Orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation has recently emerged as a promising paradigm for ensuring reliable communications in doubly-selective channels. This work investigates the spectra and orthogonality characteristics of analog (direct) and approximate digital implementations of ODDM systems. We first determine the time and frequency domain representations of the basis functions for waveform in analog and approximate digital ODDM systems. Thereafter, we derive their power spectral densities and show that while the spectrum of analog ODDM waveforms exhibits a step-wise behavior in its transition regions, the spectrum of approximate digital ODDM waveforms is confined to that of the ODDM sub-pulse. Next, we prove the orthogonality characteristics of approximate digital ODDM waveforms and show that, unlike analog ODDM waveforms, the approximate digital ODDM waveforms satisfy orthogonality without the need of additional time domain resources. Additionally, we examine the similarities and differences that implementations of approximate digital ODDM share with the other variants of DD modulations, focusing on the domain changes the symbols undergo, the type of pulse shaping and windowing used, and the domains and the sequence in which they are performed. Finally, we present numerical results to validate our findings and draw further insights.

The orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation has been proposed as a promising paradigm for ensuring reliable communications in doublyselective channels. Although ODDM functions as a multicarrier modulation on the DD plane, academia and industry are more accustomed to understanding and altering the time and frequency resources of signals and waveforms. Recognizing this, in this work, we investigate the time and spectral occupancies of the transmitted signals in both analog (direct) and digital (approximate) implementations of ODDM systems. We begin by explicitly determining the basis functions for both ODDM systems in time and frequency domains, and highlight their phase term difference in the time domain and their envelope difference in the frequency domain. We then derive the spectral responses of their transmit signals. We reveal that while the spectral response of signals in analog ODDM systems exhibits a step-wise behavior in its transition regions, the spectral response of signals in digital ODDM systems is confined to that of the ODDM sub-pulse. Finally, through numerical results, we verify our findings and show that out-of-band-emission of ODDM systems can be further improved by increasing the duration of the ODDM sub-pulse.

We investigate the coexistence of orthogonal time-frequency space (OTFS) modulation with current fourth- and fifth-generation (4G/5G) communication systems that primarily use orthogonal frequency-division multiplexing (OFDM) waveforms. We first derive the input-output-relation of OTFS in the considered coexisting system. In this derivation, we consider 1) the inclusion of multiple cyclic prefixes (CPs) with unequal lengths to the OTFS signal and 2) edge carrier unloading (ECU), to account for the impacts of CP length, frame structure, and subcarrier arrangement described in 3GPP standards for 4G/5G systems. Our analysis reveals that the inclusion of multiple CPs to the OTFS signal and ECU lead to the channel response exhibiting spreading effects/leakage along the Doppler and delay dimensions, respectively. Consequently, the effective sampled delay-Doppler (DD) domain channel model for OTFS in coexisting systems may exhibit reduced sparsity. We also show that the effective DD domain channel coefficients for OTFS in coexisting systems are influenced by the unequal lengths of CPs. Subsequently, we propose an interference cancellation-based channel estimation (CE) technique for OTFS in coexisting systems. Through numerical results, we validate our analysis, highlight the importance of not ignoring the unequal lengths of CPs during signal detection, and show the significance of the proposed CE technique.

This study examines the coexistence of orthogonal time-frequency space (OTFS) modulation with current fourth-and fifth-generation (4G/5G) wireless communication systems that primarily use orthogonal frequency-division multiplexing (OFDM) waveforms. We first derive the input-output-relation (IOR) of OTFS when it coexists with an OFDM system while considering the impact of unequal lengths of the cyclic prefixes (CPs) in the OTFS signal. We show analytically that the inclusion of multiple CPs to the OTFS signal results in the effective sampled delay-Doppler (DD) domain channel response to be less sparse. We also show that the effective DD domain channel coefficients for OTFS in coexisting systems are influenced by the unequal lengths of the CPs. Subsequently, we propose an embedded pilotaided channel estimation (CE) technique for OTFS in coexisting systems that leverages the derived IOR for accurate channel characterization. Using numerical results, we show that ignoring the impact of unequal lengths of the CPs during signal detection can degrade the bit error rate performance of OTFS in coexisting systems. We also show that the proposed CE technique for OTFS in coexisting systems outperforms the state-of-the-art threshold-based CE technique.

Orthogonal delay-Doppler division multiplexing (ODDM) modulation was recently proposed as a promising solution for high-mobility communication systems. To achieve the potential of ODDM, reliable signal detection is essential, hence, in this work, we propose a contrastive learning-based signal detection approach for ODDM systems, named CL-ODDM. Unlike the conventional deep learning-based methods which focus on positive samples alone, we creatively leverage contrastive learning to exploit both positive and negative samples in the training dataset. By doing so, more distinguishable information of signals can be captured and extracted, contributing to reliable detection results. Moreover, we employ a convolutional neural network and recurrent encoder-decoder (CREN) to represent the comprehensive properties and features of ODDM signals. In addition, an adaptive correction method (ACM) is proposed to increase the convergence rate and improve the stability of the detection model. Extensive simulation results validate that the proposed CL-ODDM is significantly superior state-of-the-art related work, regarding the detection accuracy and convergence rate.

Deep learning (DL) demonstrates tremendous potential in high-mobility communication systems, especially from the perspective of signal detection. However, most existing DL-based detection methods are data/environment specific and the re-training process is resource intensive. To address these shortcomings, we propose a contrastive learning-based environmentally robust signal detection approach in orthogonal delay-Doppler division multiplexing (CL-ODDM) to achieve fast convergence, high accuracy and strong robustness to variations in wireless environments. Specifically, unlike conventional methods which explore only positive samples in the dataset for detection, in this work, we propose to leverage contrastive learning to fully exploit both positive and negative samples in the training dataset. This enables us to extract more comprehensive features of signals, which can accelerate convergence, improve detection accuracy, and enhance the generalized ability of our CL-ODDM. Moreover, we creatively employ a convolutional neural network and recurrent encoder-decoder (CREN) to represent the underlying properties of ODDM signals and extract high-quality features. To further improve environmental robustness, we propose novel training strategies, i.e., data augmentation (DA) and adaptive updating scheme (AUS). The proposed DA method is expected to increase the diversity of the dataset and represent more effective signal features. The designed AUS leverages transfer learning to adapt partial layers of CREN to make our CL-ODDM suitable for various wireless environments. Numerous simulation results validate that the proposed CL-ODDM significantly outperforms state-of-the-art related works, in terms of detection accuracy, environmental robustness and convergence rate.

Orthogonal time frequency space (OTFS) modulation is a recently proposed delay-Doppler (DD) domain communication scheme, which has shown promising performance in general wireless communications, especially over high-mobility channels. In this paper, we investigate DD domain Tomlinson-Harashima precoding (THP) for downlink multiuser multiple-input and multiple-output OTFS (MU-MIMO-OTFS) transmissions. Instead of directly applying THP based on the huge equivalent channel matrix, we propose a simple implementation of THP that does not require any matrix decomposition or inversion. Such a simple implementation is enabled by the DD domain channel property, i.e., different resolvable paths do not share the same delay and Doppler shifts, which makes it possible to pre-cancel all the DD domain interference in a symbol-by-symbol manner. We also study the achievable rate performance for the proposed scheme by leveraging the information-theoretical equivalent models. In particular, we show that the proposed scheme can achieve a near optimal performance in the high signal-to-noise ratio (SNR) regime. More importantly, scaling laws for achievable rates with respect to number of antennas and users are derived, which indicate that the achievable rate increases logarithmically with the number of antennas and linearly with the number of users. Our numerical results align well with our findings and also demonstrate a significant improvement compared to existing MU-MIMO schemes on OTFS and orthogonal frequency-division multiplexing (OFDM).

In this paper, we investigate the delay-Doppler (D-D) domain Tomlinson-Harashima precoding (THP) for downlink multiuser multiple-input and multiple-output orthogonal time frequency space (MU-MIMO-OTFS) transmissions. Instead of directly applying THP based on the huge equivalent channel matrix, we propose a simple implementation of THP that does not require any matrix decomposition or inversion. Such a simple implementation is enabled by the DD domain channel property, i.e., different resolvable paths do not share the same delay and Doppler shifts, which makes it possible to pre-cancel all the DD domain inter-ference in a symbol-by-symbol manner. We also demonstrate the theoretical results on the sum-rate performance of the proposed scheme. In particular, we show that the sum-rate of the proposed scheme increases logarithmically with the number of antennas, while increases linearly with the number of users. Our numerical results align well with our findings and also verify the effectiveness of the proposed scheme.

IEEE 802.11e EDCA induces service differentiation by appropriate joint tuning of four adjustable contention parameters. Existing and emerging work has devoted considerable attention to the nonsaturated performance of EDCA networks due to the difficulty of predicting the joint influence of the four parameters. However, most existing nonsaturated EDCA models adopt complex extensions of a Markov-chain approach. In sharp contrast, this paper invokes an extension of a renewal-reward approach. Our extension has the following unparalleled advantages: good scalability, ease of understanding, fast computation speed, high accuracy, models joint differentiation of all four parameters, captures the impact of an arbitrary buffer size, and predicts a wide range of performance indicators including the buffer overflow probability and the MAC access delay distribution. Our nonsaturated EDCA model is a nontrivial augmentation of our previously proposed nonsaturated DCF model. Our results indicate that if we accurately model the nonsaturated collision probability, the same formulas used for the saturated performance descriptors can produce accurate results for nonsaturated operation, and therefore it is unnecessary to construct specific formulas for nonsaturated performance descriptors, as done in previous work. To illustrate the utility of our model, we also develop an admission control policy based on the proposed EDCA model for a CWmin-differentiation system. Simulations validate that this policy enables the system to run slightly below a critical point, beyond which the system performance deteriorates drastically.

We propose an approximate model for a nonsaturated IEEE 802.11 DCF network. This model captures the significant influence of an arbitrary node transmit buffer size on the network performance. We find that increasing the buffer size can improve the throughput slightly but can lead to a dramatic increase in the packet delay without necessarily a corresponding reduction in the packet loss rate. This result suggests that there may be little benefit in provisioning very large buffers, even for loss-sensitive applications. Our model outperforms prior models in terms of simplicity, computation speed, and accuracy. The simplicity stems from using a renewal theory approach for the collision probability instead of the usual multidimensional Markov chain, and it makes our model easier to understand, manipulate and extend; for instance, we are able to use our model to investigate the important problem of convergence of the collision probability calculation. The remarkable improvement in the computation speed is due to the use of an efficient numerical transform inversion algorithm to invert generating functions of key parameters of the model. The accuracy is due to a carefully constructed model for the service time distribution. We verify our model using ns-2 simulation and show that our analytical results based on an M/G/1/K queuing model are able to accurately predict a wide range of performance metrics, including the packet loss rate and the waiting time distribution. In contradiction to claims by other authors, we show that 1) a nonsaturated DCF model like ours that makes use of decoupling assumptions for the collision probability and queuing dynamics can produce accurate predictions of metrics other than just the throughput, and 2) the actual service time and waiting time distributions for DCF networks have truncated heavy-tailed shapes (i.e., appear initially straight on a log-log plot) rather than exponential shapes. Our work will help developers select appropriate buffer sizes for 802.11 devices, and will help system administrators predict the performance of applications.

This paper proposes a simple and practical call admission control (CAC) scheme for one-hop IEEE 802.11 distributed coordination function (DCF) networks in heterogeneous environments. The proposed scheme is the first CAC scheme derived from an asymptotic analysis of the critical traffic load, where the critical traffic load represents the threshold for queue stability. The salient feature of our CAC scheme is that it can be performed quickly and easily without the need for network performance measurements and complex calculations. Using the proposed scheme, we specifically investigate the voice capacity of 802.11 DCF networks with unbalanced traffic. Extensive simulations covering both ad hoc and infrastructure-based networks, and a variety of nonsaturated traffic types, show that the proposed CAC scheme is very effective.

We define and evaluate the downlink flow-level capacity of a fractionally loaded OFDMA network utilizing round robin (RR) or proportional fair (PF) scheduling. The flow-level capacity is the maximum traffic intensity that can be supported by a sector while satisfying a minimum flow throughput requirement for bursty, elastic traffic. We obtain a simple, insightful capacity expression for RR scheduling; for PF scheduling, we exploit a fast convergence property of the multi-user diversity gain to implement a computationally efficient, iterative algorithm to solve for the capacity. A hybrid simulation/analysis approach is applied, where a detailed rate distribution obtained via simulation is used as input to a generalized processor sharing queue model. The analytical expressions and numerical results indicate that enhancement of edge throughputs can significantly improve the flow-level capacity.

We develop an accurate analytical model for a dedicated short range communication (DSRC) network that uses the IEEE 802.11 distributed coordination function (DCF) MAC protocol, as adopted by the forthcoming IEEE 802.11p specification for DSRC. The specific focus is on broadcast vehicle-to-vehicle safety messages. We derive explicit expressions for the mean of the total packet delay and the packet delivery ratio (PDR) in an unsaturated network formed by moving vehicles on a highway. Our model is validated using extensive simulations and we show that our model yields better predictive accuracy than other existing models. The model is then used to investigate the performance of a modified DCF that uses a fixed number of sequential retransmissions to improve the reliability of packet delivery. We find that with sequential retransmissions, the PDR improves at low vehicle density (i.e. low traffic load), but degrades at heavy loads where higher collisions induced by the retransmissions outweighs the benefit of repeated attempts.

This paper proposes a new call admission control (CAC) scheme for one-hop homogeneous 802.11 DCF networks. Using the proposed scheme, we can perform admission control quickly and easily without the need for network performance measurements and complex calculations. The CAC rule is derived under asymptotic conditions, but our extensive numerical examples show that it works well for practical-sized networks with a finite retransmission limit and realistic nonsaturated traffic.

We consider the sector capacity of an OFDMA data network, defined in terms of the number of users that can be supported while satisfying a minimum flow throughput requirement. A closed queueing network model to evaluate flow throughputs is extended to the case of reuse partitioning. The model is used to evaluate the sector capacity of reuse 1, fractional frequency reuse (FFR) and soft frequency reuse (SFR). A hybrid simulation/analysis approach is taken, where the queueing model is coupled with a peak rate distribution obtained via simulation. Numerical results indicate that FFR with a large edge band size can deliver the highest capacity when the flow throughput requirement is not very high; for a high throughput requirement, reuse 1 is the best choice.

We analyze the MAC access delay of the IEEE 802.11e EDCA mechanism under saturation. We develop a detailed analytical model to evaluate the influence of all EDCA differentiation parameters, namely AIFS, CWmin, CWmax and TXOP limit, as well as the backoff multiplier $\beta$. Explicit expressions for the mean, standard deviation and generating function of the access delay distribution are derived. By applying numerical inversion on the generating function, we are able to efficiently compute values of the distribution. Comparison with simulation confirms the accuracy of our analytical model over a wide range of operating conditions. We derive simple asymptotics and approximations for the mean and standard deviation of the access delay, which reveal the salient model parameters for performance under different differentiation mechanisms. We also use the model to numerically study the differentiation performance and find that $\beta$ differentiation, though rejected during the standardization process, is an effective differentiation mechanism that has some advantages over the other mechanisms.

We propose an approximate model for a nonsaturated IEEE 802.11 DCF network that is simpler than others that have appeared in the literature. Our key simplification is that the attempt rate in the nonsaturated setting can be approximated by scaling the attempt rate of the saturated setting with an appropriate factor. Use of different scaling factors leads to variants of the model for a small buffer and an infinite buffer. We develop a general fixed-point analysis that we demonstrate can have nonunique solutions for the infinite buffer model variant under moderate traffic. Nevertheless, in an asymptotic regime that applies to light traffic, we are able to prove uniqueness of the fixed point and predict the offered load at which the maximum throughput is achieved. We verify our model using ns-2 simulation and show that our MAC access delay results are the most accurate among related work, while our collision probability and throughput results achieve comparable accuracy to (D. Malone et al., 2007), (K. Duffy et al., 2007).

We compare the performance of different backoff functions for the multiple access protocol in an IEEE 802.11 wireless LAN (WLAN). We provide a unified analytical model with explicit expressions for the mean and standard deviation of the access delay for generalized exponential, polynomial and linear backoff functions. Using our model, we show that linear and polynomial backoffs with appropriate parameter settings can improve upon binary exponential backoff specified in the 802.11 WLAN standards, in terms of throughput, access delay statistics and packet drop rate.

Energy efficiency has become one of the major considerations for protocol design in wireless networks, especially sensor networks. Carrier sense multiple access with collision avoidance (CSMA-CA) mechanisms that incorporate energy saving features have been proposed for contention-based medium access for such networks (e.g., in IEEE 802.15.4 standard). In this paper, we develop a new analytical model for the performance of an energy conserving CSMA-CA in both saturated and periodic traffic conditions. The accuracy of the throughput predicted by the analysis is confirmed via comparison with simulation.

The MAC access delay in a saturated IEEE 802.11 DCF wireless LAN is analyzed. We develop a unified analytical model and obtain explicit expressions for the first two moments as well as the generating function. We show via comparison with simulation that our model accurately predicts the mean, standard deviation, and distribution of the access delay for a wide range of operating conditions. In addition, we show that the obtained generating function is much more accurate than others that have appeared in the literature. Using our model, we prove that the binary exponential backoff mechanism induces a heavy-tailed delay distribution for the case of unlimited retransmissions. We show using numerical examples that the distribution has a truncated power-law tail when a retransmission limit exists. This finding suggests that DCF is prone to long delays and not suited to carrying delay-sensitive applications

This paper presents a framework to minimize energy consumption in the medium access control (MAC) layer for wireless sensor networks. While satisfying a range of quality of service (QoS) requirements, such as the packet transmission success rate and maximum delay constraint, we optimally choose the lengths of periods in which sensors are active and inactive, such that the energy consumption per unit time in the entire network is minimized. We first use our framework to optimize the values of the MAC attributes macBeaconOrder and macSuperframeOrder in an IEEE 802.15.4 beacon-enabled star network. Then we consider a much simpler protocol, which we call "select-and-transmit" (S&T), and the same framework is applied to find the optimal lengths of the active and inactive portions. Finally, we compare the minimal energy consumption of the IEEE 802.15.4 MAC and S&T under the same QoS requirements and show that the IEEE 802.15.4 MAC outperforms S&T in most cases. However, the S&T MAC performs better than the standard under our framework in certain scenarios, e.g., event-driven sensor networks where the packet transmission success rate is usually low.

In this paper, we analyze the MAC access delay of the EDCA mechanism in the IEEE 802.11e standard under saturation. We model the effect of differentiation based on both contention window size and inter-frame spacing. Explicit expressions for the mean, the standard deviation and the generating function of the distribution of the access delay are obtained. By applying numerical inversion on the generating function, we are able to compute values of the distribution. We show that our analytical model is accurate through comparison with simulation.

In this paper, we study the MAC access delay of EDCA in the draft IEEE 802.11e standard under saturated conditions. We obtain explicit expressions for the mean, the standard deviation and the generating function of the distribution of the access delay. By using numerical inversion on the generating function, we are able to compute values of the distribution. We show that our analytical model has high accuracy via comparison with simulation

We propose a new low-complexity MAC solution for multimedia CDMA cellular networks considering packet reservation and scheduling jointly. The proposed MAC, which we call joint PRMA and packet scheduling (JPPS), treats real-time traffic and non-real-time traffic separately. Once a real-time traffic flow (a continuous packet burst) is admitted to the system, its code channel(s) will be implicitly reserved until its last packet is transmitted, as in PRMA. Real-time traffic has delay priority over non-real-time, and we also prioritize within various non-real-time traffic flows. Packet scheduling techniques are then used to schedule all the real-time and non-real-time packets. Furthermore, an optimal channel access scheme based on a simple linear program is proposed. Simulation results comparing the performance of JPPS versus the well-known MAC protocol WISPER demonstrate lower delay for real time traffic and lower overall packet loss ratio for JPPS