A Belief Propagation Based Framework for Soft Multiple-Symbol Differential Detection

Soft noncoherent detection, which relies on calculating the \textit{a posteriori} probabilities (APPs) of the bits transmitted with no channel estimation, is imperative for achieving excellent detection performance in high-dimensional wireless communications. In this paper, a high-performance belief propagation (BP)-based soft multiple-symbol differential detection (MSDD) framework, dubbed BP-MSDD, is proposed with its illustrative application in differential space-time block-code (DSTBC)-aided ultra-wideband impulse radio (UWB-IR) systems. Firstly, we revisit the signal sampling with the aid of a trellis structure and decompose the trellis into multiple subtrellises. Furthermore, we derive an APP calculation algorithm, in which the forward-and-backward message passing mechanism of BP operates on the subtrellises. The proposed BP-MSDD is capable of significantly outperforming the conventional hard-decision MSDDs. However, the computational complexity of the BP-MSDD increases exponentially with the number of MSDD trellis states. To circumvent this excessive complexity for practical implementations, we reformulate the BP-MSDD, and additionally propose a Viterbi algorithm (VA)-based hard-decision MSDD (VA-HMSDD) and a VA-based soft-decision MSDD (VA-SMSDD). Moreover, both the proposed BP-MSDD and VA-SMSDD can be exploited in conjunction with soft channel decoding to obtain powerful iterative detection and decoding based receivers. Simulation results demonstrate the effectiveness of the proposed algorithms in DSTBC-aided UWB-IR systems.Comment: 14 pages, 12 figures, 3 tables, accepted to appear on IEEE Transactions on Wireless Communications, Aug. 201

Massive MIMO for Internet of Things (IoT) Connectivity

Massive MIMO is considered to be one of the key technologies in the emerging 5G systems, but also a concept applicable to other wireless systems. Exploiting the large number of degrees of freedom (DoFs) of massive MIMO essential for achieving high spectral efficiency, high data rates and extreme spatial multiplexing of densely distributed users. On the one hand, the benefits of applying massive MIMO for broadband communication are well known and there has been a large body of research on designing communication schemes to support high rates. On the other hand, using massive MIMO for Internet-of-Things (IoT) is still a developing topic, as IoT connectivity has requirements and constraints that are significantly different from the broadband connections. In this paper we investigate the applicability of massive MIMO to IoT connectivity. Specifically, we treat the two generic types of IoT connections envisioned in 5G: massive machine-type communication (mMTC) and ultra-reliable low-latency communication (URLLC). This paper fills this important gap by identifying the opportunities and challenges in exploiting massive MIMO for IoT connectivity. We provide insights into the trade-offs that emerge when massive MIMO is applied to mMTC or URLLC and present a number of suitable communication schemes. The discussion continues to the questions of network slicing of the wireless resources and the use of massive MIMO to simultaneously support IoT connections with very heterogeneous requirements. The main conclusion is that massive MIMO can bring benefits to the scenarios with IoT connectivity, but it requires tight integration of the physical-layer techniques with the protocol design.Comment: Submitted for publicatio

Short Packets over Block-Memoryless Fading Channels: Pilot-Assisted or Noncoherent Transmission?

We present nonasymptotic upper and lower bounds on the maximum coding rate achievable when transmitting short packets over a Rician memoryless block-fading channel for a given requirement on the packet error probability. We focus on the practically relevant scenario in which there is no \emph{a priori} channel state information available at the transmitter and at the receiver. An upper bound built upon the min-max converse is compared to two lower bounds: the first one relies on a noncoherent transmission strategy in which the fading channel is not estimated explicitly at the receiver; the second one employs pilot-assisted transmission (PAT) followed by maximum-likelihood channel estimation and scaled mismatched nearest-neighbor decoding at the receiver. Our bounds are tight enough to unveil the optimum number of diversity branches that a packet should span so that the energy per bit required to achieve a target packet error probability is minimized, for a given constraint on the code rate and the packet size. Furthermore, the bounds reveal that noncoherent transmission is more energy efficient than PAT, even when the number of pilot symbols and their power is optimized. For example, for the case when a coded packet of $168$ symbols is transmitted using a channel code of rate $0.48$ bits/channel use, over a block-fading channel with block size equal to $8$ symbols, PAT requires an additional $1.2$ dB of energy per information bit to achieve a packet error probability of $10^{-3}$ compared to a suitably designed noncoherent transmission scheme. Finally, we devise a PAT scheme based on punctured tail-biting quasi-cyclic codes and ordered statistics decoding, whose performance are close ($1$ dB gap at $10^{-3}$ packet error probability) to the ones predicted by our PAT lower bound. This shows that the PAT lower bound provides useful guidelines on the design of actual PAT schemes.Comment: 30 pages, 5 figures, journa

Multiuser non coherent massive MIMO schemes based on DPSK for future communication systems

The explosive usage of rich multimedia content in wireless devices has overloaded the communication networks. Moreover, the fifth generation (5G) of wireless communications involves new requirements in the radio access network (RAN) which require higher network capacities and new capabilities such as ultra-reliable and low-latency communication (URLLC), vehicular communications or augmented reality. All this has encouraged a remarkable spectrum crisis in the RF bands. A need for searching alternative techniques with more spectral efficiency to accommodate the needs of future emerging wireless communications is emerging. In this context, massive MIMO (m-MIMO) systems have been proposed as a promising solution for providing a substantial increase in the network capacity, becoming one of the key enabling technologies for 5G and beyond. m-MIMO provides high spectral- and energy-efficiency thanks to the deployment of a large number of antennas at the BS. However, we have to take into account that the current communication technologies are based on coherent transmission techniques so far, which require the transmission of a huge amount of signaling. This drawback is escalating with the excessive available number of antennas in m-MIMO. Therefore, the differential encoding and non coherent (NC) detection are an alternative solution to circumvent the drawbacks of m-MIMO in coherent systems. This Ph.D. Thesis is focused on signal processing techniques for NC detection in conjunction with m-MIMO, proposing new constellation designs and NC detection algorithms, where the information is transmitted in the signal differential phase. First, we design new constellation schemes for an uplink multiuser NC m-MIMO system in Rayleigh fading channels. These designs allow us to separate the users' signals at the receiver thanks to a one-to-one correspondence between the constellation for each user and the received joint constellation. Two approaches are considered in terms of BER: each user achieves a different performance and, on the other hand, the same performance is provided for all users. We analyze the number of antennas needed for those designs and compare to the required number by other designs in the literature. It is shown that our designs based on DPSK require a lower number of antennas than that required by their counterpart schemes based on energy. In addition, we compare the performance to their coherent counterpart systems, resulting NC-m-MIMO based on DPSK capable of outperforming the coherent systems with the suitable designs. Second, in order to reduce the number of antennas required for a target performance we propose a multi-user bit interleaved coded modulation - iterative decoding (BICM-ID) scheme as channel coding for a NC-m-MIMO system based on DPSK. We propose a novel NC approach for calculating EXIT curves based on the number of antennas. Then using the EXIT chart we find the best channel coding scheme for our NC-m-MIMO proposal. We show that the number of users served by the BS can be increased with a 70% reduction in the number of antennas with respect to the case without channel coding. In particular, we show that with 100 antennas for error protection equal design for all users and a coding rate of 1/2 we achieve the minimum probability of error. Third, we consider that current scenarios such as backhaul wireless systems, rural or suburban environments, and even new device-to-device (D2D) communications or the communications in higher frequencies (millimeter and the emerging ones in terahertz frequencies) can have a predominant line-of-sight (LOS) component, modeled by Rician fading. For all these new possible scenarios in 5G, we analyze the behavior of the NC m-MIMO systems when we have a Rician fading. We present a new constellation design to overcome the problem of the LOS channel component, as well as an associated detection algorithm to separate each user in reception taking into account the characterization of the constellation. In addition, for contemplating a more realistic scenario, we propose grouping users which experience a Rayleigh fading with those with Rician fading, analyzing the SINR and the performance of such combination in a multi-user NC m-MIMO system based on M-DPSK. The adequate user grouping allows unifying the constellation for both groups of users and the detection algorithm, reducing the complexity of the receiver. Also, the number of users that may be multiplexed may be further increased thanks to the improved performance. In the fourth part of this Thesis, we analyse the performance of multi-user NC m- MIMO based on DPSK in real environments and practical channels defined for the current standards such as LTE, the future technologies such as 5G and even for communications in the terahertz band. For this purpose, we use a metric to model the time-varying characteristics of the practical channels. We employ again the EXIT charts tool for analyzing and designing iteratively decoded systems. This analysis allows us to obtain an estimate of the degradation of the system's performance imposed by realistic channels. Hence, we show that our proposed system is robust to temporal variations, thus it is more recommendable the employment of NC-m-MIMO-DPSK in the future communication standards such as 5G. In order to reduce he number of hardware resources required in terms of RF chains, facilitating its implementation in a real system, we propose incorporating differential spatial modulation (DSM). We present and analyze a novel multiuser scheme for NC-m-MIMO combined with DSM with which we can see that the number of antennas is not a affected by the incorporation of DSM, even we have an improvement on the performance with respect to the coherent case. Finally, we study the viability of multiplexing users by constellation schemes against classical multiplexing techniques such as time division multiple access (TDMA). In order to fully characterize the system performance we analyze the block error rate (BLER) and the throughput of a NC-m-MIMO system. The results show a significant advantage regarding the number of antennas for multiplexing in the constellation against TDMA. However, in some cases, the demodulation of multiple users in constellation could require an excessively large number of antennas compared to TDMA. Therefore, it is necessary to properly manage the tradeoff between throughout and the number of antennas, to reach an optimal operational point, as shown in this Thesis.El inmenso uso de contenido multimedia en los dispositivos inalámbricos ha sobrecargado las redes de comunicaciones. Además, la quinta generación (5G) de sistemas de comunicaciones demanda nuevos requisitos para la red de acceso radio, la cual requiere ofrecer capacidades de red mayores y nuevas funcionalidades como comunicaciones ultra fiables y con muy poca letancia (URLLC), comunicaciones vehiculares o aplicaciones como la realidad aumentada. Todo esto ha propiciado una crisis notable en el espectro electromagnético, lo que ha llevado a una necesidad por buscar técnicas alternativas con más eficiencia espectral para acomodar todos los requisitos de las tecnologías de comunicaciones emergentes y futuras. En este contexto, los sistemas multi antena masivos, conocidos como massive MIMO, m-MIMO, han sido propuestos como una solución prometedora que proporciona un incremento substancial de la capacidad de red, convirtiéndose en una de las tecnologías claves para el 5G. Los sistemas m-MIMO elevan enormemente el número de antenas en la estación base, lo que les permite ofrecer alta eficiencia espectral y energética. No obstante, tenemos que tener en cuenta que las actuales tecnologías de comunicaciones emplean técnicas coherentes, las cuales requieren de información del estado del canal y por ello la transmisión de una enorme cantidad de información de señalización. Este inconveniente se ve agravado en el caso del m-MIMO debido al enorme número de antenas. Por ello, la codificación diferencial y la detección no coherente (NC) son una solución alternativa para solventar el problema de m-MIMO en los sistemas coherentes. Esta Tesis se centra en las técnicas de procesado de señal para detección NC junto con m-MIMO, proponiendo nuevos esquemas de constelación y algoritmos de detección NC, donde la información sea transmitida en la diferencia de fase de la señal. Primero, diseñamos nuevas constelaciones para un sistema multi usuario NC en m- MIMO en enlace ascendente (uplink) en canales con desvanecimiento tipo Rayleigh. Estos diseños nos permiten separar las señales de los usuarios en el receptor gracias a la correspondencia unívoca entre la constelación de cada usuario individual y la constelación conjunta recibida en la estación base. Hemos considerado dos enfoques para el diseño en términos de probabilidad de error: cada usuario consigue un rendimiento distinto, mientras que por otro lado, todos los usuarios son capaces de recibir las mismas prestaciones de probabilidad de error. Analizamos el número de antenas necesario para estos diseños y comparamos con el número requerido por otros diseños propuestos en la literatura. Nuestro diseño basado en DPSK requiere un número menor de antenas comparado con los sistemas basados en detección de energía. También comparamos con su homólogo coherente, resultando que NC-m-MIMO basado en DPSK es capaz de superar a los sistemas coherentes con los diseños adecuados. En segundo lugar, para reducir el número de antenas requerido para un rendimiento dado, proponemos incluir un esquema de codificación de canal. Hemos optado por un esquema de modulación codificado por bit entrelazado y decodificación iterativa (BICMID). Hemos empleado la herramienta EXIT chart para el diseño de la codificación de canal, proponiendo un nuevo enfoque para calcular las curvas EXIT de forma NC y basadas en el número de antenas. Los resultados muestran que el número de usuarios servidos por la estación base puede ser incrementado reduciendo un 70% el número de antenas con respecto al caso sin codificación de canal. En particular, para un array de 100 antenas y un diseño que ofrezca iguales prestaciones a todos los usuarios, con un código de tasa 1=2, podemos conseguir la mínima probabilidad de error. En tercer lugar, consideramos escenarios donde el canal tenga una componente predominante de visión directa (LOS) con la estación base modelada mediante un desvanecimiento tipo Rician. Por ejemplo, sistemas inalámbricos de backhaul, entornos rurales o sub urbanos, comunicaciones entre dispositivos (D2D), también cuando nos movemos hacia frecuencias superiores como son en la banda de milimétricas o más recientemente, la banda de terahercios para buscar mayores anchos de banda. Todos estos escenarios están contemplados en el futuro 5G. Los diseños presentados para canales Rayleigh ya no son válidos debido a la componente LOS del canal, por ello presentamos un nuevo diseño de constelación que resuelve el problema de la componente LOS, así como una guía para diseñar nuevas constelaciones. También proponemos un algoritmo asociado al diseñno de la constelación para poder separar a los usuarios en recepción. Además, para contemplar un escenario más realista donde podamos encontrar tanto desvanecimiento Rayleigh como Rice, proponemos agrupar usuarios de ambos grupos, analizando su rendimiento y relación señal a interferencia en la combinación. El adecuado agrupamiento permite unificar el diseño de la constelación para ambos desvanecimientos y por tanto reducir la complejidad en el receptor. También, el número de usuarios multiplicados en la constelación podría ser incrementado, gracias a la mejora en el rendimiento. El cuarto módulo de esta tesis es dedicado a analizar el rendimiento de los diseños propuestos en presencia de canales reales, donde disponemos de variabilidad temporal y en frecuencia. Proponemos usar una métrica que modela las características de la variabilidad temporal y, usando de nuevo la herramienta EXIT, analizamos los sistemas decodificados iterativamente considerando ahora los parámetros prácticos del canal. Este análisis nos permite obtener una estimación de la degradación que sufre el rendimiento del sistema impuesto por canales reales. Los resultados muestran que los sistemas NC-m-MIMO basados en DPSK son muy robustos a la variabilidad temporal por lo que son recomendables para los nuevos escenarios propuestos por el 5G, donde el canal cambia rápidamente. Otra consideración para introducir los sistemas NC con m-MIMO es la problemática de necesitar muchas cadenas de radio frecuencia que llevarían a tamaños de dispositivos enormes. Para reducir este número se propone la modulación espacial. En esta Tesis, estudiamos su uso con los sistemas NC, proponiendo una solución de modulación espacial diferencial para esquemas con múltiples usuarios combinado con NC-m-MIMO. Finalmente, estudiamos la viabilidad de multiplexar usuarios en la constelación frente a usar técnicas clásicas de multiplexación como TDMA. Para caracterizar completamente el rendimiento del sistema, analizamos la tasa de error de bloque (BLER) y el throughput de un sistema NC-m-MIMO. Los resultados muestran una ventaja significativa en cuanto al número de antennas para multiplexar usuarios en la constelación frente al requerido por TDMA. No obstante, en algunos casos, la demodulación de múltiples usuarios en la constelación podría requerir un número de antennas excesivamente grande comparado con la multiplexación en el tiempo. Por ello, es necesario gestionar adecuadamente un balance entre el throughput y el número de antenas para alcanzar un punto operacional óptimo, como se muestra en esta Tesis.Programa Oficial de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Ana Isabel Pérez Neira.- Secretario: Máximo Morales Céspedes.- Vocal: María del Carmen Aguayo Torre

Bit-Interleaved Coded Energy-Based Modulation with Iterative Decoding

This paper develops a low-complexity near-optimal non-coherent receiver for a multi-level energy-based coded modulation system. Inspired by the turbo processing principle, we incorporate the fundamentals of bit-interleaved coded modulation with iterative decoding (BICM-ID) into the proposed receiver design. The resulting system is called bit-interleaved coded energy-based modulation with iterative decoding (BICEM-ID) and its error performance is analytically studied. Specifically, we derive upper bounds on the average pairwise error probability (PEP) of the non-coherent BICEM-ID system in the feedback-free (FF) and error-free feedback (EFF) scenarios. It is revealed that the definition of the nearest neighbors, which is important in the performance analysis in the FF scenario, is very different from that in the coherent BICM-ID counterpart. The analysis also reveals how the mapping from coded bits to energy levels influences the diversity order and coding gain of the BICEM-ID systems. A design criterion for good mappings is then formulated and an algorithm is proposed to find a set of best mappings for BICEM-ID. Finally, simulation results corroborate the main analytical findings

Low-Complexity Joint Channel Estimation and List Decoding of Short Codes

A pilot-assisted transmission (PAT) scheme is proposed for short blocklengths, where the pilots are used only to derive an initial channel estimate for the list construction step. The final decision of the message is obtained by applying a non-coherent decoding metric to the codewords composing the list. This allows one to use very few pilots, thus reducing the channel estimation overhead. The method is applied to an ordered statistics decoder for communication over a Rayleigh block-fading channel. Gains of up to $1.2$ dB as compared to traditional PAT schemes are demonstrated for short codes with QPSK signaling. The approach can be generalized to other list decoders, e.g., to list decoding of polar codes.Comment: Accepted at the 12th International ITG Conference on Systems, Communications and Coding (SCC 2019), Rostock, German

Differential Modulation for Short Packet Transmission in URLLC

One key feature of ultra-reliable low-latency communications (URLLC) in 5G is to support short packet transmission (SPT). However, the pilot overhead in SPT for channel estimation is relatively high, especially in high Doppler environments. In this paper, we advocate the adoption of differential modulation to support ultra-low latency services, which can ease the channel estimation burden and reduce the power and bandwidth overhead incurred in traditional coherent modulation schemes. Specifically, we consider a multi-connectivity (MC) scheme employing differential modulation to enable URLLC services. The popular selection combining and maximal ratio combining schemes are respectively applied to explore the diversity gain in the MC scheme. A first-order autoregressive model is further utilized to characterize the time-varying nature of the channel. Theoretically, the maximum achievable rate and minimum achievable block error rate under ergodic fading channels with PSK inputs and perfect CSI are first derived by using the non-asymptotic information-theoretic bounds. The performance of SPT with differential modulation and MC schemes is then analysed by characterizing the effect of differential modulation and time-varying channels as a reduction in the effective SNR. Simulation results show that differential modulation does offer a significant advantage over the pilot-assisted coherent scheme for SPT, especially in high Doppler environments.Comment: 15 pages, 9 figure

Lens antenna arrays: an efficient framework for sparse-aware large-MIMO communications

The recent increase in the demand for higher data transmission rates in wireless communications has entailed many implementation issues that can only be resolved by going through a full paradigm shift. Making use of the millimetric spectrum bands is a very attractive solution to the shortage of radio resources but, to garner all their potential, new techniques must be developed. Most of them are contained in the Massive Multiple Input Multiple Output (M-MIMO) framework: the idea of using very large antenna arrays for cellular communications. In this thesis, we propose the usage of Lens Antenna Arrays (LAA) to avoid the unbearable power and infrastructure costs posed by traditional M-MIMO architectures. This novel communication system exploits the angular-dependent power focusing capabilities of an electromagnetic lens to discern between waves with different angles of arrival and departure, without explicit signal processing. The work presented in this document motivates the use of LAAs in mmWave communications, studies some of their mathematical properties and proposes their application in noncoherent schemes. Numerical results validate the performance of this novel kind of systems and confirm their strengths in both multi-user and block fading settings. LAAs that use noncoherent methods appear to be very suitable for vehicular communications and densely populated cellular networks.En los últimos tiempos, el incremento en la demanda de mayor velocidad de transmisión de datos en redes de comunicación inalámbricas ha conllevado varios problemas de implementación que solo se podrán resolver a través de un cambio total de paradigma. Utilizar bandas milimétricas del espectro es una solución muy atractiva a la escasez de recursos de radio pero, para poder extraer todo su potencial, es necesario desarrollar nuevas técnicas. La mayor parte de éstas pasa por la infraestructura Massive Multiple Input Multiple Output (M-MIMO): la idea de usar matrices de antenas muy grandes para comunicaciones celulares. En esta tesis, proponemos el uso de matrices de antenas con lente, o Lens Antenna Arrays (LAA), para evitar los inasumibles costes energéticos y de instalación propios de las arquitecturas M-MIMO tradicionales. Este novedoso sistema de comunicaciones explota las capacidades de concentración de energía con dependencia angular de las lentes electromagnéticas para distinguir entre ondas con distintas direcciones de llegada y de salida, sin procesado de la señal explícito. El trabajo presentado en este documento motiva el uso de los LAAs en comunicaciones en bandas milimétricas (mmWave), estudia varias propiedades matemáticas y propone su aplicación en esquemas no coherentes. Resultados numéricos validan su ejecución y confirman sus fortalezas en entornos multiusuario y con desvanecimiento en bloque. Los LAAs que utilizan métodos no coherentes parecen ser idóneos para comunicaciones vehiculares y para redes celulares altamente pobladas.En els darrers temps, l'increment en la demanda de major velocitat de transmissió de dades en xarxes de comunicació inalàmbriques ha comportat diversos problemes d'implementació que tan sols es podran resoldre a través d'un canvi total de paradigma. Utilitzar les bandes mil·limètriques de l'espectre és una solució molt atractiva a l'escassetat de recursos de ràdio però, per tal d'extreure'n tot el seu potencial, és necessari desenvolupar noves tècniques. La majoria d'aquestes passa per la infraestructura Massive Multiple Input Multiple Output (M-MIMO): la idea d'utilitzar matrius d'antenes molt grans per a comunicacions cel·lulars. En aquesta tesi, proposem l'ús de matrius d'antenes amb lent, o Lens Antenna Arrays (LAA), per tal d'evitar els inassumibles costos energètics i d'instal·lació propis d'arquitectures M-MIMO tradicionals. Aquest innovador sistema de comunicacions explota les capacitats de concentració d'energia amb dependència angular de les lents electromagnètiques per tal de distingir entre ones amb diferents direccions d'arribada i de sortida, sense processament de senyal explícit. El treball presentat en aquest document motiva l'ús dels LAAs per comunicacions en bandes mil·limètriques (mmWave), n'estudia diverses propietats matemàtiques i proposa la seva aplicació en esquemes no coherents. Resultats numèrics en validen l'execució i confirmen les seves fortaleses en entorns multi-usuari i amb esvaïment en bloc. Els LAAs que utilitzen mètodes no coherents semblen ser idonis per a comunicacions vehiculars i per a xarxes cel·lulars altament poblades

On the Impact of Phase Noise in Communication Systems –- Performance Analysis and Algorithms

The mobile industry is preparing to scale up the network capacity by a factor of 1000x in order to cope with the staggering growth in mobile traffic. As a consequence, there is a tremendous pressure on the network infrastructure, where more cost-effective, flexible, high speed connectivity solutions are being sought for. In this regard, massive multiple-input multiple-output (MIMO) systems, and millimeter-wave communication systems are new physical layer technologies, which promise to facilitate the 1000 fold increase in network capacity. However, these technologies are extremely prone to hardware impairments like phase noise caused by noisy oscillators. Furthermore, wireless backhaul networks are an effective solution to transport data by using high-order signal constellations, which are also susceptible to phase noise impairments. Analyzing the performance of wireless communication systems impaired by oscillator phase noise, and designing systems to operate efficiently in strong phase noise conditions are critical problems in communication theory. The criticality of these problems is accentuated with the growing interest in new physical layer technologies, and the deployment of wireless backhaul networks. This forms the main motivation for this thesis where we analyze the impact of phase noise on the system performance, and we also design algorithms in order to mitigate phase noise and its effects. First, we address the problem of maximum a posteriori (MAP) detection of data in the presence of strong phase noise in single-antenna systems. This is achieved by designing a low-complexity joint phase-estimator data-detector. We show that the proposed method outperforms existing detectors, especially when high order signal constellations are used. Then, in order to further improve system performance, we consider the problem of optimizing signal constellations for transmission over channels impaired by phase noise. Specifically, we design signal constellations such that the error rate performance of the system is minimized, and the information rate of the system is maximized. We observe that these optimized constellations significantly improve the system performance, when compared to conventional constellations, and those proposed in the literature. Next, we derive the MAP symbol detector for a MIMO system where each antenna at the transceiver has its own oscillator. We propose three suboptimal, low-complexity algorithms for approximately implementing the MAP symbol detector, which involve joint phase noise estimation and data detection. We observe that the proposed techniques significantly outperform the other algorithms in prior works. Finally, we study the impact of phase noise on the performance of a massive MIMO system, where we analyze both uplink and downlink performances. Based on rigorous analyses of the achievable rates, we provide interesting insights for the following question: how should oscillators be connected to the antennas at a base station, which employs a large number of antennas