Unified Spectral Efficiency Analysis of Cellular Systems with Channel-Aware Schedulers

Spectral efficiency is a key characteristic of cellular communications systems, as it quantifies how well the scarce spectrum resource is utilized. It is influenced by the scheduling algorithm as well as the signal and interference statistics, which, in turn, depend on the propagation characteristics. In this paper we derive analytical expressions for the short-term and long-term channel-averaged spectral efficiencies of the round robin, greedy Max-SINR, and proportional fair schedulers, which are popular and cover a wide range of system performance and fairness trade-offs. A unified spectral efficiency analysis is developed to highlight the differences among these schedulers. The analysis is different from previous work in the literature in the following aspects: (i) it does not assume the co-channel interferers to be identically distributed, as is typical in realistic cellular layouts, (ii) it avoids the loose spectral efficiency bounds used in the literature, which only considered the worst case and best case locations of identical co-channel interferers, (iii) it explicitly includes the effect of multi-tier interferers in the cellular layout and uses a more accurate model for handling the total co-channel interference, and (iv) it captures the impact of using small modulation constellation sizes, which are typical of cellular standards. The analytical results are verified using extensive Monte Carlo simulations.

Modern energy access to all in rural India: An integrated implementation strategy

Expanding energy access to the rural population of India presents a critical challenge for its government. The presence of 364 million people without access to electricity and 726 million who rely on biomass for cooking indicate both the failure of past policies and programs, and the need for a radical redesign of the current system. We propose an integrated implementation framework with recommendations for adopting business principles with innovative institutional, regulatory, financing and delivery mechanisms. The framework entails establishment of rural energy access authorities and energy access funds, both at the national and regional levels, to be empowered with enabling regulatory policies, capital resources and the support of multi-stakeholder partnership. These institutions are expected to design, lead, manage and monitor the rural energy interventions. At the other end, trained entrepreneurs would be expected to establish bioenergy-based micro-enterprises that will produce and distribute energy carriers to rural households at an affordable cost. The ESCOs will function as intermediaries between these enterprises and the international carbon market both in aggregating carbon credits and in trading them under CDM. If implemented, such a program could address the challenges of rural energy empowerment by creating access to modern energy carriers and climate change mitigation. (C) 2011 Elsevier Ltd. All rights reserved.

A channel-aware, fast sub-channel to user assignment algorithm in OFDMA systems

Channel-aware assignment of sub-channels to users in the downlink of an OFDMA system demands extensive feedback of channel state information (CSI) to the base station. Since the feedback bandwidth is often very scarce, schemes that limit feedback are necessary. We develop a novel, low feedback splitting-based algorithm for assigning each sub-channel to its best user, i.e., the user with the highest gain for that sub-channel among all users. The key idea behind the algorithm is that, at any time, each user contends for the sub-channel on which it has the largest channel gain among the unallocated sub-channels. Unlike other existing schemes, the algorithm explicitly handles multiple access control aspects associated with the feedback of CSI. A tractable asymptotic analysis of a system with a large number of users helps design the algorithm. It yields 50% to 65% throughput gains compared to an asymptotically optimal one-bit feedback scheme, when the number of users is as small as 10 or as large as 1000. The algorithm is fast and distributed, and scales with the number of users.

Joint evaluation of channel feedback schemes, rate adaptation, and scheduling in OFDMA downlinks with feedback delays

Orthogonal frequency-division multiple access (OFDMA) systems divide the available bandwidth into orthogonal subchannels and exploit multiuser diversity and frequency selectivity to achieve high spectral efficiencies. However, they require a significant amount of channel state feedback for scheduling and rate adaptation and are sensitive to feedback delays. We develop a comprehensive analysis for OFDMA system throughput in the presence of feedback delays as a function of the feedback scheme, frequency-domain scheduler, and rate adaptation rule. Also derived are expressions for the outage probability, which captures the inability of a subchannel to successfully carry data due to the feedback scheme or feedback delays. Our model encompasses the popular best-n and threshold-based feedback schemes and the greedy, proportional fair, and round-robin schedulers that cover a wide range of throughput versus fairness tradeoff. It helps quantify the different robustness of the schedulers to feedback overhead and delays. Even at low vehicular speeds, it shows that small feedback delays markedly degrade the throughput and increase the outage probability. Further, given the feedback delay, the throughput degradation depends primarily on the feedback overhead and not on the feedback scheme itself. We also show how to optimize the rate adaptation thresholds as a function of feedback delay.

Accurate performance analysis of single and opportunistic AF relay cooperation with imperfect cascaded channel estimates

Given the significant gains that relay-based cooperation promises, the practical problems of acquisition of channel state information (CSI) and the characterization and optimization of performance with imperfect CSI are receiving increasing attention. We develop novel and accurate expressions for the symbol error probability (SEP) for fixed-gain amplify-and-forward relaying when the destination acquires CSI using the time-efficient cascaded channel estimation (CCE) protocol. The CCE protocol saves time by making the destination directly estimate the product of the source-relay and relay-destination channel gains. For a single relay system, we first develop a novel SEP expression and a tight SEP upper bound. We then similarly analyze an opportunistic multi-relay system, in which both selection and coherent demodulation use imperfect estimates. A distinctive aspect of our approach is the use of as few simplifying approximations as possible, which results in new results that are accurate at signal-to-noise-ratios as low as 1 dB for single and multi-relay systems. Using insights gleaned from an asymptotic analysis, we also present a simple, closed-form, nearly-optimal solution for allocation of energy between pilot and data symbols at the source and relay(s).

Bounds on the sum-rate capacity of the Gaussian MIMO X channel

We consider the MIMO X channel (XC), a system consisting of two transmit-receive pairs, where each transmitter communicates with both the receivers. Both the transmitters and receivers are equipped with multiple antennas. First, we derive an upper bound on the sum-rate capacity of the MIMO XC under individual power constraint at each transmitter. The sum-rate capacity of the two-user multiple access channel (MAC) that results when receiver cooperation is assumed forms an upper bound on the sum-rate capacity of the MIMO XC. We tighten this bound by considering noise correlation between the receivers and deriving the worst noise covariance matrix. It is shown that the worst noise covariance matrix is a saddle-point of a zero-sum, two-player convex-concave game, which is solved through a primal-dual interior point method that solves the maximization and the minimization parts of the problem simultaneously. Next, we propose an achievable scheme which employs dirty paper coding at the transmitters and successive decoding at the receivers. We show that the derived upper bound is close to the achievable region of the proposed scheme at low to medium SNRs.

Design and Analysis of an Acknowledgment-Aware Asynchronous MPR MAC Protocol for Distributed WLANs

Multi-packet reception (MPR) promises significant throughput gains in wireless local area networks (WLANs) by allowing nodes to transmit even in the presence of ongoing transmissions in the medium. However, the medium access control (MAC) layer must now be redesigned to facilitate rather than discourage - these overlapping transmissions. We investigate asynchronous MPR MAC protocols, which successfully accomplish this by controlling the node behavior based on the number of ongoing transmissions in the channel. The protocols use the backoff timer mechanism of the distributed coordination function, which makes them practically appealing. We first highlight a unique problem of acknowledgment delays, which arises in asynchronous MPR, and investigate a solution that modifies the medium access rules to reduce these delays and increase system throughput in the single receiver scenario. We develop a general renewal-theoretic fixed-point analysis that leads to expressions for the saturation throughput, packet dropping probability, and average head-of-line packet delay. We also model and analyze the practical scenario in which nodes may incorrectly estimate the number of ongoing transmissions.

Interplay Between Optimal Selection Scheme, Selection Criterion, and Discrete Rate Adaptation in Opportunistic Wireless Systems

An opportunistic, rate-adaptive system exploits multi-user diversity by selecting the best node, which has the highest channel power gain, and adapting the data rate to selected node's channel gain. Since channel knowledge is local to a node, we propose using a distributed, low-feedback timer backoff scheme to select the best node. It uses a mapping that maps the channel gain, or, in general, a real-valued metric, to a timer value. The mapping is such that timers of nodes with higher metrics expire earlier. Our goal is to maximize the system throughput when rate adaptation is discrete, as is the case in practice. To improve throughput, we use a pragmatic selection policy, in which even a node other than the best node can be selected. We derive several novel, insightful results about the optimal mapping and develop an algorithm to compute it. These results bring out the inter-relationship between the discrete rate adaptation rule, optimal mapping, and selection policy. We also extensively benchmark the performance of the optimal mapping with several timer and opportunistic multiple access schemes considered in the literature, and demonstrate that the developed scheme is effective in many regimes of interest.

En Masse relay selection algorithms for multi-source, multi-relay, decode-and-forward cooperative systems

Opportunistic relay selection in a multiple source-destination (MSD) cooperative system requires quickly allocating to each source-destination (SD) pair a suitable relay based on channel gains. Since the channel knowledge is available only locally at a relay and not globally, efficient relay selection algorithms are needed. For an MSD system, in which the SD pairs communicate in a time-orthogonal manner with the help of decode-and-forward relays, we propose three novel relay selection algorithms, namely, contention-free en masse assignment (CFEA), contention-based en masse assignment (CBEA), and a hybrid algorithm that combines the best features of CFEA and CBEA. En masse assignment exploits the fact that a relay can often aid not one but multiple SD pairs, and, therefore, can be assigned to multiple SD pairs. This drastically reduces the average time required to allocate an SD pair when compared to allocating the SD pairs one by one. We show that the algorithms are much faster than other selection schemes proposed in the literature and yield significantly higher net system throughputs. Interestingly, CFEA is as effective as CBEA over a wider range of system parameters than in single SD pair systems.

Optimal capacity relay node placement in a multi-hop network on a line

We use information theoretic achievable rate formulas for the multi-relay channel to study the problem of optimal placement of relay nodes along the straight line joining a source node and a destination node. The achievable rate formulas that we utilize are for full-duplex radios at the relays and decode-and-forward relaying. For the single relay case, and individual power constraints at the source node and the relay node, we provide explicit formulas for the optimal relay location and the optimal power allocation to the source-relay channel, for the exponential and the power-law path-loss channel models. For the multiple relay case, we consider exponential path-loss and a total power constraint over the source and the relays, and derive an optimization problem, the solution of which provides the optimal relay locations. Numerical results suggest that at low attenuation the relays are mostly clustered close to the source in order to be able to cooperate among themselves, whereas at high attenuation they are uniformly placed and work as repeaters. We also prove that a constant rate independent of the attenuation in the network can be achieved by placing a large enough number of relay nodes uniformly between the source and the destination, under the exponential path-loss model with total power constraint.

Channel quantization for physical layer network-coded two-way relaying

The design of modulation schemes for the physical layer network-coded two way relaying scenario is considered with the protocol which employs two phases: Multiple access (MA) Phase and Broadcast (BC) phase. It was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA phase. In other words, the set of all possible channel realizations (the complex plane) is quantized into a finite number of regions, with a specific network coding map giving the best performance in a particular region. We obtain such a quantization analytically for the case when M-PSK (for M any power of 2) is the signal set used during the MA phase. We show that the complex plane can be classified into two regions: a region in which any network coding map which satisfies the so called exclusive law gives the same best performance and a region in which the choice of the network coding map affects the performance, which is further quantized based on the choice of the network coding map which optimizes the performance. The quantization thus obtained analytically, leads to the same as the one obtained using computer search for 4-PSK signal set by Koike-Akino et al., for the specific value of M = 4.

Joint Scheduling & Jamming for Data Secrecy in Wireless Networks

The broadcast nature of the wireless medium jeopardizes secure transmissions. Cryptographic measures fail to ensure security when eavesdroppers have superior computational capability; however, it can be assured from information theoretic security approaches. We use physical layer security to guarantee non-zero secrecy rate in single source, single destination multi-hop networks with eavesdroppers for two cases: when eavesdropper locations and channel gains are known and when their positions are unknown. We propose a two-phase solution which consists of finding activation sets and then obtaining transmit powers subject to SINR constraints for the case when eavesdropper locations are known. We introduce methods to find activation sets and compare their performance. Necessary but reasonable approximations are made in power minimization formulations for tractability reasons. For scenarios with no eavesdropper location information, we suggest vulnerability region (the area having zero secrecy rate) minimization over the network. Our results show that in the absence of location information average number of eavesdroppers who have access to data is reduced.

Performance analysis of beacon-less IEEE 802.15.4 multi-hop networks

We develop an approximate analytical technique for evaluating the performance of multi-hop networks based on beacon-less CSMA/CA as standardised in IEEE 802.15.4, a popular standard for wireless sensor networks. The network comprises sensor nodes, which generate measurement packets, and relay nodes which only forward packets. We consider a detailed stochastic process at each node, and analyse this process taking into account the interaction with neighbouring nodes via certain unknown variables (e.g., channel sensing rates, collision probabilities, etc.). By coupling these analyses of the various nodes, we obtain fixed point equations that can be solved numerically to obtain the unknown variables, thereby yielding approximations of time average performance measures, such as packet discard probabilities and average queueing delays. Different analyses arise for networks with no hidden nodes and networks with hidden nodes. We apply this approach to the performance analysis of tree networks rooted at a data sink. Finally, we provide a validation of our analysis technique against simulations.

BER Analysis of Space Shift Keying in Cooperative Multi-hop Multi-branch DF Relaying

Space shift keying (SSK) is an attractive modulation technique for multi-antenna communications. In SSK, only one among the available transmit antennas is activated during one channel use, and the index of the chosen transmit antenna conveys information. In this paper, we analyze the performance of SSK in multi-hop, multi-branch cooperative relaying systems. We consider the decode-and-forward relaying protocol, where a relay forwards the decoded symbol if it decodes the symbol correctly from the received signal. We derive closed-form expressions for the end-to-end bit error rate of SSK in this system. Analytical and simulation results match very well.

EESM-Based Link Adaptation in Point-to-Point and Multi-Cell OFDM Systems: Modeling and Analysis

In contemporary wideband orthogonal frequency division multiplexing (OFDM) systems, such as Long Term Evolution (LTE) and WiMAX, different subcarriers over which a codeword is transmitted may experience different signal-to-noise-ratios (SNRs). Thus, adaptive modulation and coding (AMC) in these systems is driven by a vector of subcarrier SNRs experienced by the codeword, and is more involved. Exponential effective SNR mapping (EESM) simplifies the problem by mapping this vector into a single equivalent fiat-fading SNR. Analysis of AMC using EESM is challenging owing to its non-linear nature and its dependence on the modulation and coding scheme. We first propose a novel statistical model for the EESM, which is based on the Beta distribution. It is motivated by the central limit approximation for random variables with a finite support. It is simpler and as accurate as the more involved ad hoc models proposed earlier. Using it, we develop novel expressions for the throughput of a point-to-point OFDM link with multi-antenna diversity that uses EESM for AMC. We then analyze a general, multi-cell OFDM deployment with co-channel interference for various frequency-domain schedulers. Extensive results based on LTE and WiMAX are presented to verify the model and analysis, and gain new insights.