring low computational complexity.

This paper considers the problem of acquiring the channel state information (CSI) at the base station in large-scale multiple input multiple output (MIMO) systems, so-called massive MIMO systems. Clearly, acquiring the CSI plays a central role to provide high system performance. Even though, in frequency-division duplexed systems, acquiring this information requires a prohibitive amount of feedback, since it increases with the number of transmit antenna at the base station. In this work, we design an efficient transmit antenna selection strategy aware of the amount of required CSI for a massive MIMO system in the broadcast channel. The proposed strategy has to reduce both the CSI feedback and the computational complexity, and also to improve the system sum-rate. Contrary to what is generally proposed in the literature, the decision in our strategy is performed in a distributed fashion at the users. Named Successive Removal for Antenna Selection, the strategy proposed in this work can be implemented with three proposed schemes, which aims to solve differently the tradeoff between the computational complexity and sum-rate performance. Computer simulations show that the proposed algorithms are able to achieve good performances while a significant reduction in both CSI feedback overhead and computational complexity is observed.

It is largely accepted that the innovative technology of large-scale multiantenna systems (named Massive multiple input multiple output (MIMO) systems) will very probably be deployed in the fifth generation of mobile cellular networks. In order to render this technology feasible and efficient, many challenges have to be investigated before. In this paper, we consider the problem of antenna selection and user scheduling in Massive MIMO systems. Our objective is to maximize the sum of broadcasting data rates achieved by all the mobile users in one cell served by a massive MIMO transmitter. The optimal solution of this problem can be obtained through a highly complex exhaustive brute force search (BFS) over all possible combinations of antennas and users. This BFS solution cannot be implemented in practice even for small size systems because of its high computational complexity. Therefore, in this paper, we propose an algorithm that efficiently solves the problem of joint antenna selection and user scheduling. The proposed algorithm aims to maximize the achievable sum-rate and to benefit from both the spatial selectivity gain and multi-user diversity gain offered by the antenna selection and user scheduling, respectively. Compared with the optimal solution obtained by the highly complex BFS, the conducted performance evaluation and complexity analysis show that the proposed algorithm is able to achieve near-optimal performance with low computational complexity.

This study proposes a transmit power allocation (TPA) scheme for bi‐directional relay networks with an objective of minimising the total power consumption to meet both the service quality (i.e. the outage probability) and individual power requirements. This new scheme focuses on the amplify‐and‐forward protocol‐based multiple‐access broadcast mode with asymmetric network traffics where the bi‐directional relay channel (BDRC) statistics are assumed to be available at the transmitters. A two‐step method is devised to solve the optimisation problem pertaining to the total power minimisation. In the proposed method, the system outage probability is first minimised subject to both the individual and total power constraints, and then the total power consumption of the network is minimised subject to the given service quality constraint based on the preliminary solutions achieved in the first step. This two‐step optimisation mechanism leads to a novel TPA algorithm for the relay and two sources of the network. Simulation results are provided to validate the proposed algorithm, showing that the proposed new power allocation scheme can significantly reduce the total power consumption, especially when the BDRC or the network traffic is asymmetric.

In this paper, we propose an FPGA implementation of a genetic algorithm (GA) for linear and nonlinear auto regressive moving average (ARMA) model parameters identification. The GA features specifically designed genetic operators for adaptive filtering applications. The design was implemented using very low bit-wordlength fixed-point representation, where only 6-bit wordlength arithmetic was used. The implementation experiments show high parameters identification capabilities and low footprint.

This paper investigates opportunistic relaying of a half-duplex two-way relay network, where two source users exchange information through a shared amplify-and-forward (AF) relay which is opportunistically selected from a set of candidates. Unlike existing works, in our considered network scenario, the two source users have different target rates. A novel protocol for opportunistic relaying is developed, which adaptively switches between the max-min and the pure-max policies according to the information of system traffic. The performance of the new relaying strategy in terms of the system outage probability is analyzed over Rayleigh fading channels. Simulation results demonstrate that the proposed protocol can implement opportunistic relaying efficiently, and can achieve significant performance gains in terms of the outage probability across all traffics.

This paper presents a new precoding approach based on a genetic algorithm to search for coded codewords applied to a multi-user MIMO system. The main idea hinges on the definition of coded codewords in which no codebook is previously stored at transmitter and receiver. In this manner, the precoder aims to maximize the sum capacity in order to solve the optimization problem by searching for the best coded codewords for all users. The performance evaluation and complexity analysis show that our approach offers outstanding performance and low complexity compared with the multi-user MIMO precoding scheme based on the Grassmannian codebook. The proposed method uses a multiplier-free precoding suitable for VLSI implementation.

The Fast Fourier Transform (FFT) is a key role in signal processing applications that is useful for the frequency domain analysis of signals. The FFT computation requires an indexing scheme at each stage to address input/output data and coefficient multipliers properly. Most of these indexing schemes are based on bit-reversal techniques that are boosted by a look-up table requiring extra memory storage. This paper describes a novel data reordering technique based on the vector calculation of size r. FFTs are considered in-place (or in situ) algorithms that transform a data structure by using a constant amount of memory storage. We demonstrate that our proposed method reduces memory usage by eliminating the look-up table traditionally employed in the computation of bit-reversal indexes.

Biomedical implants require wireless power and bidirectional data transfer. We propose a novel topology for a multiple carrier inductive link and compare two geometries for it. The orthogonal approach and the coplanar approach are these geometries. The principal challenge with multiple carriers is minimization of crosstalk, especially of power into data under lateral misalignment of the inner and outer coils. We show that a coplanar design allows keeping coupling of power into data under 15% with respect to the data coupling, even under lateral misalignments over 5 mm. In comparison, the orthogonal geometry reaches over 50% of parasitic coupling after a displacement of only 3 mm.

The FFT process is an operation that could be performed through different stages. In each stage, the butterfly operation is computed in which the accessed data is multiplied by certain Walpha, added or subtracted and finally it is stored or held for further processing. This process is repeated to each stage until the final stage where the processed data is driven to the output. In this paper, an appropriate indexing or mapping schemes between the input data and the coefficient multipliers throughout the different stages are yield to a computation single stage by collapsing all stages into a computation single stage. The result is a reduction of communication load and arithmetic operations.

A multistage multiuser detection (MUD) technique, the adaptive duplicated filters plus interference canceller (ADIC), is proposed in the DS-CDMA context. Of particular interest is the use of adaptive filters block (AFB) dedicated to each user with its respective input signals independent from other users' contributions. These AFB are mixed with interference canceller block in a cascade arrangement. As shown in this paper, this proposed MUD can outperform the decision feedback soft multistage interference canceller (DF-Soft-MPIC) MUD with complexity reduction of 4. Algorithmic description and performance of low complexity MUD method are considered in this paper and FPGA implementation in a companion paper, Part II.

Many multiuser detection (MUD) methods are proposed in the literature to increase the performance of 3G cellular networks. However, it is known that the implementation complexity represents a key issue for deployment of the MUD. A VLSI implementation strategy and hardware resources evaluation of a new MUD based on the adaptive duplicated filters plus interference canceller (ADIC) method (Nougaru et al., 2007), is proposed. The maximum number of users in FPGA devices is presented with respect to WCDMA constraints. The two papers provide a low complexity MUD giving a good tradeoff performance and implementation cost.

This paper investigates a beamforming receivers based on maximum ratio combining (MRC) and noise constraint least mean square (NC-LMS) using rapid prototyping method for FPGA implementation. Non-adaptive and adaptive beamforming techniques approaches are considered. A performance evaluation of these algorithms in a DS-CDMA system is presented and FPGA design is evaluated in term of hardware resources for Xilinx family devices using rapid prototyping methodology with Matlab-Simulink tools. Both approaches offer a good performance-complexity tradeoff favorable for FPGA implementation. However, due to the adaptive approach, the NC-LMS presents a better robustness to the fixed point arithmetic than the MRC

This paper presents a full-differential analog design of an indirect inverse control law based on dynamic back propagation neural networks developed. The on-line adaptation algorithms of the synaptic weights are modeled by means of continuous-time integration circuits. The simulation results obtained at a post-layout simulation level show a very good computing precision as well as interesting power consumption and integration area. The speed of the circuit is largely sufficient to meet real-time requirements in numerous applications of the control fields

This work is devoted to the problem of asynchronous multiuser delay acquisition and time varying channel tracking in DS-CDMA systems. A multiuser-LMS-like structure along with smoothing/prediction filters to improve tracking quality is suggested. A performance versus complexity analysis is conducted, in cdma2000 and WCDMA environments, over highly interesting settings including different data rates, channel types and mobile speeds. It has been concluded that the proposed multiuser LMS structure offers improvements compared with the correlator method.

In this paper we propose two algorithms for adaptation of linear and successive interference cancellation (SIC) MIMO receivers based on the MMSE criterion. The algorithms are compared to the so-called fast V-BLAST algorithm in terms of implementation simplicity and the required number of arithmetic operation. We conclude that both proposed algorithm offer advantages over the algorithm fast V-BLAST. When compared to the latter, the first proposed algorithm has much simpler implementation but the same arithmetic complexity, while the second proposed algorithm lowers by 33% the required number of arithmetic operations.

In this paper, a reduced complexity turbo detection receiver for coded DS-CDMA signals employing the BPSK modulation technique is presented. The new scheme is based on a new family of MMSE filter whose coefficients are thought to be the solution of a (forced) real valued cost function in the bit rather than a complex one as in conventional MMSE receivers. The new receiver provides, on average, 2 dB gain with less number of iterations. Simulation results for performance evaluation are conducted under the most interesting scenarios including asynchronous multipath channels, time varying channels and multirate systems.

Digital communication systems operating on time varying depressive channels often employ a signalling format in which customer data are organized in blocks proceeded by a known sequence. The training sequence at the beginning of each block is used to train an adaptive equalizer and/or data sequence detector to combat intersymbol interference (ISI). This paper addresses the problem of comparing the Schroeder sequences as a very close to optimal training sequence for channel estimation (start up) in communication systems over time dispersive frequency selective channels. Schroeder sequences of comparable lengths to the designed -computer searched- sequences demonstrated a tight performance for both the optimal sequences designed using Discrete Fourier Transform (DFT) technique and the sequences designed via Least Sum of Squared Errors (LSSE) channel estimation. Performance results are provided for Schroeder sequences of lengths 36 and 28 (the choice of 28 is driven by the fact that channel estimation sequences for GSM system are of length 28).

The problem of improving the performance of the implementation in VLSI technology of Kalman-based algorithms for signal reconstruction in real time is discussed. A systolic approach is proposed to develop architecture expressly for this specific application. Implemented algorithms are based on the steady-state version of the Kalman filter, which performs for a broad field of specific applications, but the use of a co-processor for the Kalman gain is allowed. We show that the autoregressive model of Kalman filtering is particularly adapted to parallel processing and is well suited for implementation. Although intended to improve signal reconstruction, other applications where a similar autoregressive model of Kalman filtering is required are allowed. The performance of the systolic architecture is validated by comparison with Motorola's general-purpose DSP56002 digital signal for real-world spectrometric signal reconstruction.