283 research outputs found
Minimum error probability MIMO-aided relaying: multihop, parallel, and cognitive designs
No full textA design methodology based on the minimum error probability (MEP) framework is proposed for a nonregenerative multiple-input multiple-output (MIMO) relayaided system. We consider the associated cognitive, the parallel and the multi-hop source-relay-destination (SRD) link design based on this MEP framework, including the transmit precoder, the amplify-and-forward (AF) relay matrix and the receiver equalizer matrix of our system. It has been shown in the literature that MEP based communication systems are capable of improving the error probability of other linear counterparts. Our simulation results demonstrate that the proposed scheme indeed achieves a significant BER reduction over the existing linear schemes
The Combined Effect Of Reduced Feedback, Frequency-Domain Scheduling, And Multiple Antenna Techniques On The Performance Of LTE
No full textFrequency-domain scheduling, multiple antenna techniques, and rate adaptation enable next generation orthogonal frequency division multiple access (OFDMA) cellular systems such as Long Term Evolution (LTE) to achieve significantly higher downlink spectral efficiencies. However, this comes at the expense of increased feedback overhead on the uplink. LTE uses a pragmatic combination of several techniques to reduce the channel state feedback required by a frequency-domain scheduler.
In subband-level feedback scheme specified in LTE, the user reduces feedback by only reporting the channel quality indicator (CQI) computed over groups of resource blocks called subbands. LTE also specifies an alternate user selected subband feedback scheme, in which the feedback overhead is reduced even further by making each user feed back the indices of the best M subbands and only one CQI value averaged over all the M subbands. The coarse frequency granularity of the feedback in the above schemes leads to an occasional incorrect determination of rate by the scheduler for some resource blocks. The overall throughput of LTE depends on the method used to generate the CQI and the statistics of the channel, which depends on the multiple antenna technique used.
In this thesis, we develop closed-form expressions for the throughput achieved by the user selected and subband-level CQI feedback schemes of LTE. The comprehensive analysis quantifies the joint effects of four critical components on the overall system throughput, namely, scheduler, multiple antenna mode, CQI feedback scheme, and CQI generation method. The performance of a wide range of schedulers, namely, round robin, greedy, and proportional fair schedulers and several multiple antenna diversity modes such as receive antenna diversity and open-and closed-loop transmit diversity is analyzed. The analysis clearly brings out the dependence of the overall system throughput on important parameters such as number of resource blocks per subband and the rate adaptation thresholds. The effect of the coarse subband-level frequency granularity of feedback is explicitly captured. The analysis provides an independent theoretical reference and a quick system parameter optimization tool to an LTE system designer. It also helps us theoretically understand the behavior of OFDMA feedback reduction techniques when operated under practical system constraints.
Another contribution of this thesis is a new statistical model for the effective exponential SNR mapping (EESM), which is a highly non-linear mapping that is widely used in the design, analysis, and simulation of OFDMA systems. The statistical model is shown to be both accurate and analytically tractable, and plays a crucial role in facilitating the analysis of the throughput of LTE when EESM is used to generate the CQI
On The Best-m Feedback Scheme In OFDM Systems With Correlated Subchannels
No full textOrthogonal frequency division multiplexing (OFDM) in next generation wireless systems provides high downlink data rates by employing frequency-domain scheduling and rate adaptation at the base station (BS). However, in order to control the significant feedback overhead required by these techniques, feedback reduction schemes are essential. Best-m feedback is one such scheme that is implemented in OFDM standards such as Long Term Evolution. In it, the sub channel (SC) power gains of only the m strongest SCs and their corresponding indices are fed back to the BS.
However, two assumptions pervade most of the literature that analyze best-m feedback in OFDM systems. The first one is that the SC gains are uncorrelated. In practice, however, the SC gains are highly correlated, even for dispersive multipath channels. The second assumption deals with the treatment of unreported SCs, which are not fed back by the best-m scheme. If no user reports an SC, then no data transmission is assumed to occur. In this thesis, we eschew these assumptions and investigate best-m feedback in OFDM systems with correlated SC gains.
We, first, characterize the average throughput as a function of correlation and
m. A uniform correlation model is assumed, i.e., the SC gains are correlated with each other by the same correlation coefficient. The system model incorporates greedy, modified proportional- fair, and round robin schedulers, discrete rate adaptation, and non-identically distributed SC gains of different users. We, then, generalize the model to account for feedback delay. We show in all these cases that correlation degrades the average throughput. We also show that this effect does not arise when users report all the SC power gains to the BS.
In order to mitigate the reduction in the average throughput caused by unreported SCs, we derive a novel, constrained minimum mean square error channel estimator for the best-m scheme to estimate the gains of these unreported SCs. The estimator makes use of the additional information, which is unique to the best-m scheme, that the estimated SC power gains must be less than those that were reported. We, then, study its implications on the downlink average cell throughput, again for different schedulers. We show that our approach reduces the root mean square error and increases the average throughput compared to several approaches pursued in the literature. The more correlated the SC gains, greater is the improvement
Correlation-aware Splitting Algorithms for Opportunistic Selection
No full textOpportunistic selection is a key technique to improve the performance of wireless systems. In it, the best set of users among the available ones is selected on the basis of their instantaneous channel gains or local parameters such as battery energy state. For example, in cellular systems, scheduling the user with the highest downlink signal-to-noise ratio improves the downlink throughput. Formally, the process of selection is as follows. Each user possesses a real-valued metric that only it knows, and the goal is to select the best user, which has the highest metric. While opportunistic selection is appealing, finding the best user is a challenge because the users are geographically separated and the metric of a user is known only to itself; no user knows who the best is. Moreover, the time taken for selecting the best user should be small so that more time is available for data transmission.
In this thesis, we focus on the splitting algorithm, which is a popular distributed, fast, and scalable algorithm to implement opportunistic selection. We first show that this algorithm, which has thus far been designed assuming that the metrics are independent and identically distributed (i.i.d.), is no longer scalable in the practically important scenario in which the metrics are correlated.
We make the following three contributions in this thesis. Firstly, we propose a novel correlation-aware splitting algorithm (CASA) that selects the best user when the metrics are correlated and non-identical. We show how it can be applied to several practically relevant probability distributions and correlation models. We present computationally feasible techniques for pre-computing the thresholds that CASA specifies, thereby ensuring that CASA can be implemented in practice. We benchmark its performance with conventional algorithms, and show that it reduces the average selection time significantly as the number of users or the correlation among them increase.
We then extend CASA to CASA-m to select the best m users with the m largest metrics. We instantiate CASA-m for a generalized correlation model and benchmark its performance with conventional algorithms, and show that CASA-m reduces the average time of selecting multiple users as the number of users or the correlation among them increase. As an application, we then consider the example of a cooperative relay system that employs CASA-m to select multiple relays for cooperative beamforming. We study the system-level implications of correlation and selection using CASA-m for this system and benchmark its system throughput and energy efficiency with that of other selection algorithms. We find that in the presence of correlation, the average selection time, system throughput, and energy efficiency of the system is lower than that of the uncorrelated scenario. However, the percentage by which it is lower is less when CASA-m is used to select the relays compared to conventional algorithms.
Lastly, we propose a novel and faster approach for computing multivariate probabilities for Rayleigh and exponential distributions with an arbitrary covariance matrix. Compared to the
existing approaches in the literature, which seldom reported results on multivariate probabilities for more than 5 variates, our approach can accurately compute these for even 50 variates. This is due to its significantly lower computational complexity that does not scale with the number of variates. We also demonstrate the utility of the approach in the performance analysis of the selection combining diversity technique
Performance Analysis of Opportunistic Selection and Rate Adaptation in Time Varying Channels
No full textOpportunistic selection and rate adaptation play a vital role in improving the spectral and power efficiency of current multi-node wireless systems. However, time-variations in wireless channels affect the performance of opportunistic selection and rate-adaptation in the following ways. Firstly, the selected node can become sub-optimal by the time data transmission commences. Secondly, the choice of transmission parameters such as rate and power for the selected node become sub-optimal. Lastly, the channel changes during data transmission.
In this thesis, we develop a comprehensive and tractable analytical framework that accurately accounts for these effects. It differs from the extensive existing literature that primarily focuses on time-variations until the data transmission starts. Firstly, we develop a novel concept of a time-invariant effective signal-to-noise ratio (TIESNR), which tractably and accurately captures the time-variations during the data transmission phase with partial channel state information available at the receiver. Secondly, we model the joint distribution of the signal-to-noise ratio at the time of selection and TIESNR during the data transmission using generalized bivariate gamma distribution.
The above analytical steps facilitate the analysis of the outage probability and average packet error rate (PER) for a given modulation and coding scheme and average throughput with rate adaptation. We also present extensive numerical results to verify the accuracy of each step of our approach and show that ignoring the correlated time variations during the data transmission phase can significantly underestimate the outage probability and average PER, whereas it overestimates the average throughput even for packet durations as low as 1 msec
Timer-Based Selection Schemes for Wireless Networks
No full textOpportunistic selection is a practically appealing technique that is often used in multi-node wireless systems such as scheduling and rate adaptation in cellular systems and opportunistic wireless local area networks, wireless sensor networks, cooperative communications, and vehicular networks. In it, each node maintains a local preference number called metric that is function of its channel gains, and the best node with the highest metric is selected. Identifying the best node is challenging as the information about a node's metric is available only locally at each node.
In our work, we focus on the popular, simple, and low feedback timer scheme for selection. In it, each node sets a timer as a function of its metric and transmits a packet when the timer expires. The metric-to-timer mapping maps larger metric values to smaller timer values, which ensures that the best node's timer expires first. However, it can fail to select the best node if another node transmits a packet within D s of the transmission by the best node.
In this thesis, we make three contributions to the design and understanding of the timer-based selection scheme. Firstly, we introduce feedback overhead-aware contention resolution in the timer-based selection scheme. The outcome is a novel selection scheme that is faster than the splitting scheme and more reliable than the timer-based selection scheme. We analyze and minimize the average time required by the scheme to select the best node.
Secondly, we characterize the optimal metric-to-timer mapping when the number of nodes in the system is not known, as is the case in several practical deployments. When the prior distribution of the nodes is known, we propose an optimal mapping that maximizes the success probability averaged over the distribution on the number of nodes. When even the prior distribution is not known, we propose a robust mapping that maximizes the worst case average success probability over all possible probability distributions on the number of nodes. In both cases, we show that the timers can expire only at 0, D, 2D, ... in the optimal timer mapping. For the known prior case, we develop recursive techniques to effectively compute the optimal timer mapping for binomial and Poisson priors.
Lastly, we consider a discrete rate adaptive system and design an optimal timer scheme to maximize the end-to-end performance measure of system throughput. We derive several novel, insightful results about the optimal mapping that culminate in an iterative algorithm to compute it. We show that the design of the selection scheme is intimately related to the rate adaptation rule and the selection policy used. In all cases, extensive benchmarking with several ad hoc schemes proposed in the literature shows the significant gains that the proposed designs can deliver
Optimal Relay Selection in Interference-Constrained Underlay Cooperative Cognitive Radio
No full textCognitive radio (CR) promises to significantly improve the utilization of scarce wireless spectrum. In the underlay mode of CR, which is the focus of the thesis, a secondary user (SU) can simultaneously transmit on the same band as a higher priority primary user (PU) so long as the interference it causes to the PU must be constrained. These interference constraints severely limit the performance of the SUs. Cooperative relaying combined with selection exploits spatial diversity to improve the performance of interference-constrained SUs. In it, one among the available relays is selected for every instantaneous channel power gains of the various links that include the secondary communication links as well as the interference links between the secondary transmitters and the primary receiver. The mapping between the channel power gains and the selected relay is determined by the relay selection (RS) rule employed by the secondary network. Furthermore, it also depends on the interference constraint, which sets underlay CRapart from conventional wireless communications. Although the peak interference constraint is well-studied in the literature on underlay CR, cooperative relaying for the less conservative average interference constraint has not been as thoroughly studied.
In this thesis, we focus on developing optimal RS rules that either minimize the average symbol error probability (SEP) or maximize the average rate of the secondary network that is subject to an average interference constraint. We first develop an SEP-optimal RS rule and its two practically implementable variants when the relays are not aware of the instantaneous state of the direct source-to-destination (SD) link. The proposed rules determine which relay to select and whether to select none of the relays at all as a function of the various channel power gains. They outperform several ad hoc RS rules proposed in the literature for underlay CR and generalize the conventional interference-unconstrained RS rule.
Next, we present a novel, SD-aware SEP-optimal RS rule for an average interference-constrained underlay CR network. Akey point that the rule highlights -- for the first time -- is that, for the average interference constraint, the signal-to-interference-plus-noise-ratio (SINR) ofthe direct SD link affects the choice of the optimal relay. Furthermore, as the SINR increases, the odds that no relay transmits increase. We also propose a low feedback and near-optimal variant of the SD-aware SEP-optimal RS rule that requires just one bit of feedback about the state of the direct SD link to the relays. Compared to the SD-unaware RS rules, these rules markedly reduce the SEP by up to two orders of magnitude.We then analyze the average SEPs and diversity order of the proposed RS rules to quantify their performance.
Thereafter, we propose a rate-optimal RS rule that maximizes the fading-averaged transmission rate of an average interference-constrained underlay CR network. It differs functionally from the several ad hoc incremental relaying schemes proposed in the literature, but requires a feedback overhead that is comparable to them. We then analyze the average rate of the secondary network for this RS rule. We gain several insights by studying the asymptotic regimes of low and high average SINRs.
Lastly, we study a practically-motivated channel state information (CSI) model for an underlay CR network with multiple primary receivers, in which the channel gains of only a subset of the interference links are available at the source and relays. Moreover, this available CSI is imperfect due to channel estimation error. Based on such incomplete and imperfect CSI, the source and relays back-off their transmit powers in order to satisfy an interference outage constraint. We derive the outage probability and average rate of the secondary network for the rate-optimal RS rule. An interesting observation that comes out of our study is that full diversity order is still achievable even with such incomplete and imperfect CSI
Interference Modeling in Wireless Networks
No full textCognitive radio (CR) networks and heterogeneous cellular networks are promising approaches to satisfy the demand for higher data rates and better connectivity. A CR network increases the utilization of the radio spectrum by opportunistically using it. Heterogeneous networks provide high data rates and improved connectivity by spatially reusing the spectrum and by bringing the network closer to the user. Interference presents a critical challenge for reliable communication in these networks. Accurately modeling it is essential in ensuring a successful design and deployment of these networks.
We first propose modeling the aggregate interference power at a primary receiver (PU-Rx) caused from transmissions by randomly located cognitive users (CUs) in a CR network as a shifted lognormal random process. Its parameters are determined using a moment matching method. Extensive benchmarking shows that the proposed model is more accurate than the lognormal and Gaussian process models considered in the literature, even for a relatively dense deployment of CUs. It also compares favorably with the asymptotically exact stable and symmetric truncated stable distribution models, except at high CU densities. Our model accounts for the effect of imperfect spectrum sensing, interweave and underlay modes of CR operation, and path-loss, time-correlated shad-owing and fading of the various links in the network. It leads to new expressions for the probability distribution function, level crossing rate (LCR), and average exceedance duration (AED). The impact of cooperative spectrum sensing is also characterized. We also apply and validate the proposed model by using it to redesign the primary exclusive zone to account for the time-varying nature of interference.
Next we model the uplink inter-cell aggregate interference power in homogeneous and heterogeneous cellular systems as a simpler lognormal random variable. We develop a new moment generating function (MGF) matching method to determine the lognormal’s parameters. Our model accounts for the transmit power control, peak transmit power constraint, small scale fading and large scale shadowing, and randomness in the number of interfering mobile stations and their locations. In heterogeneous net-works, the random nature of the number and locations of low power base stations is also accounted for. The accuracy of the proposed model is verified for both small and large values of interference. While not perfect, it is more accurate than the conventional Gaussian and moment-matching-based lognormal and Gamma distribution models. It is also performs better than the symmetric-truncated stable and stable distribution models, except at higher user density
Optimal Amplify-And-Forward Relaying For Cooperative Communications And Underlay Cognitive Radio
No full textRelay-assisted cooperative communication exploits spatial diversity to combat wireless fading, and is an appealing technology for next generation wireless systems. Several relay cooperation protocols have been proposed in the literature. In amplify-and-forward (AF)relaying, which is the focus of this thesis, the relay amplifies the signal it receives from the source and forwards it to the destination. AF has been extensively studied in the literature on account of its simplicity since the relay does not need to decode the received signal.
We propose a novel optimal relaying policy for two-hop AF cooperative relay systems. In this, an average power-constrained relay adapts its gain and transmit power to minimize the fading-averaged symbol error probability (SEP) at the destination. Next, we consider a generalization of the above policy in which the relay operates as an underlay cognitive radio (CR). This mode of communication is relevant because it promises to address the spectrum shortage constraint. Here, the relay adapts its gain as a function of its local channel gain to the source and destination and also the primary such that the average interference it causes to the primary receiver is also constrained.
For both the above policies, we also present near-optimal, simpler relay gain adaptation policies that are easy to implement and that provide insights about the optimal policies. The SEPs and diversity order of the policies are analyzed to quantify their performance. These policies generalize the conventional fixed-power and fixed-gain AF relaying policies considered in cooperative and CR literature, and outperform them by 2.0-7.7 dB. This translates into significant energy savings at the source and relay, and motivates their use in next generation wireless systems
Role of Channel State Information in Adaptation in Current and Next Generation Wireless Systems
No full textMotivated by the increasing demand for higher data rates, coverage, and spectral efficiency, current and next generation wireless systems adapt transmission parameters and even who is being transmitted to, based on the instantaneous channel states. For example, frequency-domain scheduling(FDS) is an instance of adaptation in orthogonal frequency division multiple access(OFDMA) systems in which the base station opportunistically assigns different subcarriers to their most appropriate user. Likewise ,transmit antenna selection(AS) is another form of adaptation in which the transmitter adapts which subset of antennas it transmits with. Cognitive radio(CR), which is a next generation technology, itself is a form of adaptation in which secondary users(SUs) adapt their transmissions to avoid interfering with the licensed primary users(PUs), who own the spectrum. However, adaptation requires channel state information(CSI), which might not be available apriori at the node or nodes that are adapting. Further, the CSI might not be perfect due to noise or feedback delays. This can result in suboptimal adaptation in OFDMA systems or excessive interference at the PUs due to transmissions by the SUs in CR.
In this thesis, we focus on adaptation techniques in current and next generation wireless systems and evaluate the impact of CSI –both perfect and imperfect –on it. We first develop a novel model and analysis for characterizing the performance of AS in frequency-selective OFDMA systems. Our model is unique and comprehensive in that it incorporates key LTE features such as imperfect channel estimation based on dense, narrow band demodulation reference signal and coarse, broad band sounding reference signal. It incorporates the frequency-domain scheduler, the hardware constraint that the same antenna must be used to transmit over all the subcarriers that are allocated to a user, and the scheduling constraint that the allocated subcarriers must all be contiguous. Our results show the effectiveness of combined AS and FDS in frequency-selective OFDMA systems even at lower sounding reference signal powers.
We then investigate power adaptation in underlay CR, in which the SU can transmit even when the primary is on but under stringent interference constraints. The nature of the interference constraint fundamentally decides how the SU adapts its transmit power. To this end, assuming perfect CSI, we propose optimal transmit power adaptation policies that minimize the symbol error probability of an SU when they are subject to different interference and transmit power constraints. We then study the robustness of these optimal policies to imperfections in CSI. An interesting observation that comes out of our study is that imperfect CSI can not only increase the interference at the PU but can also decrease it, and this depends on the choice of the system parameters, interference, and transmit power constraints. The regimes in which these occur are characterized
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