The literature on compressive parameter estimation has been mostly focused on the use of sparsity dictionaries that encode a discretized sampling of the parameter space; these dictionaries, however, suffer from coherence issues that must be controlled for successful estimation. To bypass such issues with discretization, we propose the use of statistical parameter estimation methods within the Approximate Message Passing (AMP) algorithm for signal recovery. Our method leverages the recently proposed use of custom denoisers in place of the usual thresholding steps (which act as denoisers for sparse signals) in AMP. We introduce the design of analog denoisers that are based on statistical parameter estimation algorithms, and we focus on two commonly used examples: frequency estimation and bearing estimation, coupled with the Root MUSIC estimation algorithm. We first analyze the performance of the proposed analog denoiser for signal recovery, and then link the performance in signal estimation to that of parameter estimation. Numerical experiments show significant improvements in estimation performance versus previously proposed approaches for compressive parameter estimation.

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The Fifth Generation (5G) mobile communication system is the latest technology in wireless communications. This technique brings several advantages, in particular by using multiple receiver antennas that serve multiple transmitters. This configuration used in 5G is called Massive Multiple Input Multiple Output (MIMO), and it increases link reliability and information throughput. However, MIMO systems face two challenges at link layer: channel estimation and MIMO detection. In this work, the focus is only on the MIMO detection problem. It consists in retrieving the original messages, sent by the transmitters, at the receiver side when the received message is a noisy signal. The optimal technique to solve the problem is called Maximum Likelihood (ML), but it does not scale and therefore with MIMO systems it cannot be used. Several sub-optimal techniques have been tested during years in order to solve MIMO detection problem, trying to balance the complexity-performance trade-off. In recent years, Approximate Message Passing (AMP) based techniques brought interesting results. Moreover, deep learning (DL) is spreading in several and different fields, and also in MIMO detection, it has been tested with promising results. A neural network called MMNet brought the most interesting results, but new techniques have been developed. These new techniques, despite they are promising, have not been compared with MMNet. In this thesis, two new techniques AMP and DL based, called Ortoghonal AMP Network Second (OAMP-Net2) and Learnable Vector AMP (LVAMP), have been tested and compared with the state of art. The aim of the thesis is to discover if one or both the techniques can provide better results than MMNet, in order to discover a valid alternative solution while dealing with MIMO detection problem. OAMP-Net2 and LVAMP have been developed and tested on different channel models (i.i.d. Gaussian and Kronecker) and on MIMO systems of different sizes (small and medium-large). OAMP-Net2 revealed to be a consistent technique that can be used in solving MIMO detection problem. It provides interesting results on both i.i.d Gaussian and Kronecker channel models and with different sizes matrices. Moreover, OAMP-Net2 has good adaptability, in fact it provides good results on Kronecker channel models also when it is trained with i.i.d. Gaussian matrices. LVAMP instead has performances that are similar to MMSE, but with a lower complexity. It adapts well to complex channels such as OAMP-Net2. / Femte generationens (5G) mobila kommunikationssystem är den senaste tekniken inom trådlös kommunikation. Denna teknik ger flera fördelar, i synnerhet genom att använda flera mottagarantenner som betjänar flera sändare. Denna konfiguration som används i 5G kallas Massive Multiple Input Multiple Output (MIMO), och den ökar länktillförlitligheten och informationsgenomströmningen. MIMO-system står dock inför två utmaningar i länkskiktet: kanaluppskattning och MIMO-detektering. I detta arbete ligger fokus endast på MIMO-detekteringsproblemet. Den består i att hämta de ursprungliga meddelandena, skickade av sändarna, på mottagarsidan när det mottagna meddelandet är en brusig signal. Den optimala tekniken för att lösa problemet kallas Maximum Likelihood (ML), men den skalas inte och därför kan den inte användas med MIMO-system. Flera suboptimala tekniker har testats under flera år för att lösa MIMO-detekteringsproblem och försöka balansera komplexitet-prestanda-avvägningen. Under de senaste åren har Approximate Message Passing (AMP)-baserade tekniker gett intressanta resultat. Dessutom sprids djupinlärning (DL) inom flera och olika områden, och även inom MIMO-detektering har det testats med lovande resultat. Ett neuralt nätverk kallat MMNet gav de mest intressanta resultaten, men nya tekniker har utvecklats. Dessa nya tekniker, trots att de är lovande, har inte jämförts med MMNet. I detta examensarbete har två nya tekniker AMP- och DL-baserade, kallade Ortoghonal AMP Network Second (OAMP-Net2) och Learnable Vector AMP (LVAMP), testats och jämförts med den senaste tekniken. Syftet med avhandlingen är att ta reda på om en eller båda teknikerna kan ge bättre resultat än MMNet, för att upptäcka en giltig alternativ lösning samtidigt som man hanterar MIMO-detekteringsproblem. OAMP-Net2 och LVAMP har utvecklats och testats på olika kanalmodeller (i.i.d. Gaussian och Kronecker) och på MIMO-system av olika storlekar (small och medium-large).OAMP-Net2 visade sig vara en konsekvent teknik som kan användas för att lösa MIMO-detekteringsproblem. Det ger riktigt intressanta resultat på både i.i.d Gaussian och Kronecker kanalmodeller och med matriser i olika storlekar. Dessutom har OAMP-Net2 god anpassningsförmåga, faktiskt ger den bra resultat på Kronecker kanalmodeller även när den tränas med i.i.d. Gaussiska matriser. LVAMP har istället prestanda som liknar MMSE, men med lägre komplexitet. Den anpassar sig väl till komplexa kanaler somOAMPNet2.

In this dissertation, two classes of distributed algorithms are developed for sparse signal recovery in large sensor networks. All the proposed approaches consist of local computation (LC) and global computation (GC) steps carried out by a group of distributed local sensors, and do not require the local sensors to know the global sensing matrix. These algorithms are based on the original approximate message passing (AMP) and iterative hard thresholding (IHT) algorithms in the area of compressed sensing (CS), also known as sparse signal recovery. For distributed AMP (DiAMP), we develop a communication-efficient algorithm GCAMP. Numerical results demonstrate that it outperforms the modified thresholding algorithm (MTA), another popular GC algorithm for Top-K query from distributed large databases. For distributed IHT (DIHT), there is a step size $\mu$ which depends on the $\ell_2$ norm of the global sensing matrix A. The exact computation of $\|A\|_2$ is non-separable. We propose a new method, based on the random matrix theory (RMT), to give a very tight statistical upper bound of $\|A\|_2$, and the calculation of that upper bound is separable without any communication cost. In the GC step of DIHT, we develop another algorithm named GC.K, which is also communication-efficient and outperforms MTA. Then, by adjusting the metric of communication cost, which enables transmission of quantized data, and taking advantage of the correlation of data in adjacent iterations, we develop quantized adaptive GCAMP (Q-A-GCAMP) and quantized adaptive GC.K (Q-A-GC.K) algorithms, leading to a significant improvement on communication savings. Furthermore, we prove that state evolution (SE), a fundamental property of AMP that in high dimensionality limit, the output data are asymptotically Gaussian regardless of the distribution of input data, also holds for DiAMP. In addition, compared with the most recent theoretical results that SE holds for sensing matrices with independent subgaussian entries, we prove that the universality of SE can be extended to far more general sensing matrices. These two theoretical results provide strong guarantee of AMP's performance, and greatly broaden its potential applications.

In many modern wireless and wireline communication networks, the interference power from other communication and non-communication devices is increasingly dominating the background noise power, leading to interference limited communication systems. Conventional communication systems have been designed under the assumption that noise in the system can be modeled as additive white Gaussian noise (AWGN). While appropriate for thermal noise, the AWGN model does not always capture the interference statistics in modern communication systems. Interference from uncoordinated users and sources is particularly harmful to communication performance because it cannot be mitigated by current interference management techniques. Based on previous statistical-physical models for uncoordinated wireless interference, this dissertation derives similar models for uncoordinated interference in PLC networks. The dissertation then extends these models for wireless and powerline interference to include temporal dependence among amplitude samples. The extensions are validated with measured data. The rest of this dissertation utilizes the proposed models to design receivers in interference limited environments. Prior designs generally adopt suboptimal approaches and often ignore the problem of channel estimation which limits their applicability in practical systems. This dissertation uses the graphical model representation of the OFDM system to propose low-complexity message passing OFDM receivers that leverage recent results in soft-input soft-output decoding, approximate message passing, and sparse signal recovery for joint channel/interference estimation and data decoding. The resulting receivers provide huge improvements in communication performance (more than 10dB) over the conventional receivers at a comparable computational complexity. Finally, this dissertation addresses the design of robust receivers that can be deployed in rapidly varying environments where the interference statistics are constantly changing. / text

Sparse regression codes (SPARCs) are a recently introduced coding scheme for the additive white Gaussian noise channel, for which polynomial time decoding algorithms have been proposed which provably achieve the Shannon channel capacity. One such algorithm is the approximate message passing (AMP) decoder. However, directly implementing these decoders does not yield good empirical performance at practical block lengths. This thesis develops techniques for improving both the error rate performance, and the time and memory complexity, of the AMP decoder. It focuses on practical and efficient implementations for both single- and multi-user scenarios. A key design parameter for SPARCs is the power allocation, which is a vector of coefficients which determines how codewords are constructed. In this thesis, novel power allocation schemes are proposed which result in several orders of magnitude improvement to error rate compared to previous designs. Further improvements to error rate come from investigating the role of other SPARC construction parameters, and from performing an online estimation of a key AMP parameter instead of using a pre-computed value. Another significant improvement to error rates comes from a novel three-stage decoder which combines SPARCs with an outer code based on low-density parity-check codes. This construction protects only vulnerable sections of the SPARC codeword with the outer code, minimising the impact to the code rate. The combination provides a sharp waterfall in bit error rates and very low overall codeword error rates. Two changes to the basic SPARC structure are proposed to reduce computational and memory complexity. First, the design matrix is replaced with an efficient in-place transform based on Hadamard matrices, which dramatically reduces the overall decoder time and memory complexity with no impact on error rate. Second, an alternative SPARC design is developed, called Modulated SPARCs. These are shown to also achieve the Shannon channel capacity, while obtaining similar empirical error rates to the original SPARC, and permitting a further reduction in time and memory complexity. Finally, SPARCs are implemented for the broadcast and multiple access channels, and for the multiple description and Wyner-Ziv source coding models. Designs for appropriate power allocations and decoding strategies are proposed and are found to give good empirical results, demonstrating that SPARCs are also well suited to these multi-user settings.

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