This paper studies the optimal tradeoff between secrecy and non-secrecy rates of the MISO wiretap channels for different power constraint settings: sum power constraint only, per-antenna power constraints only, and joint sum and per-antenna power constraints. The problem is motivated by the fact that channel capacity and secrecy capacity are generally achieved by different transmit strategies. First, a necessary and sufficient condition to ensure a positive secrecy capacity is shown. The optimal tradeoff between secrecy rate and transmission rate is characterized by a weighted rate sum maximization problem. Since this problem is not necessarily convex, equivalent problem formulations are introduced to derive the optimal transmit strategies. Under sum power constraint only, a closed-form solution is provided. Under per-antenna power constraints, necessary conditions to find the optimal power allocation are derived. Sufficient conditions are provided for the special case of two transmit antennas. For the special case of aligned channels, the optimal transmit strategies can deduced from an equivalent point-to-point channel problem. Last, the theoretical results are illustrated by numerical simulations.

Nowadays, wireless communications have become an essential part of our daily life. During the last decade, both the number of users and their demands for wireless data have tremendously increased. Multi-antenna communication is a promising solution to meet this ever-growing traffic demands. In this dissertation, we study the optimal transmit strategies for multi-antenna systems with advanced power constraints, in particular joint sum and per-antenna power constraints. We focus on three different models including multi-antenna point-to-point channels, wiretap channels and massive multiple-input multiple-output (MIMO) setups. The solutions are provided either in closed-form or efficient iterative algorithms, which are ready to be implemented in practical systems.

The first part is concerned with the optimal transmit strategies for point-to-point multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) channels with joint sum and per-antenna power constraints. For the Gaussian MISO channels, a closed-form characterization of an optimal beamforming strategy is derived. It is shown that we can always find an optimal beamforming transmit strategy that allocates the maximal sum power with phases matched to the complex channel coefficients. An interesting property of the optimal power allocation is that whenever the optimal power allocation of the corresponding problem with sum power constraint only exceeds per-antenna power constraints, it is optimal to allocate maximal per-antenna power to those antennas to satisfy the per-antenna power constraints. The remaining power is distributed among the other antennas whose optimal allocation follows from a reduced joint sum and per-antenna power constraints problem with fewer channel coefficients and a reduced sum power constraint. For the Gaussian MIMO channels, it is shown that if an unconstraint optimal power allocation for an antenna exceeds a per-antenna power constraint, then the maximal power for this antenna is used in the constraint optimal transmit strategy. This observation is then used in an iterative algorithm to compute the optimal transmit strategy in closed-form.

In the second part of the thesis, we investigate the optimal transmit strategies for Gaussian MISO wiretap channels. Motivated by the fact that the non-secure capacity of the MISO wiretap channels is usually larger than the secrecy capacity, we study the optimal trade-off between those two rates with different power constraint settings, in particular, sum power constraint only, per-antenna power constraints only, and joint sum and per-antenna power constraints. To characterize the boundary of the optimal rate region, which describes the optimal trade-off between non-secure transmission and secrecy rates, related problems to find optimal transmit strategies that maximize the weighted rate sum with different power constraints are derived. Since these problems are not necessarily convex, equivalent problem formulation is used to derive optimal transmit strategies. A closed-formsolution is provided for sum power constraint only problem. Under per-antenna power constraints, necessary conditions to find the optimal power allocation are provided. Sufficient conditions, however, are available for the case of two transmit antennas only. For the special case of parallel channels, the optimal transmit strategies can deduced from an equivalent point-to-point channel problem. In this case, there is no trade-off between secrecy and non-secrecy rate, i.e., there is onlya transmit strategy that maximizes both rates.

Finally, the optimal transmit strategies for large-scale MISO and massive MIMO systems with sub-connected hybrid analog-digital beamforming architecture, RF chain and per-antenna power constraints are studied. The system is configured such that each RF chain serves a group of antennas. For the large-scale MISO system, necessary and sufficient conditions to design the optimal digital and analog precoders are provided. It is optimal that the phase at each antenna is matched tothe channel so that we have constructive alignment. Unfortunately, for the massive MIMO system, only necessary conditions are provided. The necessary conditions to design the digital precoder are established based on a generalized water-filling and joint sum and per-antenna optimal power allocation solution, while the analog precoder is based on a per-antenna power allocation solution only. Further, we provide the optimal power allocation for sub-connected setups based on two properties: (i) Each RF chain uses full power and (ii) if the optimal power allocation of the unconstraint problem violates a per-antenna power constraint then it is optimal to allocate the maximal power for that antenna. The results in the dissertation demonstrate that future wireless networks can achieved higher data rates with less power consumption. The designs of optimal transmit strategies provided in this dissertation are valuable for ongoing implementations in future wireless networks. The insights offered through the analysis and design of the optimal transmit strategies in the dissertation also provide the understanding of the optimal power allocation on practical multi-antenna systems.

Trådlös kommunikation har idag kommit att bli en viktig del av våra dagliga liv. Under det senaste decenniet har både antalet användare och deras efterfrågan på trådlös data ökat enormt. Att utöka antalet antenner i sändare och mottagare är lovande strategier för att möta det ständigt ökande trafikbehovet. I den här avhandlingen studerar vi optimala transmissionsstrategier för multi-antennsystem med avancerade effektbegränsningar. Mer specifikt antas sammanlänkade begränsningar på total effekt och effekt per antenn. Vi fokuserar på tre olika modeller, nämligen multi-antenn punkt-till-punkt kanaler, wiretap-kanaler samt s.k. massiv MIMO (eng. multiple-input multiple-output) scenarier. Lösningar ges antingen i form av slutna matematiska uttryck, alternativt genom effektiva iterativa algoritmer redo att implementeras i praktiska system.

Den första delen av avhandlingen studerar optimala transmissionsstrategier för punkt-till-punkt MISO (eng. multiple-input single-output) samt MIMO-kanaler med sammanlänkade begränsningar på total effekt och effekt per antenn. För Gaussiska MISO-kanaler härleds en sluten karakterisering av en optimal ’beamforming’ -strategi. Vi visar att det alltid går att hitta en optimal ’beamforming’-strategi som allokerar den maximala totaleffekten med faser matchade till de komplexa kanalkoefficienterna. En intressant egenskap hos den optimala effektallokeringen är att närhelst den optimala effektallokeringen med enbart total effektbegränsning endast överskrider de individuella begränsningarna för specifika antenner, erhålls en optimal lösning genom att allokera maximal per-antenn effekt till just dessa antenner. Den återstående effekten distribueras sedan över de övriga antennerna enligt ett ekvivalent men reducerat optimeringsproblem med färre kanalkoefficienter. För Gaussiska MIMO-kanaler visas att om en obegränsad optimal effektallokering för en antenn överskrider den individuella, per antenn angivna, begränsningen så är maximal effekt allokerad för just dessa antenner i den optimala strategin. Denna observation används för att beskriva en iterativ algoritm som beräknar den optimala transmissionsstrategin.

I den andra delen av avhandlingen undersöker vi optimala transmissionsstrategier för Gaussiska MISO wiretap-kanaler. Motiverat av faktumet att den icke-säkrade kapaciteten över MISO wiretap-kanalen vanligtvis är större än den säkrade s.k. ’secrecy’-kapaciteten, studerar vi den optimala avvägningen mellan dessa två överföringshastigheter givet olika effektbegränsningar. Mer specifikt studeras total effektbegränsning enskilt, individuell effektbegränsning per antenn enskilt, samt sammanlänkade begränsningar på båda dessa. För att hitta regionsgränsen för optimala hastigheter, vilken beskriver den optimala avvägningen mellan icke-säkrad sändning och ’secrecy’-hastighet, härleds lösningar till relaterade problem där vi söker optimala transmissionsstrategier som maximerar den viktade summan av hastigheter med olika effektbegränsningar. Ekvivalenta formuleringar av optimeringsproblemen används för att härleda optimala transmissionsstrategier eftersom ursprungsproblemen ej är konvexa. En optimal lösning för problemet med total effektbegränsning ges i sluten form. För individuell effektbegränsning per antenn tillhandahåller vi nödvändiga villkor för att finna en optimal effektallokering. Tillräckliga villkor är endast tillgängliga i fallet av två sändarantenner. För specialfallet av parallella kanaler kan transmissionsstrategier härledas från ett ekvivalent problem för en punkt-till-punkt kanal. I detta fall existerar ingen avvägning mellan icke-säkrade och ’secrecy’ kapaciteten, endast en optimal strategi som maximerar båda kapaciteter.

Avslutningsvis studeras optimala strategier för storskaliga MISO samt massiva MIMO system med sammankopplad hybrid analog-digital ’beamforming’-arkitektur,  radiofrekvens-kedja samt individuella effektbegränsningar per antenn. Studerat system är konfigurerat så att varje radiofrekvens-kedja matar en grupp av antenner. För det storskaliga MISO systemet tillhandahålls nödvändiga och tillräckliga villkor för att design av optimala analoga och digitala kodningsstrategier ska vara möjligt. Optimal strategi uppnås då fasförskjutningen i varje antenn är matchad till motsvarande kanal, varvid konstruktiv samverkan uppstår. För massiv MIMO ges dessvärre endast nödvändiga villkor. De nödvändiga villkoren för att designa digitala kodningsstrategier etableras baserat på en generaliserad s.k. ’water-filling’ effektallokeringsmetod med sammanlänkade begränsningar på total effekt och effekt per antenn, medan villkoren för de analoga kodningsstrategierna endast är baserade på effektbegränsningar per antenn. Vidare beskriver vi optimal effektallokering för sammankopplade system baserat på två egenskaper: (i) Varje radiokedja utnyttjas till full effekt, samt (ii) i fallet då optimala effektallokeringen i det obegränsade problemet överskrider specifika antenners begränsningar fås den optimala lösningen genom att allokera maximal effekt till motsvarande antenner.Resultaten i denna avhandling visar att framtida trådlösa nätverk kan uppnå högre datahastigheter med lägre effektförbrukning. Den design av optimala transmissionsstrategier som beskrivs i denna avhandling är därför värdefulla i den pågående implementeringen av framtida trådlösa nätverk. De insikter som ges genom analys och design av optimala transmissionsstrategier i avhandlingen ger också förståelse inom optimal effektallokering i praktiska implementeringar av multi-antennsystem.

This paper studies the optimal tradeoff between secrecy and non-secrecy rates of the MISO wiretap channels for different power constraint settings:sum power constraint only, per-antenna power constraints only and joint sum and per-antenna power constraints. The problem is motivated by the fact thatchannel capacity and secrecy capacity are generally achieved by different transmit strategies. First, a necessary and sufficient condition to ensure a positive secrecy capacity is shown. The optimal tradeoff between secrecy rate and transmission rate is characterized by a weighted rate sum maximization problem. Since this problem is not necessarily convex, equivalent problem formulations are introduced to derive the optimal transmit strategies. Under sum power constraint only, a closed-form solution is provided. Under per-antenna power constraints, necessary conditions to find the optimal power allocation are provided. Sufficient conditions are provided for the special case of two transmit antennas. For the special case of parallel channels, the optimal transmit strategies can deduced from an equivalent point-to-point channel problem. Lastly, the theoretical results are illustrated by numerical simulations.

This paper provides the necessary conditions to design precoding matrices for massive MIMO systems with a sub-connected architecture, RF power constraints and per-antenna power constraints. The system is configured such that each RFchain serves a group of antennas. The necessary condition to design the digital precoder is established based on a generalized water-filling and joint sum and per-antenna optimal power allocation solution, while the analog precoder is based on a per-antenna power allocation solution only. We study the analytically most interesting case where the power constraint on the RF chain is smaller than the sum of the corresponding per-antenna power constraints. For this, the optimal power is allocated based on two properties: Each RF chain uses full power and if the optimal power allocation of the unconstraint problem violates a per-antenna power constraint then it is optimal to allocate the maximal power for that antenna.

This letter considers optimal transmit beamforming for a sub-connected large-scale MISO system with RF chain and per-antenna power constraints. The system is configured such that each RF chain serves a group of antennas. For the hybrid scheme, necessary and sufficient conditions to design the optimal digital and analog precoders are provided. It is shown that, in the optimum, the optimal phase shift at each antenna has to match the channel coefficient and the phase of the digital precoder. In addition, an iterative algorithm is provided to find the optimal power allocation. We study the case where the power constraint on each RF chain is smaller than the sum of the corresponding per-antenna power constraints. Then, the optimal power is allocated based on two properties: each RF chain uses full power and if the optimal power allocation of the unconstraint problem violates a per-antenna power constraint then it is optimal to allocate the maximal power for that antenna.

The future wireless networks require both high data transmission rates and secure communications. However, there exists a trade-off between secure and non-secure rates since only a fraction of the maximal achievable reliable rate in a wiretap channel can be considered as secure. This paper studies the optimal transmit strategies that achieve the optimal trade-off between the communication rate and secrecy rate for the MISO wiretap channels with different power constraint settings including sum power constraint only, per-antenna power constraints only, and joint sum and per-antenna power constraints. First, a necessary and sufficient condition to ensure a positive secrecy capacity is shown. After that, closed-form solutions to find an optimal transmit strategy of related problems are derived. This provides a parametrization of the boundary of the maximal achievable rate and secrecy rate without additional time-sharing. The optimal trade-off is characterized by the convex hull of the region. Lastly, the results are illustrated by numerical examples.

This paper studies optimal transmit strategies for multiple-input multiple-output (MIMO) Gaussian channels with joint sum and per-antenna power constraints. It is shown that if an unconstraint optimal allocation for an antenna exceeds a per-antenna power constraint, then the maximal power for this antenna is used in the constraint optimal transmit strategy. This observation is then used in an iterative algorithm to compute the optimal transmit strategy in closed-form. Finally, a numerical example is provided to illustrate the theoretical results.

The energy efficiency (EE) of a multi-user multi-relay system with the maximum diversity network coding (MDNC) is studied. We explicitly find the connection among the outage probability, energy consumption, and EE, and formulate the maximizing EE problem under the outage probability constraint. Relay scheduling (RS) and power allocation (PA) are applied to schedule the relay states (transmitting, sleeping, and so on) and optimize the transmitting power under the practical channel and power consumption models. Since the optimization problem is NP hard, to reduce computational complexity, the outage probability is first tightly approximated to a log-convex form. Furthermore, the EE is converted into a subtractive form based on the fractional programming. Then, a convex mixed-integer nonlinear problem is eventually obtained. With a generalized outer approximation algorithm, RS and PA are solved in an iterative manner. The Pareto-optimal curves between the EE and the target outage probability show the EE gains from PA and RS. Moreover, by comparing with the no network coding (NoNC) scenario, we conclude that with the same number of relays, MDNC can lead to EE gains. However, if RS is implemented, NoNC can outperform MDNC in terms of the EE when more relays are needed in the MDNC scheme.

In this paper, the energy efficiency (EE) of a cooperative diversity system with maximum diversity network coding (MDNC) is studied. In the considered system, channel state information (CSI) is only available at the receivers for all the channels. We formulate the problem of maximizing the EEunder the constraint on the outage probability. The problem is NP-hard due to the non-convexity of the outage probability function and the nonlinear fractional structure of the introducedEE. To solve the optimization problem efficiently, first, the outage probability function is tightly approximated as a log-convex form in the high signal-to-noise ratio (SNR) region. Further, based on the fractional programming, we transform the introduced EEinto a subtractive-form, which is proved to be a convex form. The tradeoff between outage probability and EE is given. The results show that our power allocation (PA) policy can substantially increase the EE. We show that EE can be increased if more relays forward the messages. Additionally, we also investigate the effect of the relay locations on the EE and demonstrate that the increase in the transmission distance in the first hop causes the loss of the EE. The loss can be reduced by our PA policy.

This paper considers the optimal transmit strategy for multi-antenna bidirectional broadcast channels with per-antenna power constraints. First, an equivalent formulation of the weighted rate sum maximization problem is provided. This allows us to come up with an effective solution to characterize the boundary of the capacity region which relies on the weighted rate sum optimal rate pair. To that end, an iterative algorithm to find the optimal transmit strategy is derived, the convergence to the optimum is proved, and a closed-form solution of the corresponding off-diagonal elements of the optimal transmit strategy is provided. Further, we provide a parametrization of the curved section of the capacity region. Finally, the theoretical results and algorithm performance are illustrated by numerical examples.