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Precoding and Relaying Algorithms for Multiuser MIMO Downlink Channels Idoia Jimenez Ramirez Supervisor: Mikel Mendicute Errasti MONDRAGON UNIBERTSITATEA A thesis submitted for the degree of Doctor por Mondragon Unibertsitatea Department of Electronics and Computer Science Mondragon Goi Eskola Politeknikoa Mondragon Unibertsitatea April 2013

Familixandako, Ta Ionendako. Learn from yesterday, live for today, hope for tomorrow. The important thing is not to stop questioning. Albert Einstein

Agradecimientos Algo más de cuatro años han pasado desde que empezó esta aventura. Durante este periodo he tenido la oportunidad de conocer a muchos investigadores que han ayudado a que esta tesis llegue hoy a su ﬁn. A todos los que han estado en los buenos pero sobre todo en los malos momentos gracias. En primer lugar, me gustaría agradecer a mi director de tesis Mikel Mendicute su inestimable ayuda. Gracias por su disponibilidad y por los consejos dados que han hecho posible el buen ﬁn de esta tesis. Por otro lado, me gustaría agradecer a Mondragon Goi Eskola Politeknikoa la beca de investigación que me otorgó hace ya cuatro largos años. Quisiera agradecer muy especialmente a Stephan Weiss de Strathclyde University su cálida acogida así como su aportación. Gracias también a mis compañeros del Centre for excellence in Signal and Image Processing (CeSIP), especialmente a Andrew Millar por hacerme sentir una más y hacer más fácil la adaptación cuando estas lejos de casa. Gracias a mis compañeros de departamento por brindarme su ayuda así como por esos largos cafes que ayudan a la desconexión. Me gustaría agradecer especialmente a Iker Sobron, Maitane Barrenechea, Lorena Martinez y Pello Otxandiano su inestimable ayuda. No me gustaría olvidarme de Aritz Legarda, Maite Beamurgia, Iñaki Garitano, Lorea Belategi y Joxe Aizpurua así como de los recien llegados Aitor Lizeaga, Alain Perez y Enaitz Ezpeleta. Gracias por la ayuda prestada y por los buenos momentos vividos pero sobre todo por hacer más fácil el día a día. Finalmente me gustaría expresar mi más sincera gratitud a mis padres y a mis hermanos Txapu, Inma y Fran. Gracias por interesarse por esta tesis y por los buenos consejos. No me gustaría olvidarme de mis sobrinos Danel, Elene, Beñat, Luken y como no, del gran Markeltxo. No menos importante ha sido la ayuda prestada por mis amig@s. Gracias por haberme dado ánimos en momentos de ﬂaqueza. Pero sobre todo gracias en mayúsculas a Zubi, por estar siempre ahí, por animarme a seguir aprendiendo y sobre todo por obligarme a parar cuando más bloqueada estaba. iii

Acknowledgments More than four years have passed since I started this adventure. During this period, I have had the opportunity to meet many researchers who have helped making this thesis comes to an end today. To all those who have been in good times but especially in bad times thank you. First of all, I would like to thank my thesis supervisor Mikel Mendicute his invaluable help. Thank you for your availability and all the advice given that made possible the success of this thesis. Furthermore, I would like to thank to Mondragon Goi Eskola Politeknikoa the research grant that awarded me four years ago. I would like to extend special thanks to Stephan Weiss of Strathclyde University for his warm welcome as well as for his contribution to this PhD dissertation. Thanks also to my workmates at Centre for Excellence in Signal and Image Processing (CESIP) and specially thanks to Andrew Millar for making me feel one more and for making easier the adaptation when you are away from home. I would also like to express my gratitude to my fellow colleagues, for the enjoyable coﬀee breaks and all the great moments of laughter and jokes we shared together. I would like to show special appreciation to Iker Sobrón, Maitane Barrenechea, Lorena Martinez and Pello Otxandiano for their irreplaceable help. I would not like to forget Aritz Legarda, Maite Beamurgia, Iñaki Garitano, Lorea Belategi and Joxe Aizpurua as well as the newcomers Aitor Lizeaga, Alain Perez and Enaitz Ezpeleta. Thanks for the cheering me up and for the good moments lived that makes easier the day-to-day. Finally I would like to express my sincere gratitude to my parents and my siblings Txapu, Inma and Fran. Thanks for your interest and for your good advice. I would not like to forget my nephews Danel, Beñat, Elene, Luken and of course, the great Markeltxo. Not less important was the help given by my friends. Thanks for bucking me up in moments of weakness. But mostly thanks to Zubi, for always being there, for encouraging me to keep learning and specially for forced me to stop when I was locked. iv

Abstract In the last years, research has focused on multiple-input multiple-output (MIMO) wireless technology due to the capacity and performance improvement it provides, oﬀering a higher spectral eﬃciency. In addition, when multiple users take part in the network, the scenario becomes much more complex, since resources like bandwidth, time or transmission power must be shared. Furthermore, the performance of the system is degraded as a consequence of the noise and multiuser interference (MUI). When the transmission is conducted from a base station (BS) to multiple users, a pre-equalization stage called precoding is applied. By means of this, each user will be able to interpret the signal independently, without the knowledge of the channel. Precoding techniques are classiﬁed into linear and non-linear. In fact, the non-linear Tomlinson-Harashima precoding (THP) and vector precoding (VP) techniques have been shown to achieve very good results in multiuser broadcast channels, outperforming the per- formance of linear systems considerably. Nevertheless, the computational complexity also increases as a consequence of successive interference cancellation in THP or the search for the closest point in an inﬁnite lattice for the case of VP. In order to improve the coverage and range of the network in fading environments, as well as for MUI mitigation, a relaying terminal can be introduced between the BS and the users, being the signal modiﬁed either regeneratively or not to reach the destination. Hence, apart form incorporating a precoding stage at the BS for the separation of user streams, multiuser MIMO relaying systems can include a processing stage at the relay. By means of this, the signal will be provided by the characteristic necessary to reach the destination in a more eﬃcient way. Throughout this thesis, the design of transceivers for non-regenerative multiuser MIMO relay systems is addressed, where the main challenge resides on the joint design of the precoder at the base station and the relaying matrix. We propose the use of linear and non-linear precoding techniques such as THP and VP at the downlink relayed transmission scenario. Apart from the joint design of the linear and non-linear transceiver design, block diagonalization (BD) is proposed in combination with the mentioned precoding techniques. v

BD, which maps each user signal at the null space created by the interfering users, is applied at the relay for interference cancellation whilst linear processing and VP are set at the BS for users signal separation and overall error minimization. The main contributions of this research work are the novel optimal proposals based on non-linear precoding techniques and the consideration of BD for the joint design. Fur- thermore, simple and computationally eﬃcient suboptimal approaches based on linear and non-linear precoding techniques are ﬁrst here proposed. In addition, block diagonal geomet- ric mean decomposition is presented in combination with VP for the optimal and suboptimal design of the transmitter. To conclude, a complete complexity analysis is given in order to show the eﬀectiveness of the proposed schemes.

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