# Multiple-Input transmit and receive antennas that can be

Multiple-Input and Multiple-Output (MIMO) system technology is becoming emerging technology for wireless communication networks and is included into wireless broadband standards like LTE and Wi-Fi 1. The large number of antennas at the transmitter and receiver is provided with more the possible signal paths and yield better performance in terms of data rate and reliability 2. Large Scale MIMO system uses large number of transmit and receive antennas that can be operated fully coherently and adaptively 3. The advantages of the massive MIMO include low power, latency reduction, simplified Media Access Control (MAC), and robustness 4. Several detection algorithms 5,6 are introduced in the literature to address this problem. Except a few algorithms 7,8 all others belong to a category of neighborhood search algorithms that are classified into Likelihood Ascent Search (LAS) and Reactive Tabu Search (RTS) algorithms.

In 9, the lattice reduction aided detection scheme uses precoding technique that gives better simulation results scheme for 2×2 channels. In 10, the complex Lenstra-Lenstra-Lovasz (LLL) algorithm is introduced to the channel matrix which defines the basis of a complex lattice. In 11, proposed an efficient method to generate the correlation matrices for clustered channel models which uses an array approximation to avoid numerical integrals and provides a closed form expression for the correlation coefficients with the assumption of Laplacian Angle Distribution (LAD). In 12, presented a low complexity detector in which uncoded near exponential diversity performance is achieved for hundreds of antennas.

In 13, single user beam forming and precoding methods are considered in millimeter (mm) wave systems with large arrays. In this system, the structure of mm wave channels is exploited to formulate the precoder design to solve constrained least squares problem. In 14, a low complexity algorithm is presented to detect the signals based on the LAS algorithm. In 15, a low complexity algorithm for large MIMO detection was introduced which is based on a layered local neighborhood search to achieve lower bound on the ML bit error performance. In 16, Single bit quantization technique is introduced for the Ultra Wide Band (UWB) impulse radio receiver.

1. SYSTEM MODEL

A MIMO system which uses number of transmitting antennas and number of receive antennas with. The system input and output relationship can be mathematically modeled as

(1)

where is received signal vector and represents the data received at receive antenna. is transmitted signal vector. denotes the data transmitted through the antenna and is a set of M complex symbols such as square M-QAM constellation. represents the channel matrix and denotes the i.i.d additive white Gaussian noise (AWGN) vector. This complex model can be formulated as

(2)

where Y=is () real received vector.is () real transmit vector. represents () real equivalent transmit vector.denotes equivalent channel matrix as

(3)

At the receiver side, the actual transmit time vector among all possible transmit vectors which is closest to the received signal vector to be found for the given channel matrix . This can be mathematically stated as,

(4)

The equation (4) well known as ML detection. This detection scheme cannot be applied practically for small number of transmit and receive antennas since its computational complexity is exponential in nature. In large scale MIMO, for up to hundred of antenna pairs, several existing algorithms have been suggested in the literature. These algorithms are initialized with a initial solution vector and search for the best solution in the neighborhood and proceed iteratively until there is no further reduction. The neighboring vector can be stated mathematically as

= (5)

Where =1,2,3,…., j=1,2,…. and =1,2,.., and represents the element of neighbor of .

PRUNING OF SIGNALS BASED ON CROSS CORRELATION

Signal modulation techniques can be used to find the real transmitted signals from the received signals among the various received signal vector coming from the multiple antennas. It consumes more time to find the ML vectors from the multiple signal vectors received. Thus the performance would be degraded in the Massive MIMO system. To improve the performance of the massive MIMO system, we introduce the cross correlation based pruning technique which attempts to find the similar signal vectors which is similar based on more signal components. The cross correlation between two real signal vectors can be defined as

(6)

3. MODIFIED B&B ALGORITHM AND BACK JUMPING

The Branch and Bound (B&B) algorithm is a depth first search algorithm using chronological backtracking. The algorithm will generate sub-trees that are identical to previously explored sub-trees when using chronological backtracking. It contributes inefficiency of the search. Whenever B&B algorithm discovers a dead end, it will backtrack. The back tracking process can be changed into back jumping with a few alterations. We introduce novel modified algorithm of B&B with back jumping called as modified B&B. It has an array that stores the latest variable in the ordering list that conflict with the current value. This provides better performance for the different QAM modulation techniques compared to the existing detection methods.

4.1 Modified B&B Algorithm:

4. SIMULATION RESULTS

The performance of PRUN-MLD-LCDA receiver for massive MIMO system is assessed through the Monte-Carlo simulations using Matlab. The BER analysis of proposed and existing receivers and their simulation results are discussed as follows. The BER performance of PRUN-MLD-LCDA, modified B&B, ZFML, RNS and QP detector are obtained for various transmit and receive antenna configurations with M-QAM modulation by using Rayleigh fading channels. The BER performance is plotted at an average of SNR in db. Fig.1 shows the performance of BER of PRUN-MLD-LCDA, modified B&B, ZFML, RNS and QP detector receivers using 16-QAM modulation with ==32. From the fig.1 it shows that the proposed research method implemented in the 16-QAM leads to provide better BER performance than the existing research methodologies Fig.2 shows the performance of BER of PRUN-MLD-LCDA, modified B&B, ZFML, RNS and QP detector receivers using 32-QAM modulation with ==32. Fig.3 shows the performance of BER of PRUN-MLD-LCDA, modified B&B, ZFML, RNS and QP detector receivers using 64-QAM modulation with ==32. From the simulation results, it is observed that BER performance of PRUN-MLD-LCDA provides optimum results for large antennas at both base station and user terminal than the existing detections algorithms.

Figure.1 BER Performance Comparison for ==32 with 16-QAM

Figure.2 BER Performance Comparison for ==32 with 32-QAM

Figure.3 BER Performance Comparison for ==32 with 64-QAM

Message size plays a major role in the reconstruction of signal where the large messages that are transmitted would increase the complexity. Thus the proposed method must be capable of working efficiently even in case of increased message size. The error rate effect of the different modulation techniques namely 16-QAM and 64-QAM are shown in fig.4 and fig.5 for the varying message sizes. The comparison results show that the proposed method provides better result than the existing methods for the different QAM modulation techniques.

Figure.4 BER Performance Comparison of Varying Message Size with 16-QAM

Figure.5 BER Performance Comparison of Varying Message Size with 64-QAM

5. CONCLUSION

The novel algorithm namely PRUN-MLD-LCDA which consists of cross correlation based pruning technique and modified branch and bound algorithm is proposed in this research paper. The algorithm includes cross correlation based pruning technique which attempts to find the similar signal which is similar based on more signals and modified B&B provides less error rate performance. The PRUN-MLD-LCDA algorithm is derived and the simulation results carried out using Rayleigh fading channel for the large antennas at both user terminal and base station. The BER characteristics of the proposed and conventional receivers are compared. The overall Simulation results show that PRUN-MLD-LCDA receiver algorithm is superior to other detection algorithms.