Decentralized coordinated transceiver design with large antenna arrays

The benefits of MIMO technology have made it a solution for the present and future wireless networking demands. Increasing the number of antennas is an intuitive approach for boosting the network capacity; however, processing load and implementation limitations put a practical bound on this goal. Recently a solution known as massive MIMO has shown that a very large antenna array at the base station can simplify the processing, in a way that even matched filter (MF) can be used for detection purpose. The ultimate performance of massive MIMO can be achieved only under some optimistic assumptions about the channel and hardware deployment. In practice, there are some restrictions that do not allow the ultimate performance for a massive MIMO system. Under some realistic assumptions, an efficient use of all the resources becomes important in a way that the application of simple algorithms like MF and zero forcing (ZF) becomes questionable. Thus, in this thesis work, more efficient approach based on optimal minimum power beamforming is considered as the benchmark. The idea is to investigate the behavior of this algorithm and the performance differences with respect to some sub-optimal methods when the system dimensions grow large. Two solutions for the minimum power beamforming are reviewed (SOCP and uplink-downlink duality). The solution that is on focus is based on the second order cone programming (SOCP). Intercell interference(ICI) plays a critical role in the SOCP algorithm as it couples the sub-problems at the base stations. Thus, a large dimension approximation for the optimal ICI, using random matrix theory tools, is derived which tackles both of the processing simplification and the backhaul exchange rate reduction goals. This approximation allows derivation of an approximated optimal intercell interference based on the channel statistics that results a procedure for decoupling the subproblems at base stations. The comparison between the SOCP algorithm and the sub-optimal methods is carried out via simulation. The results show that the performance gap with respect to the sub-optimal methods grows when correlation between the antenna elements at the BS side increase. In a network simulation with 7 cell and 28 users, this gap remains significant even with 100 antennas at the BS side. These performance differences justify the application of more complex algorithms like SOCP for a MIMO system with a large antenna array when the practical restrictions are taken into account

Resource management in large-scale wireless networks via random matrix methods

Abstract Random matrix (RM) methods are exploited to develop radio resource management techniques for future wireless networks wherein the dimensions of the system, including bandwidth, the number of nodes and antennas, are expected to be large. RM methods provide deterministic approximations of network performance, which become arbitrarily tight as the dimensions increase in size. The focus areas of this thesis include non-orthogonal multiple access (NOMA); coordinated multi-point (CoMP); and two-stage beamforming (TSB), which combines large-dimensional statistical pre/postprocessing with lower dimensional digital processing. A multi-carrier NOMA system based on low density spreading (LDS) in the frequency dimension is considered. The allocation of resources, solely based on statistical channel-state-information (CSI), is studied to maximize the ergodic sum-rate subject to constraints on the sparsity of the LDS-codes. While the optimum is attainable only via exhaustive search, a low complexity method with minimal coordination overhead is proposed that yield close-to-optimum resource allocation solutions. Minimum power beamforming with user-specific rate constraints is considered in a downlink CoMP network. Deterministic expressions in terms of statistical CSI are derived for user-specific inter-cell interference (ICI) strength. Relying on the deterministic ICI terms as coordination messages, low-complexity distributed coordination algorithms, suitable for dense networks with limited backhaul, are proposed. The algorithms decouple the sub-problems at base stations (BSs) as long as the CSI statistics remain unchanged. The maximization of minimum signal-to-interference-plus-noise ratio (SINR) is considered in a dense CoMP network with random topology. Deterministic approximations are derived for the optimal SINR assignment in terms of system parameters such as cell radius, load, and power-budgets at BSs. The results enable the assessment of network performance based on given system parameters. Finally, complexity reduction of the optimal linear receiver via TSB is considered in the uplink of a cellular system. A novel TSB method is proposed that adjusts the structure and dimension of outer-beamforming matrices based on CSI statistics and the amount of overlap among users in the angular domain. The proposed method yields close-to-optimum SINRs while the computational burden of obtaining the beamformers is greatly reduced.Tiivistelmä Satunnaismatriiseja (RM) käyttäviä menetelmiä hyödynnetään kehitettäessä radioresurssien hallintatekniikoita tuleville langattomille verkoille, joissa järjestelmän mittojen, kuten kaistanleveyden sekä verkkoelementtien ja antennien määrän, odotetaan olevan suuria. RM-menetelmät tarjoavat deterministisiä arvioita verkon suorituskyvystä, jotka tarkentuvat järjestelmän ulottuvuuksien kasvaessa suuriksi. Erityistä huomiota kiinnitetään seuraaviin: ei-ortogonaaliseen monipääsytekniikkaan (NOMA); koordinoituihin monipistelähetyksiin (CoMP); ja kaksivaiheiseen keilanmuodostukseen (TSB), jossa yhdistyvät suuriulotteinen tilastollinen esi-/jälkikäsittely ja alemman ulottuvuuden digitaalinen käsittely. Aluksi tarkastellaan monen kantoaallon NOMA-järjestelmä, joka perustuu matalatiheyksiseen hajautukseen taajuustasossa (LDS). Resurssien allokointia, joka perustuu yksinomaan tilastolliseen kanavatilatietoon (CSI), tutkitaan ergodisen kokonaistiedonsiirtonopeuden maksimoimiseksi ottaen huomioon LDS-koodien tiheysrajoitukset. Koska optimaalinen ratkaisu on saavutettavissa vain täydellisen haun avulla, tässä työssä ehdotetaan matalan monimutkaisuuden menetelmää, joka vaatii minimaalista koordinointia ja joka tuottaa lähes-optimaalisia resurssien allokointiratkaisuja. Seuraavaksi kehitetään lähetystehon minimoivia keilanmuodostusmenetelmiä laskevan siirtotien CoMP-verkossa ottaen huomioon käyttäjäkohtaiset vähimmäistiedonsiirtovaatimukset. Työssä johdetaan tilastolliseen kanavatietoon pohjautuvia deterministisiä matemaattisia lausekkeita käyttäjäkohtaisille solujen välistä häiriötä kuvaaville (ICI) termeille. Determinististen ICI-termien käyttö koordinointisanomina mahdollistaa matalan monimutkaisuuden hajautetun toteutuksen tiheissä verkoissa, joiden runkoliityntäyhteys on rajallinen. Signaali-häiriö-plus-kohinasuhteen (SINR) maksimointia tarkastellaan tiheässä satunnaistopologiaan perustuvassa CoMP-verkossa. Deterministisiä lausekkeita johdetaan optimaalisille SINR-arvoille järjestelmäparametrien, kuten solusäteen, kuorman ja tehobudjettien funktiona. Tulokset mahdollistavat verkon suorituskyvyn arvioinnin annettujen järjestelmäparametrien perusteella. Lopuksi tarkastellaan optimaalisen lineaarisen vastaanottimen monimutkaisuuden vähentämistä hyödyntäen kaksivaiheista keilanmuodostusta nousevan siirtotien solukkoverkkojärjestelmässä. Työssä ehdotetaan uutta TSB-menetelmää, jolla säädellään ulompien keilanmuodostusmatriisien rakennetta ja dimensioita perustuen tilastolliseen kanavatietoon ja käyttäjien päällekkäisyyksiin kulmatasossa. Ehdotettu menetelmä tuottaa lähellä optimaalisia SINR-arvoja, samalla kun keilanmuodostuksen laskennallinen rasite vähenee huomattavasti

Capacity approaching low density spreading in Uplink NOMA via asymptotic analysis

Abstract Low-density spreading non-orthogonal multiple-access (LDS-NOMA) is considered where K single-antenna user-equipments (UEs) communicate with a base-station (BS) over F fading sub-carriers. Each UE k spreads its data symbols over dk≪F sub-carriers. The performance of LDS-NOMA system depends on the allocation of the non-zero elements in the LDS-codes. We aim to identify the LDS resource allocations, based solely on pathlosses, that maximize the ergodic mutual information (EMI). This problem can be solved only via an exhaustive search. Thus, relying on analysis in the regime where F , K , and dk,∀k converge to +∞ at the same rate, we present EMI as a deterministic equivalent plus a residual term. The deterministic equivalent is a function of pathloss values and LDS-codes, and the small residual term scales as O(1min(d2k)) . First, we formulate an optimization problem to identify the resource allocations that maximize the deterministic equivalent of EMI. The Karush-Kuhn-Tucker conditions give a simple resource allocation rule that facilitates the construction of desired LDS-codes via an efficient partitioning algorithm. The finite-regime analysis shows that such sparse solutions additionally harness the small incremental gain inherent in the residual term, and thus, provides a near-optimal performance. The spectral efficiency enhancement relative to regular and random spreading is validated numerically

Resource allocation in low density spreading uplink NOMA via asymptotic analysis

Abstract Low density spreading non-orthogonal multiple- access (LDS-NOMA) is considered where K single-antenna user equipments (UEs) communicate with a base station (BS) over F fading sub-carriers. Each UE k spreads its data symbol over d k <; F sub-carriers. Given d k , ∀k as design parameters, we characterize the resource allocation solutions that closely maximize the ergodic mutual information (EMI) in a scenario where the BS assigns resources solely based on the UEs’ pathlosses. Conducting analysis in asymptotic limit where F, K, and d k , ∀k converge to +∞ at the same rate, we present EMI in terms of a deterministic equivalent plus a residual term. The deterministic equivalent is given in terms of pathloss values and LDS-codes, and the small residual term scales as O(1/d 2 ) where d = min{d k , ∀k}. We formulate an optimization problem to get the set C̅* of all spreading codes, irrespective of sparsity constraints, which maximize the deterministic equivalent of EMI. The spreading codes in C̅* with desired sparsity are obtained via a simple and efficient algorithmic solution. In the finite regime, the residual term is shown to be a small incremental gain for the sparse solutions in C̅*, which is dictated mainly by d k , ∀k values. Accordingly, we show that the solutions in C̅* with desired sparsity yield close to optimum values of EMI in the finite regime. Numerical simulation validates the attainable spectral efficiency enhancement as compared to regular, and random spreading

Two-stage beamformer design via deterministic equivalents

Abstract Complexity reduction of optimal linear receiver is considered in a scenario where both the number of single antenna user equipments (UEs) K and base station (BS) antennas N are large. Two-stage beamforming (TSB) greatly alleviates the high implementation complexity of large scale multiantenna receiver by concatenating a statistical outer beamformer (OBF) with an instantaneous inner beamformer (IBF) design. Using asymptotic large system analysis, we propose a novel TSB method that adjusts the dimensions of user specific OBF matrices based on the projection of the optimal minimum mean square error (MMSE) vectors into the beam domain. The beam domain is first divided into S narrow sectors such that each sector contains D DFT beams. Then, so called deterministic equivalents are computed for the amplitude-projection of the optimal MMSE vectors into each sector in asymptotic regime where N, K and D grow large with a non-trivial ratio N/K = C and N/D = S. Given the approximations for the sector specific values, the structure and dimension of each UE specific OBF vector are optimized based on the statistical channel properties and the amount of overlap among users in angular domain. The numerical analysis shows that the attained SINR values closely follow the optimal MMSE receiver while the computational burden is greatly reduced

Decentralizing multicell beamforming via deterministic equivalents

Abstract This paper focuses on developing a decentralized framework for coordinated minimum power beamforming wherein L base stations (BSs), each equipped with N antennas, serve K single-antenna users with specific rate constraints. This is realized by considering user specific intercell interference (ICI) strength as the principal coupling parameter among BSs. First, explicit deterministic expressions for transmit powers are derived for spatially correlated channels in the asymptotic regime in which N and K grow large with a non-trivial ratio K/N. These asymptotic expressions are then used to compute approximations of the optimal ICI values that depend only on the channel statistics. By relying on the approximate ICI values as coordination parameters, a distributed non-iterative coordination algorithm, suitable for large networks with limited backhaul, is proposed. A heuristic algorithm is also proposed relaxing coordination requirements even further as it only needs pathloss values for non-local channels. The proposed algorithms satisfy the target rates for all users even when N and K are relatively small. Finally, the potential benefits of grouping users with similar statistics are investigated to further reduce the overhead and computational effort of the proposed solutions. Simulation results show that the proposed methods yield near-optimal performance

Contextual bandit learning for machine type communications in the null space of multi-antenna systems

Abstract Ensuring an effective coexistence of conventional broadband cellular users with machine type communications (MTCs) is challenging due to the interference from MTCs to cellular users. This interference challenge stems from the fact that the acquisition of channel state information (CSI) from machine type devices (MTD) to cellular base stations (BS) is infeasible due to the small packet nature of MTC traffic. In this paper, a novel approach based on the concept of opportunistic spatial orthogonalization (OSO) is proposed for interference management between MTC and conventional cellular communications. In particular, a cellular system is considered with a multi-antenna BS in which a receive beamformer is designed to maximize the rate of a cellular user, and, a machine type aggregator (MTA) that receives data from a large set of MTDs. The BS and MTA share the same uplink resources, and, therefore, MTD transmissions create interference on the BS. However, if there is a large number of MTDs to chose from for transmission at each given time for each beamformer, one MTD can be selected such that it causes almost no interference on the BS. A comprehensive analytical study of the characteristics of such an interference from several MTDs on the same beamformer is carried out. It is proven that, for each beamformer, an MTD exists such that the interference on the BS is negligible. To further investigate such interference, the distribution of the signal-to-interference-plus-noise ratio (SINR) of the cellular user is derived, and, subsequently, the distribution of the outage probability is presented. However, the optimal implementation of OSO requires the CSI of all the links in the BS, which is not practical for MTC. To solve this problem, an online learning method based on the concept of contextual multi-armed bandits (MAB) learning is proposed. The receive beamformer is used as the context of the contextual MAB setting and Thompson sampling: a well-known method of solving contextual MAB problems is proposed. Since the number of contexts in this setting can be unlimited, approximating the posterior distributions of Thompson sampling is required. Two function approximation methods, a) linear full posterior sampling, and, b) neural networks are proposed for optimal selection of MTD for transmission for the given beamformer. Simulation results show that is possible to implement OSO with no CSI from MTDs to the BS. Linear full posterior sampling achieves almost 90% of the optimal allocation when the CSI from all the MTDs to the BS is known