MIMO (Multiple Input –Multiple Output) technology is a promising and upcoming technology for the future wireless generation system, as it has high throughput and diversity gain. MIMO makes antennas work smarter by enabling them to combine data streams arriving from different paths and at different times to effectively increase receiver signal-capturing power. MIMO is used in modern wireless standards, including IEEE 802.11, 3GPP LTE, and mobile WiMAX systems. Sphere decoding algorithm is a lattice reduction algorithm introduced for low complexity MIMO detection SD is a powerful and attractive tool to achieve a high performance close to the Maximum Likelihood (ML),Zero Forcing (ZF) but with less complexity. This paper presents a simulation study on the sphere decoding method and compares the performance with other classical MIMO schemes such as VBLAST and Zero forcing receivers. The simulation tool used is MATLAB communication tool box version 7.1. The performance metric considered is Bit Error Rate (BER) and the channel is assumed to be Rayleigh fading. It is inferred that detection is possible with complexity and gives a better result in terms of Bit Error Rate when compare with general sphere decoding and MMSE.

Wireless communication [1] using Multiple-Input Multiple-Output (MIMO) systems enable increased spectral efficiency for a given total transmitted power. MIMO technology enhance capacity and robustness of the link. The multiple antennas employed at either sides can be used to increase data rates through multiplexing or to improve performance through diversity and it can offer high capacity to wireless systems .

The transmitter and receiver are equipped with multiple antenna elements. The transmit stream go through a matrix channel which consists of multiple receive antennas at the receiver. Then the receiver gets the received signal vectors by the multiple receive antennas and decodes the received signal vectors into the original information. Figure 1 shows a basic model of MIMO system model.

Figure 1. MIMO System Model

The above system can be mathematically modeled as,

(1.1)

Where,

Y is the received vector , H is the channel matrix,X is transmitted vector,N is Channel Noise.

The underlying principles of the sphere decoder were originally developed for finding vectors of short length in lattices[5]. The sphere decoder was first applied to the ML detection problem in the early 90's but gained main stream recognition with a later series of papers.

The Sphere Decoding (SD) algorithm was first developed by Pohst in 1981 [7] for computation of minimal-length lattice vectors and later has been modified by Fincke and Pohst [8].

The algorithm has found good applications in many areas with focus on the multiple antenna channel, and the CDMA scenario, and where the sphere decoder [3] is extended to generate soft information required by concatenated coding schemes.

The maximum likelihood decoder for a MIMO receiver operates by comparing the received signal vector with all possible noiseless received signals corresponding to all possible transmitted signals under certain assumptions , this receiver achieves optimal performance in the sense of maximizing the probability of correct data detection.

However, the complexity of this decoder increase exponentially with the number of transmit antennas [2] making it impossible to implement for large array sizes and high order digital modulation schemes. The main idea of the sphere decoder [4] is to reduce the computational complexity of the maximum likelihood detector by only searching over the noiseless received signals that lie within the hyposphere of radius R around the received signal. The basic premise in sphere decoding is rather simple. They attempt to search over only lattice points that lie in a certain sphere of radius R around the given vector X thereby reducing the search space. The closest lattice point inside the sphere will also be the closest lattice point for the whole lattice.

The basic premise of the SD [6] is quite simple: it comes to find the point HX located within a sphere with radius R centered at Y, reducing the search space and therefore the calculations to be performed. The radius R has to be chosen sufficiently large such that the SD algorithm finds at least the ML solution. Selecting R too large, leads to high complexity as a large number of nodes will satisfy the sphere constraint—a too low choice of the radius might in-hibit the decoder to find any solution. This condition is true if and only if

(1.2)

Therefore the radius ,'R' represents a crucial challenge for SD detectors. Where “Y” is received vector and “X” is transmitted vector.

Figure 2 shows the sphere with Radius R . If the radius R is too large, too many points will be obtained and the search remains exponential in size. If radius is too small, no points will be inside the sphere. The covering radius of the lattice, defined to be the smallest radius of the sphere centered at the lattice points that cover the entire space. This is clear that the smallest radius guarantees the existence of a point inside the sphere for any vector X. To show that the lattice points are inside the sphere, it requires testing the distance of each lattice point from X to determine whether it is less than R, then there is no point in sphere decoding search should be exhaustive.

Figure 2 Sphere with radius R

The basic flow diagram is as shown in Figure 3. Choose radius R of greater size, search space remains large in which many points lies within sphere. Next, choose the distance of the lattice point (d)>>R i.e. no points should be within sphere. Next determine the minimum distance value u0 and eliminate higher values.Based on the minimum distance obtain the final solution.

Figure 3. Flowchart for complex Sphere Decoding

Figure 4 shows the performance of 'm 'transmitting and 'n' receiving antenna namely 4x4,4x8 4x16, 4x32 MIMO receiver configuration using BPSK modulation scheme under ,CSD,SD,MMSE techniques is considered. From The Simulation results it is inferred that CSD out performs the MMSE and Ordinary SD scheme. The channel taken is a rayleigh channel model. It is observed that CSD gives a better Bit Error Rate performance when compared to ordinary sphere decoding and MMSE detection. Here the antenna configuration is varied from 4 to 32 viz Figure 4 (.a-d) .It is observed the that the Bit Error Rate decreases and is much better than ordinary sphere decoding and MMSE detection methods.

Figure 4. (a-d) Performance of CSD mxn MIMO receiver using BPSK modulation scheme.

Sphere Decoding algorithm is a lattice reduction algorithm which achieves optimal bit error rate and hence preferred Wireless communication systems. In Figure 4 (a) for a 4x4 antenna configuration at a particular SNR say 30 db the BER for CSD is 10-1.7 compared to SD which is 10-1.5 and MMSE which is 10-1.1.When the receiver antenna configuration is varied to 4 x 32 at 30 db the BER for CSD is 10-1.6 compared to SD which is 10-0.9 and MMSE which is 10-0.8. It is inferred that detection is possible with complexity and gives a better result in terms of Bit Error Rate when comparing general sphere decoding and MMSE.

This paper presented the simulation study of complex sphere decoding scheme for MIMO receiver is studied with BPSK modulation scheme using MATLAB communication tool box. Better algorithms can be derived considering the search space, and architecture .Other modulation schemes can also be considered such as QPSK and QAM.

The authors express their sincere thanks to, The Management, The Director Academic (SNR Charitable Trust),The Principal, Sri Ramakrishna Engineering College, for their constant support and encouragement given to them. The authors also express their sincere thanks to the valuable suggestions cited by the DC members for their valuable suggestions.