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## Maximum-Likelihood detection

At the receiver side, the mission is to detect the transmitted vector from the received signal. The optimal detector which minimizes the probability of detection error is ruled by the ML criterion which minimizes the Euclidean distance between the received vector y and the mixed vector Hx such that x belongs to the set « N. The ML solution reads then as: ˆxML = arg min x2!N ky −Hxk22 (2.4) To obtain the exact solution for the ML optimization criterion, we need an ex- haustive search which requires exponential complexity proportional to N. Therefore, it can only be implemented for small values of N. When N is large the computation of the ML solution becomes infeasible due to the high complexity. Knowing the exact ML solution is desired in order to make it a benchmark helping designers to assess how proposed detectors perform compared to the optimal one. An alternative is the sphere decoding, but its complexity is also exponential especially in low and medium SNR values when the number of antennas N is high. To overcome thisproblem, designers choose to compare their algorithms taking the case of non-faded SISO AWGN for which a lower bound of ML performance can be computed.

### Successive interference cancellation

Successive interference cancellation-based detectors [11] are considered as non-linear detectors. Symbols are estimated one after the other and their contribution to the interference is canceled immediately. The principle is to first compute the linear detection matrix and the post SINR. Then, sources are sorted according to the descending order arrangement of SINR. Sources with highest SINR are detected first to reduce the error propagation phenomenon.

An early test of MIMO wireless communication architecture using successive interference cancellation technique known as vertical BLAST (Bell Laboratories Layered Space-Time) or V-BLAST was implemented in real-time in the Bell Labs laboratory [1] in 1990s. The detection algorithm is now referred to as ZF-successive interference cancellation (ZF-SIC). The V-BLAST detection is detailed in following Algorithm 1.

#### Lattice Reduction-aided linear detection

Based on Lattice Reduction (LR)-techniques [12], we can derive new versions of linear detectors while preserving low complexity. The idea here is to transform the system model (2.1) into an equivalent system obtained by applying LR techniques. It is given by: y = ˜H ˜x+!. (2.28) ˜H is a transformed channel matrix designed to be better conditioned (orthogonality) than the original channel matrix H. The vector ˜x is a transformation of the original transmitted vector x using an unimodular matrix T . The choice of ˜H and T from H can be done based on a low-complexity iterative algorithm like the Seysen’s Algorithm (SA) detailed in [19].

The columns of H can be interpreted as components of a lattice basis. Considering the transformed matrix ˜H = HT, it generates the same lattice as H if and only if T is unimodular. The LR-technique aims to get the transformed matrix ˜H better conditioned than the original one. The matrix ˜H defines a new basis with vectors of shortest length being the more orthogonal possible. As the unimodular matrix has unitary determinant its inverse always exists. So, defining ˜H = HT and ˜x = T −1x, the system model can be written as follows: y = Hx+!.

**Comparison of selected local search algorithms**

The LAS is a local search-based algorithm where the definition of the neighbor space is static. The first detected minimum is declared as the final solution. To enhance its performance, a multistage LAS is proposed where an escape strategy is proposed and the algorithm uses more than one coordinate for the neighborhood definition. It considers all vectors that differ in more than one element of the found solution to form the neighbor space and a better local minimum can thus be found. However, the RTS algorithm uses a dynamic neighborhood definition where some candidate vectors are removed in order to avoid the cycling problem while searching for a better solution than the previous one. Compared to LAS-based algorithms, it represents a significant performance improvement thanks to the implemented escape strategy which accepts moves to neighbors even if they imply worse performance than the current solution.

**Table of contents :**

List of Figures

List of Tables

**1 Introduction **

1.1 Introduction

1.2 MIMO communication

1.2.1 Point-to-point MIMO communication

1.2.2 Multiuser MIMO communication

1.2.3 Advantages of MIMO over SISO communication

1.3 Large-scale MIMO systems

1.3.1 Description

1.3.2 Motivations

1.3.3 Challenges

1.4 Scope of the thesis

1.5 Outline of the thesis

**2 State-of-the-art **

2.1 Introduction

2.2 System model

2.3 Maximum-Likelihood detection

2.3.1 Sphere decoding

2.4 Linear detection

2.4.1 Matched filter (MF) detection

2.4.2 Zero forcing (ZF) detection

2.4.3 Minimum-mean square error (MMSE) detection

2.5 Successive interference cancellation

2.6 Lattice Reduction-aided linear detection

2.7 Local search-based detection

2.7.1 Likelihood ascent search (LAS)

2.7.2 Reactive tabu search (RTS)

2.7.3 Comparison of selected local search algorithms

2.8 Conclusion

**3 Simplicity-baseddetectionfor large-scaleMIMOsystems **

3.1 Introduction

3.2 Overview of CS recovery and detection schemes and first tracks

3.2.1 Noise-free large-scale MIMO systems

3.2.2 Noisy large-scale MIMO systems

3.3 Simplicity property exploitation to solve the noise-free recovery

3.3.1 Proposed method definition and theoretical study

3.3.2 Complexity Analysis

3.3.3 Simulation results

3.4 Application of the simplicity principle to noisy large-scale MIMO systems

3.4.1 Proposed method definition and theoretical analysis

3.4.2 Complexity Analysis

3.4.3 Simulation results

3.5 Conclusion

**4 Iterative receivers for large-scale MIMO systems **

4.1 Introduction

4.2 Iterative Detection Based on the Shadow area principle

4.2.1 Shadow area and detection reliability

4.2.2 Simulation results

4.2.3 Complexity Analysis

4.3 Proposed turbo detection scheme

4.3.1 Iterative receiver principle and notations

4.3.2 FAS Maximum Likelihood like iterative receiver (FAS-ML)

4.3.3 FAS Mean Absolute Error-based iterative receiver (FAS-MAE)

4.3.4 Simulation results

4.4 Conclusion

**5 Channel estimation in large-scale MIMO systems **

5.1 Introduction

5.2 Overview of Imperfect CSI effects

5.3 Overview of channel estimation techniques

5.3.1 System model

5.3.2 ML estimators

5.3.3 EM algorithm

5.3.4 Cramer-Rao bound of semi-blind channel estimation

5.4 Semi-blind uplink channel estimation for large-scale MIMO systems .

5.4.1 Proposed Semi-blind uplink channel estimation algorithms

5.4.2 Simulation results

5.4.3 Complexity analysis

5.5 Channel estimation for large-scale FEC-coded MIMO systems

5.5.1 Channel estimation algorithm combined with FAS-MAE

5.5.2 Simulation results

5.6 Conclusion

**6 Conclusions & Perspectives **

6.1 Conclusions

6.2 Perspectives

**7 Appendix **

7.1 Generic random matrix

7.2 Proof of Proposition 4.2.1

7.3 Symbol error probability upper-bound

7.4 Proof of equations (4.5) and (4.6) of Theorem 4.2.1

7.4.1 Proof the expression of Z⌘ given by equation (4.5)

7.4.2 Proof the expression of Y⌘ given by equation (4.6)

**Bibliography**