# Channel Estimation and Data Detection Using Machine Learning for MIMO 5G Communication Systems in Fading Channel

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Multiuser MIMO-OFDM System

#### 2.1.1. System Model

_{R}receiver antennae with N

_{I}users. Every antenna has a single omni-directional antenna. The number of antennae L

_{A}used is greater than the number of users I. The signal along with the additive white Gaussian noise (AWGN) and MAI are considered as the inputs.

_{2}M bits. After this, the blocks are modulated as M-ary quadrature amplitude modulation (M-QAM) symbols.

#### 2.1.2. Model for the Optimization Problem

#### 2.2. Proposed Joint CE and Turbo MUD

_{T}transmitter antenna. The signal is converted into blocks before transmitting the data, which are transmitted along with the CP. At the transmitter and receiver sides, the inverse FFT and FFT are used for data transmission. First, the input data streams are transmitted to the turbo encoder at the transmitter side to obtain the encoded signal and this encoded signal is conveyed in blocks. After this, the encoded signal is fed to the interleaver. Following this, the output from the interleaver is given to the 16-QAM modulator block to produce symbol blocks. We obtain the frequency domain symbol vector after N-point DFT operation. Furthermore, the subcarrier mapping, IFFT and cyclic prefix (CP) operations are conducted for the data symbol vector for all subcarriers. The same process is repeated at the recipient side. MAI can reduce the performance of MIMO-OFDM systems. The detailed architecture is illustrated in Figure 1.

#### 2.2.1. Sparse Based k-NN for Active User Detection

_{1}, I

_{2}, I

_{3}, …, I

_{p}) where p is the user dimensionality of the input space. Each input variable can be considered as a dimension of a p-dimensional input space. The complete set of received signal bits is simply stored in the “training phase”.

_{R}) between the two vectors I and Q

_{R}is defined as their usual vector distance in Euclidean units:

#### 2.2.2. Cat Swarm Optimization (CSO) Based Channel Estimation (CE)

Algorithm 1: Pseudo code for the CSO based optimal pilot pattern for reducing the largest element in mutual coherence. | |

Initialization. Let different parameters for the population size be Ps = 100, the length of all the individuals is Len = P − 1 and the maximum generation is Mg. Create the initial population randomly Φi, where i = 1, 2, … Ps. After this, compute the fitness for the initial population individually. | |

1: Produce N-cats, which represents pilot symbols. | |

2: Cats have M-dimensional space and arbitrarily gives a range of values for the maximum velocity of each cat. | |

3: By applying the position of cats in the fitness function, evaluate the fitness value for each cat. It represents the finest position of the cat (xbest) by calculating the mutual coherence of each pilot sequence. | |

4: Move the cat according to their modes, apply the process of the seeking mode if the cat is in seeking mode. Otherwise, use the tracing mode process. | |

5: Activate the tracing mode process again by selecting the number of cats and according to the MR, the seeking mode can be applied to other cats. | |

6: To terminate the program, check if the termination condition is satisfied. Otherwise, repeat step 3 to step 6. | |

Output: The optimal pilot pattern Ψ. |

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Performance of symbol error rate (SER) vs. signal-to-noise ratio (SNR) (dB) with 20 users.

Notation | Description |
---|---|

N_{R} | Number of receiver antennae |

L_{A} | Number of antennae |

${B}_{{q}_{x}}$ | Input data stream |

${q}_{x}$ | Transmitting antenna |

${B}_{{q}_{x}}^{T}$ a | The bit stream after the forward error correction encoder |

${B}_{{q}_{x}}^{I}$ | Output bit stream from the interleaver I |

${\tilde{X}}_{{q}_{x}}$ | Modulated data |

${X}_{{q}_{x}}[n,\text{}k]$ | Time domain (TD)-modulated signal |

n | Orthogonal frequency-division multiplexing (OFDM) symbol index |

K | Number of subcarriers |

${B}_{{q}_{x}}(n)$ | Transmitted user data |

${K}_{cp}$ | Cyclic prefix (CP) samples |

${L}_{CIR}$ | Length of the channel impulse responses |

${Y}^{j}[n,\text{}k]$ | Received signal for k-th subcarrier of the n-th orthogonal frequency-division multiplexing (OFDM) symbol |

${y}_{{q}_{r}}$ | Received signals |

${\tilde{\Gamma}}_{{q}_{x}}$ | Received pilot subcarriers |

${H}_{{q}_{x}}$ | Frequency-Domain Channel Transfer Functions |

${X}_{{q}_{x}}[n,k]$ | Frequency-domain channel transfer function (FD-CHTF) coefficient of the link between the x-th user and the q-th receiver antenna in the k-th subcarrier of the n-th orthogonal frequency-division multiplexing symbol |

${W}_{q}[n,k]$ | Frequency-domain additive white Gaussian noise (AWGN) |

${H}_{q}^{i}[n,k]$ | K-sparse channel impulse vector |

${Y}_{q}[n,k]$ | q-th receiver antenna element in the k-th subcarrier of the n-th orthogonal frequency-division multiplexing symbol |

$\mu \left\{{\widehat{h}}_{{q}_{x}}\right\}$ | Mutual Coherence |

${\widehat{h}}_{{q}_{x}}$ | Overall system’s Channel Impulse Response vector |

${H}_{{q}_{r}}^{i}[n]$ | Impulse vector for the K-sparse channel |

${Y}_{{q}_{r}}^{}[n]$ | Subcarrier-related signals |

${X}_{{q}_{x}}^{}[n]$ | Diagonal elements |

${F}_{{q}_{x}}$ | Partial FFT matrix |

${I}_{{q}_{x},\text{}{q}_{r}}$ | Impulse vector of K-sparse channel |

${K}_{qx}$ | Subcarriers position |

Parameters | Values |
---|---|

Users | 20, 100, 500 |

No. of cell | 7 |

No. of users per cell | 10 |

Number of transmitters | 4 |

Total pilots to each transmitter | 24 |

Cell radius | 1000 m |

Guard interval | ¼ |

Total receivers | 4 |

Number of Subcarriers N | 32, 128, 512 |

Cyclic prefix | 16 |

Signal Constellation | 16 QAM modulation |

Path loss exponent | 4 |

Bandwidth | 5 MHz |

Channel | Frequency selective Rayleigh fading |

FFT size | 2048 |

Operations (Per Iteration) | First Stage | Second Stage | Final Stage |
---|---|---|---|

Sparse k-NN algorithm | 0 | N–N_{p} | N–N_{p} |

CSO optimization algorithm | N_{p} | 0 | 0 |

Channel estimation | 0 | 0 | O(n^{2}) |

Total complexity for each stage | O(n) | O(n) | O(n^{2}) |

Methods | Complexity | Description of Notations |
---|---|---|

EM | $\mathrm{O}(KL-{N}_{p})$ | K-frequency subcarriers, L-OFDM symbols, ${N}_{p}$-pilot symbols |

CP | $\mathrm{O}(MTK)$ | M-RF chain sub frames, T-time frames, K-subcarriers |

JCCAE (Joint Channel and Clipping Amplitude Estimation) | $\mathrm{O}({N}^{3}+{N}^{2}+{N}^{2})$ | N-symbols |

Four Bayesian inference methods | $\mathrm{O}(N{K}^{2})$ | N-received symbols, K-transmitted symbols |

Proposed | $\mathrm{O}({n}^{2})$ | n-symbols |

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**MDPI and ACS Style**

Motade, S.N.; Kulkarni, A.V.
Channel Estimation and Data Detection Using Machine Learning for MIMO 5G Communication Systems in Fading Channel. *Technologies* **2018**, *6*, 72.
https://doi.org/10.3390/technologies6030072

**AMA Style**

Motade SN, Kulkarni AV.
Channel Estimation and Data Detection Using Machine Learning for MIMO 5G Communication Systems in Fading Channel. *Technologies*. 2018; 6(3):72.
https://doi.org/10.3390/technologies6030072

**Chicago/Turabian Style**

Motade, Sumitra N., and Anju V. Kulkarni.
2018. "Channel Estimation and Data Detection Using Machine Learning for MIMO 5G Communication Systems in Fading Channel" *Technologies* 6, no. 3: 72.
https://doi.org/10.3390/technologies6030072