The distributed nature of cellular networks is one of the main enablers for integrated sensing and communication (ISAC). For target positioning and tracking, making use of bistatic measurements is non-trivial due to their non-linear relationship with Cartesian coordinates. Most of the literature proposes geometric-based methods to determine the target's location by solving a well-defined set of equations stemming from the available measurements. The error covariance to be used for Bayesian tracking is then derived from local Taylor expansions. In our work we adaptively fuse any subset of bistatic measurements using a maximum likelihood (ML) framework, allowing to incorporate every possible combination of available measurements, i.e., transmitter angle, receiver angle and bistatic range. Moreover, our ML approach is intrinsically flexible, as it can be extended to fuse an arbitrary number of measurements by multistatic setups. Finally, we propose both a fixed and dynamic way to compute the covariance matrix for the position error to be fed to Bayesian tracking techniques, like a Kalman filter. Numerical evaluations with realistic cellular communications parameters at mmWave frequencies show that our proposal outperforms the considered baselines, achieving a location and velocity root mean square error of 0.25m and 0.83m/s, respectively.

The large untapped spectrum in sub-THz allows for ultra-high throughput communication to realize many seemingly impossible applications in 6G. Phase noise (PN) is one key hardware impairment, which is accentuated as we increase the frequency and bandwidth. Furthermore, the modest output power of the power amplifier demands limits on peak to average power ratio (PAPR) signal design. In this work, we design a PN-robust, low PAPR single-carrier (SC) waveform by geometrically shaping the constellation and adapting the pulse shaping filter pair under practical PN modelling and adjacent channel leakage ratio (ACLR) constraints for a given excess bandwidth. We optimize the waveforms under conventional and state-of-the-art PN-aware demappers. Moreover, we introduce a neural-network (NN) demapper enhancing transceiver adaptability.We formulate the waveform optimization problem in its augmented Lagrangian form and use a back-propagation-inspired technique to obtain a design that is numerically robust to PN, while adhering to PAPR and ACLR constraints. The results substantiate the efficacy of the method, yielding up to 2.5 dB in the requiredEb/N0under stronger PN along with a PAPR reduction of 0.5 dB. Moreover, PAPR reductions up to 1.2 dB are possible with competitive BLER and SE performance in both low and high PN conditions.

The large untapped spectrum in the sub-THz allows for ultra-high throughput communication to realize many seemingly impossible applications in 6G. One of the challenges in radio communications in sub-THz is the hardware impairments. Specifically, phase noise is one key hardware impairment, which is accentuated as we increase the frequency and bandwidth. Furthermore, the moderate output power of the sub-THz power amplifier demands limits on peak to average power ratio (PAPR) signal design. Single carrier frequency domain equalization (SC-FDE) has been identified as a suitable candidate for sub-THz, although some challenges such as phase noise and PAPR still remain to be tackled. In this work, we design a phase noise robust, modest PAPR SC waveform by geometrically shaping the constellation under practical conditions. We formulate the waveform optimization problem in its augmented Lagrangian form and use a back-propagation-inspired technique to obtain a constellation design that is numerically robust to phase noise, while maintaining a relatively low PAPR compared to the conventional waveforms.

Sub-Terahertz communication is a key enabling technology to deliver ultra-high rates up to Terabit/s - one of 6G envisioned goals. However, hardware limitation and impairments set practical challenges in realizing real-world networks operating at such high frequency range. In this paper, based on simulation findings, we analyze the performance of different single- and multi-carrier transmission concepts in the sub-Terahertz range under hardware impairments and limitations, both from a today’s New Radio (NR) up-scaling perspective, and whether it is best to deviate from the straightforward up-scaling into a new design. We therefore focus on the following sub-Terahertz network determinants: the signal peak amplitude characteristics, the phase noise of the local oscillators and the quantization effect of the analog-to-digital-converter. Insights drawn from the analysis are considered to make proposals on the signaling concepts for a practical access network design in the sub-Terahertz range. We also demonstrate how further improvement can be harvested considering signal amplitude variation optimized constellation modulation.

Turbo-AI is an iterative Machine Learning (ML) based channel estimator, processed through frequency, time and spatial domains consecutively with low complexity. Within the context of 5th Generation (5G) and Beyond 5G (B5G) wireless communications, we embed Turbo-AI into Demodulation Reference Signal (DMRS) processing in this paper. The extension is not technically obvious, comparing to our previous Turbo-AI paper series, because the main challenges come from not only estimating the channel response exactly for the DMRS pilot resource elements, but also precisely interpolating the channel response for the data resource elements, especially when the user mobility or equivalently the sparsity of the pilot structure significantly increases. Throughout this paper, we propose a universal interpolation approach, named Firecracker Algorithm, which is jointly introduced to DMRS-Turbo-AI. Numerical results show that DMRS-Turbo-AI can deliver high quality channel estimation for the users with high mobility, and demonstrate that Firecracker Algorithm is even capable of tracking the channel of a user, who moves at a supersonic speed.

In the framework of 5G-and-beyond Industry 4.0, jamming attacks for denial of service are a rising threat which can severely compromise the system performance. Therefore, in this paper we deal with the problem of jamming detection and mitigation in indoor factory deployments. We design two jamming detectors based on pseudo-random blanking of subcarriers with orthogonal frequency division multiplexing and consider jamming mitigation with frequency hopping and random scheduling of the user equipments. We then evaluate the performance of the system in terms of achievable block error rate (BLER) with ultra-reliable low-latency communications traffic and jamming missed detection probability. Simulations are performed considering a 3rd Generation Partnership Project spatial channel model for the factory floor with a jammer stationed outside the plant trying to disrupt the communication inside the factory. Numerical results show that jamming resiliency increases when using a distributed access point deployment and exploiting channel correlation among antennas for jamming detection, while frequency hopping is helpful in jamming mitigation only for strict BLER requirements.

Security attacks at the physical layer, in the form of radio jamming for denial of service, are an increasing threat in the Industry 4.0 scenarios. In this paper, we consider the problem of jamming detection in 5G-and-beyond communication systems and propose a defense mechanism based on pseudo-random blanking of subcarriers with orthogonal frequency division multiplexing (OFDM). We then design a detector by applying the generalized likelihood ratio test (GLRT) on those subcarriers. We finally evaluate the performance of the proposed technique against a smart jammer, which is pursuing one of the following objectives: maximize stealthiness, minimize spectral efficiency (SE) with mobile broadband (MBB) type of traffic, and maximize block error rate (BLER) with ultra-reliable low-latency communications (URLLC). Numerical results show that a smart jammer a) needs to compromise between missed detection (MD) probability and SE reduction with MBB and b) can achieve low detectability and high system performance degradation with URLLC only if it has sufficiently high power.

Targeting to potential evolution of future wireless systems, precise channel estimation is regarded as one of the fundamental prerequisites. In this paper, we focus on Machine Learning (ML) based channel estimation with Turbo-AI, which is an iterative training approach, and can monotonically reduce the post-processing noise variance of Gaussian inputs after each iteration, by updating the Neural Network (NN) models with re-training. After discussing about the initial results of Turbo-AI as Part I in our introductory paper, we will now deploy the same principle in a multicarrier system from a more practical view point. Multi-dimensional Turbo-AI will estimate the channel in an iterative manner through frequency, time and spatial domain cooperatively. Since the complexity of traditional channel estimation method will be extremely high due to the multi-dimensional data structure, Turbo-AI can be regarded as a complementary solution to balance the performance and complexity. Throughout this paper, we exploit 5G compliant link level simulator to show that genie-aided upper bound can be approached by Turbo-AI. Challenges of realizing Turbo-AI based channel estimation in practical systems for future wireless communication towards Beyond 5G (B5G) are focused on.

Channel estimation belongs to one of the potential applications, that can exploit Artificial Intelligence (AI) and Machine Learning (ML) to enhance Physical Layer (PHY) performance in the context of 5th Generation (5G) and Beyond 5G (B5G) wireless communication systems. In this paper, we focus on the ML-based channel estimation for 2-Dimensional (2D) antenna arrays. Due to the extremely high computational requirement for 2D massive arrays with Conventional Training, we exploit the 2D Kronecker covariance model to perform Subspace Training for the vertical and horizontal spatial domains independently, which achieves a complexity cost saving factor O(M4N4)/O(MN4+ NM4) for an M × N 2D-array. Furthermore, we propose an iterative training approach, referred to as Turbo-AI. Along with Subspace Training, the new approach can monotonically reduce the effective variance of additive noise of the observation, by updating the Neural Network (NN) models with re-training. Furthermore, we propose a concept, named Universal Training. It allows to use one NN for a wide range of Signal-to-Noise-Ratio (SNR) operation points and spatial angles, which can greatly simplify Turbo-AI usage. Numerical results exhibit that Turbo-AI can tightly approach the genie-aided channel estimation bound, especially at low SNR.

In cyclic-prefix orthogonal frequency-division multiplexing (CP-OFDM)-based radio access, the coexistence of different technologies without precise time-frequency synchronization is limited due to high out-of-band (OOB) emissions. Therefore, the spectrum enhancement techniques play a key role in relaxing the synchronization and power control requirements. This allows a higher degree of opportunistic spectrum use with minimized interference. In addition, all the transmitting devices have to fulfill specific transmitted signal quality requirements, including the maximum OOB radiated signal power. With the orthogonal frequency-division multiplexing (OFDM)-based radio access, some additional signal processing for improved spectrum containment is commonly needed to achieve these requirements. The filtering and time-domain windowing are two fundamentally different approaches for spectrum enhancement. The filtered OFDM (F-OFDM) provides better spectrum localization than the time-windowing schemes [such as windowed overlap-add (WOLA)], with the cost of higher complexity. This article introduces low-complexity solutions for spectrally enhanced narrowband OFDM transmitters based on the use of lookup tables (LUTs). The proposed LUT approach, requiring only memory units and a low number of additions, allows to avoid all computationally expensive operations in online transmitter processing, as it builds the transmitted signal by summing the stored partial waveforms optimized offline. In certain cases, completely multiplication- and summation-free designs are possible. The transmitters of narrowband Internet of Things (NB-IoT) devices are natural applications for the proposed LUT approach, as they require additional digital baseband signal processing to reach the emission requirements. It is shown that the proposed LUT schemes can provide significant savings in real-time computations of NB-IoT devices, while fulfilling the 3GPP requirements.

Advanced multiple input multiple output (MIMO) technologies in New Radio (NR), such as multiple transmit-receive-point (multi-TRP) transmission or non-linear precoding are promising significant gains in data throughput for 5G NR, given that sufficient knowledge about the channel state information (CSI) is available at the gNB. This paper compares two practical explicit CSI feedback schemes, based on time domain compression and principal component analysis (PCA), against state-of-the-art CSI feedback from NR Rel. 15, NR type II CSI. A new method for feeding back the tap location information in the time domain compression scheme is proposed, which requires less feedback overhead compared to state-of-the-art methods.

Universal Filtered Orthogonal Frequency Division Multiplexing (UF-OFDM) is considered as a promising 5G waveform candidate. It requires a relatively simple transceiver structure, while achieving much better spectral properties compared to CP-OFDM. During the early deployment of 5G systems, many frequency bands will still be occupied by 4G systems, using the legacy CP-OFDM waveform. The main focus in this work lies on using the uplink shared channel (PUSCH) with both waveforms on the same carrier. We analyze the impact of inter-carrier interference (ICI) leakage on the performance of both receivers for neighboring allocations using the different waveforms. We also propose two techniques to mitigate the effect of ICI between both waveforms, namely: 1-delaying the transmitted UF-OFDM signal relative to the transmitted CPOFDM signal to reduce the ICI on the CP-OFDM receiver and 2-windowing at the UF-OFDM receiver to suppress the power spectral leakage from the CP-OFDM signal.

Upcoming fifth generation (5G) cellular networks will demand more from the physical layer (PHY) than current- generation Orthogonal Frequency Division Multiplexing (OFDM) can deliver. The 5G waveform candidate Universal Filtered OFDM (UF-OFDM) is designed to provide the flexibility required for future applications. However, the introduction of subband filters in UFMC can increase implementation complexity and low-complexity solutions need to be found. State-of-the-art technologies provide an algorithm that performs shorter-length FFTs that can reduce complexity to two to ten times that of OFDM (depending on the allocation sizes), at the cost of only approximating the exact UFMC signal. In this paper we propose a new approximation of the UFMC signal which bases on the similarity of adjacent subcarriers that can be implemented with reduced number of operations. Analysis show that the system can be implemented with only 20% more operations than standard OFDM when accepting some increase in the subband bandwidth. A more accurate solution can be implemented at roughly 3.6 times OFDM complexity. The results can reduce implementation costs for future mobile devices.

This paper provides indications and simulative performance evaluations of how a wireless system can profit from being able to support various subcarrier spacings concurrently. We show that with using this degree of freedom high Doppler, low latency and extended coverage scenarios are improved. In our investigations we consider different options for multi-carrier numerology, frame design and pilot placement. Based on our investigation results and general considerations we propose a set of numerology settings for 5G. Furthermore we propose a tiling concept, enabling the parallel usage of different user-specific numerologies.

In this paper, we investigate channel estimation for the massive Multiple-Input Multiple-Output (MIMO) systems, by deploying superimposed pilots. The pilots are the a priori known spreading sequences, repeated cyclically and superimposed to the signal layer. They reserve a marginal fraction of the total transmit energy. Thus, the initial channel estimates can be initially obtained by separating the users with respect to the corresponding code-division orthogonality with robustness against asynchronicity. Further, during a second stage, iterative channel estimation is considered, by integrating a trellis-based channel estimator, which can significantly enhance the channel estimation during the iterations, by reusing the superimposed pilots. Notice that the so-called turbo-effect can be clearly observed, in which both data detection and channel estimation are jointly improved between consecutive iterations.

In this paper, we compare two potential multiple access schemes, namely Non-Orthogonal Multiple Access (NOMA) and Interleave Division Multiple Access (IDMA) in the case of equal rate communication without link adaptation. Especially, we focus on their performance in uplink with a real channel estimator, by exploiting superimposed pilots. The utilized superimposed pilots are the cyclically repeated spreading sequence, a priori known by the transmitter and receiver, and are assigned a marginal fraction of the total transmit power. Exploiting the orthogonality of codes, the superimposed pilots help to generate an initial channel estimation. Furthermore, iterative channel estimation is considered by introducing a trellis-based channel estimator, which can significantly enhance the channel estimation during the iterations by reusing the superimposed pilots. The behaviors of Bit Error Rate (BER) and channel estimation Mean Square Error (MSE) will be investigated for NOMA and IDMA system.

Universal Filtered Multi-Carrier (UFMC) is a novel multi-carrier modulation technique which can be seen as a generalization of filtered OFDM and filter bank based multicarrier (FBMC-FMT). Being a candidate waveform technology for 5G wireless systems, it combines the simplicity of OFDM with the advantages of FBMC. The FIR-filter, used in UFMC to filter a group of subcarriers, is a key design parameter to gain more robustness in relaxed synchronization conditions, i.e. timefrequency misalignment. It was shown in previous work that very significant SIR improvement can be achieved for UFMC by optimizing the FIR-filter, taking carrier frequency offset into account. In this paper, we optimize the FIR-filter design in UFMC by taking both carrier frequency and timing offset into account in an uplink multi-user FDMA scenario. From the simulation results, up to 3.6 dB SIR improvement can be achieved with the optimized FIR filter compared to UFMC with non-optimized Dolph-Chebyshev filter and 15.1 dB SIR gain against classical CP-OFDM system respectively, provided that the normalized carrier frequency and timing offset are uniformly distributed in the interval ±5%.

Universal Filtered Multi-Carrier (UFMC, a.k.a. UF-OFDM) is a novel multi-carrier modulation technique, which aims at replacing OFDM for next generation wireless communication systems (5G). It is a generalization of OFDM and filter bank based multi-carrier (FBMC-FMT), which combines the advantages of OFDM and FBMC while avoiding its main drawbacks. UFMC is shown to be more robust in relaxed synchronization conditions i.e. time-frequency misalignment compared to conventional CP-OFDM systems. As required in potential scenarios of 5G systems, UFMC is more efficient to support short uplink bursts communications. Without the insertion of cyclic prefix, we investigate the procedure and performance of pilot-aided channel estimation for UFMC in an uplink multi-user FDMA scenario and show that almost the same performance as CP-OFDM can be achieved despite the lack of cyclic prefix. In case of timing and frequency offset, UFMC shows its robustness over CP-OFDM in terms of symbol error rate (SER). Simulation results show that the error floor is reduced applying UFMC for considered different types of channels.

UF-OFDM is a promising 5G waveform candidate, close to CP-OFDM, but with better spectral properties. Efficient receiver implementations exist, which are close to CP-OFDM in terms of complexity. The UF-OFDM multi-carrier modulator, on the other hand, still has no efficient solution in the literature up to now. This paper addresses this problem and presents a novel frequency domain generation method for UF-OFDM, where overlapping subbands are superimposed. Our approach can bring down UF-OFDM multi-carrier modulator complexity almost as low as a factor of 2 above CP-OFDM, with a negligible approximation error. Thus the required efficient transmitter implementation is delivered by this paper's solution, ready to be used in hardware implementations.

In this paper we investigate multiple access schemes and multi-carrier waveforms in the context of future 5th Generation (5G) wireless communication systems. We compare classical Frequency Division Multiple Access (FDMA) to Interleave-Division Multiple Access (IDMA) on top of two different multicarrier waveforms: Orthogonal Frequency Division Multiplexing (OFDM) and a new approach called Universal Filtered Multi-Carrier (UFMC). A relaxation of timing and frequency alignment requirements is taken into account for supporting applications like Machine Type Communications (MTC) and the Internet of Things (IoT). This paper contains a first uplink comparison scenario where traffic with Relaxed Synchronicity (RS) is embedded into synchronous traffic. Two main users of interest are either using IDMA or FDMA on top of either OFDM or UFMC modulation. Simulation results give first suitability indications for 5G for the combination of waveform and multiple access scheme. The numerical results reveal that IDMA brings in significant enhancement for low rate users, and UFMC introduces additional protection to high-rate users. Both schemes can be combined well.

In this paper we compare three candidate multicarrier waveforms for the air interface of 5G: filtered CP-OFDM - the choice for 4G, FBMC - heavily discussed in recent years, and Universal Filtered Multi-Carrier (UFMC) - a new contender making its appearance recently. We judge their time-frequency efficiency when transmitting very small bursts (e.g. for machine to machine communications) and under very tight response time requirements (e.g. for vehicle to vehicle communications). While FBMC is very efficient when transmitting long sequences, it suffers when having to transmit short bursts/frames. Due to the cyclic prefix and wide frequency guards, OFDM is rather inefficient. UFMC proofs to be the best choice, here, outperforming OFDM by about 10% in any case and FBMC in case of very short packets while performing similar for long sequences.

Machine-to-Machine (M2M) communication has recently attracted significant interest, and is expected to play a major role in future wireless communication. Various M2M applications are being considered for integration to modern cellular networks including tracking, metering and eHealth, thus benefiting from the wide coverage and lower deployment costs. However, there exist applications supported by low end machine and sensor terminals constrained by limited battery, transmit power, complexity and cost, which suffer from the bulky signal processing and control overheads of existing systems making way for investigating new MAC and PHY approaches. In this paper we present a simple and efficient cross layer design for operation at low transmit powers and bandwidth, accommodating applications with sporadic, low volume transmissions and relatively relaxed QoS requirements. A wide range of monitoring and sensing applications fall in this category and will be a corner stone for realizing future Smart Cities. Using simulations, we identify the bounds on maximum supported machine terminals in a cell with above application characteristics, and also investigate the transmission latency and energy efficiency of the machine terminals.

The interference limitation of cellular systems can be addressed by coordinated multi-point (CoMP) transmission and reception, where different base stations act together as a distributed antenna system, sharing data. CoMP has been shown to be sensitive to accuracy of channel knowledge. This work deals with practical channel estimation in an uplink joint reception scenario for multiple users across multiple cells. In most academic work, the parameter knowledge, like second order statistics of the channel and noise, is assumed to be perfectly known. In contrast to that, in this paper, we fully estimate all parameters using pilots. Practical algorithms are designed here to achieve fast convergence of parameter estimation, avoiding the need for too many samples, with manageable complexity. This is done in a multi-stage way, where the outputs of simpler estimators provide the parameters for the more advanced stages. Even for large coordination set sizes, like 7 cells, we show that our multi-stage approach is roughly just 1 dB below perfect channel knowledge in terms of post-combining SINR.

LTE and LTE-Advanced have been optimized to deliver high bandwidth pipes to wireless users. The transport mechanisms have been tailored to maximize single cell performance by enforcing strict synchronism and orthogonality within a single cell and within a single contiguous frequency band. Various emerging trends reveal major shortcomings of those design criteria: (1) The fraction of machine-type-communications (MTC) is growing fast. Transmissions of this kind are suffering from the bulky procedures necessary to ensure strict synchronism. (2) Collaborative schemes have been introduced to boost capacity and coverage (CoMP), and wireless networks are becoming more and more heterogeneous following the non-uniform distribution of users. Tremendous efforts must be spent to collect the gains and to manage such systems under the premise of strict synchronism and orthogonality. (3) The advent of the Digital Agenda and the introduction of carrier aggregation are forcing the transmission systems to deal with fragmented spectrum. 5GNOW will question the design targets of LTE and LTE-Advanced having these shortcomings in mind. The obedience of LTE and LTE-Advanced to strict synchronism and orthogonality will be challenged. It will develop new PHY and MAC layer concepts being better suited to meet the upcoming needs with respect to service variety and heterogeneous transmission setups. A demonstrator will be built as Proof-of-Concept relying upon continuously growing capabilities of silicon based processing. Wireless transmission networks following the outcomes of 5GNOW will be better suited to meet the manifoldness of services, device classes and transmission setups being present in envisioned future scenarios like smart cities. The integration of systems relying heavily on MTC, e.g. sensor networks, into the communication network will be eased. The per-user experience will be more uniform and satisfying. To ensure this 5GNOW will contribute to upcoming 5G standardization.

It has been shown that Interference Alignment (IA) based transmit precoding achieves remarkable performance gains under ideal assumptions of perfect channel state information (CSI) and fully uncorrelated channels. In this work, we have derived a simple model for imperfect CSI to assess the gains of IA using a 3GPP compliant system level simulator. By using our model we have evaluated the performance of IA using two different receiver algorithms based on ideal and practical realizations. We have further compared the performance of IA with two other baseline state of the art coordinated and non-coordinated precoding schemes. Our results show that the gains of IA are very sensitive to CSI imperfections as compared to the other baselines. However, in case of the availability of high SINRs with very slow moving users leading to very large channel coherence time/bandwidth, IA outperforms the other schemes even with imperfect CSI. The results draw important conclusions about the application of IA in practical systems.

Several linear transmit precoding and receive combining strategies with and without base station cooperation are compared to each other. The impact on sum-rate performance is shown with varying number of transmit and receive antennas, with different amounts of training and with varying receive power levels of the cooperating set. This is done by simulations in a two-user two-cell scenario. The limited scenario size helps to carve out the crucial parameters and show their interrelation with imperfect channel knowledge (CSI). These CSI imperfections are emulated based on a novel model, introduced in this paper. We show that imperfect CSI drastically reduces the relative coordinated multi-point (CoMP) gains over non-coordinated systems. The non-coordinated systems can already perform quite well, when multi-antenna terminals apply interference suppression strategies. Our results motivate that CoMP systems need to be studied under critical system assumptions, taking into account non-idealities, as they have a severe impact on the observed gains.

To achieve multiuser diversity gains, resource allocation relies on accurate and timely feedback of the users' channel states. This feedback suffers from transmission errors and delay which can heavily degrade the sum capacity of a scheduled multiuser downlink. The order of this capacity loss and its interdependency to relevant scenario factors is characterized in this paper. From studying a simple sum capacity-maximizing scheduler, we conclude that in many mobile scenarios the upper bound of the achievable data rate is primarily defined by the feedback delay. This makes reducing feedback delay to one of the most important challenges in designing future wireless systems.

An efficient feedback compression scheme is presented for signaling of explicit channel state information (CSI) to the transmitter side for MIMO OFDM systems in general and especially with coordinated multi-point transmission (COMP). Simulation results show that the required rates can be reduced by a factor of up to 17, compared to reporting of quantized frequency domain channel representations. This is achieved by using a separation of short-term and long-term information and a time-domain representation reduced to 'rake-fingers' for removing redundancy and irrelevant information. This novel proposed solution can be used as an important enabler for coherent network MIMO in the FDD downlink.

During the fusion of audio and video information for speech recognition, the estimation of the reliability of the noise affected audio channel is crucial to get meaningful recognition results. In this paper we compare two types of reliability measures. One is the use of the statistics of the phoneme a-posteriori probabilities and the other is the analysis of the audio signal itself. We implemented the entropy and the dispersion of the probabilities and, from the audio-based criteria, the so called Voicing Index. To test the criteria a hybrid ANN/HMM audio-visual recognition system was used and 5 different types of noise at 12 SNR levels each were added to the audio signal. The best sigmoidal fit for each criterion between the fusion parameter and the value of the criterion over all noise types and SNR values was performed. The resulting individual errors and the corresponding averaged relative errors are given.