1. Ali Al-Saihati ID# 200350130 Ghassan Linjawi
King Fahd University of Petroleum & Minerals  Electrical Engineering Department EE 575 Information Theory Bit Error Rate Performance of V-BLAST Detection Schemes over MIMO Channels
Ali Al-Saihati
ID#
Ghassan Linjawi

2. OUTLINE Introduction. Theory of V-BLAST. Problem Definition.
Simulation Results.
Conclusion.

3. Introduction
MIMO system has proved to achieve high capacity compared to SISO MISO and SIMO systems.
For this reason, many algorithms have been proposed to reduce the interference in the received signals caused by other transmitters in the system.
Also, they aim achieve closer values to the Shannon capacity limit.
D-BLAST (Diagonal Bell Labs Layered Space Time) and V-BLAST (Vertical Bell Labs Layered Space Time) are such schemes used for detection and suppression the interference in MIMO systems.

4. D-Blast, which was proposed by Gerard J
D-Blast, which was proposed by Gerard J. Foschini, applies a diagonal space time coding on the data.
By applying this algorithm, it could achieve 90% of Shannon capacity rates as well as high spectral efficiency.
However, due to complexity of implementing the algorithm, V-Blast algorithm was proposed. It was established in 1996 at Bell Labs.
It demultiplexes the transmitted signal and then maps bit to symbol independently for each substream.

5. Theory of V-BLAST.
A single user scheme which has multiple transmitters.
It divides the data stream into substreams and transmits them through multiple transmitters at the same time and frequency.
The data at the receiver are received at the same time and frequency.
By implementing V-BLAST algorithm, the diversity gain is increased and the bit error rate (BER) performance is improved.
The MIMO system is assumed to undergoes flat fading channel. The system model of the output signal is given by: 
y= Hx+ η

7. Detection Process
The detection process consists of three operations: interference suppression (nulling), interference cancellation (subtraction) and optimal ordering.
The interference nulling process is carried out by projecting the received signal into the null subspace spanned by the interfering signals.
This process is done by using Gramm-Schmidt orthogonalization procedure that converts a set of linearly independent vectors into orthogonal set of vectors.
Then, the symbol is detected.
The interference cancellation process is done by subtracting the detected symbol from the received signal.
The optimal ordering ensures that the detected symbol has the highest signal to noise ratio (SNR).

8. V-BLAST algorithm integrates both, linear and nonlinear algorithms presented in interference nulling and interference cancellation respectively.
There are two disadvantages in V-BLAST algorithms:
1) Error propagates during symbol detection.
2) The number of receive antennas must be greater than or equal to the number of transmit antennas to satisfy the interference nulling process.

11. V-BLAST Detection Algorithm

12. Modified V-BLAST Algorithm
Since the amount of interference cancelled in each step becomes smaller, a new algorithm was proposed.
The algorithm stops iterating when the interference becomes very small. Hence, it reduces complexity of the system.
When the value of C becomes 1, the algorithm becomes the same as the original V-BLAST detection.
When C becomes the algorithm becomes MMSE and ZF detection.

14. GMMSE =H+ = ( HHH + ρ I )-1HH
ZF, ML and MMSE Models
The weight vector for the ZF and MMSE are given by:
GZF =H+ = ( HHH )-1HH
GMMSE =H+ = ( HHH + ρ I )-1HH
ZF and MMSE are simple to implement linear algorithms.
They do not achieve high data rate at high SNR.
The ZF detection cancels the interference only
So, it enhances the noise in each iteration. At high SNR, the MMSE detection will function like ZF detection..

15. The maximum likelihood (ML) detection is given by:
G = min |y – H x|
The ML is optimum in minimizing the error and has an excellent performance.
The order of complexity is |A|M where M is the number of transmitter and A is the number of modulation constellation.
For example, if M = 10 and A = 2 then we need to compute 1024 times during the process

16. Proposed V-BLAST Algorithms
Different proposed recursive algorithms have been proposed for V-BLAST algorithm.
Some of these are matrix recursive, vector recursive, greedy ordering, scalar recursive and adaptive scalar recursion for fast fading.
The matrix recursive algorithm tries to find an inverse matrix using the Sherman- Morrison formula with a given initial matrix recursively.
This method decreases the complexity order from quadratic to cubic but the computation of the inverse matrix is complex.

17. In vector recursive algorithm, a weight vector is found recursively to substitute the computation of inverse matrix.
The greedy ordering method selects the most reliable signals for detection.
The scalar recursion algorithm focuses on nulling the output vector.
The adaptive scalar recursion for fast fading changes and updates the weight vectors and optimum ordering based on the changes incurred during transmission.
Using this algorithm, the complexity order reduces to a square.

22. Problem Definition
It is required to find the BER performance of the ZF, MMSE and (ML) schemes implemented in the V-BLAST system

23. Results

24. Conclusion
ML detection has better BER performance than the MMSE and ZF detections by 15dB.
The performance of MMSE detection is better than ZF detection by 2- 3 dB.
Using the adaptive scalar recursion for fast fading, the complexity order reduces to square and the computation becomes less compared to other techniques. 

25. References:
[1] Nirmalend. B and Rabindranath B. “Capacity and V-BLAST Techniques for MIMO Wireless Channel”. Journal of Theoretical and Applied Information Technology, [2] P. W. Wolniansky. G. J. Foschini. G. D. Golden and R. A. Valenzuela “V-BLAST: An Architecture for Realizing Very High Data Rates Over the Rich-Scattering Wireless Channel”. Bell Laboratories. [3] S. Loyka and F. Gagnon. “Performance Analysis of the V-BLASTAlgorithm: An Analytical Approach” International Zurich Seminar on Wireless Broadband. [4] Taekyu Kim and Sin-Chong Park. “Reduced Complexity Detection for V-BLAST D Systems from Iteration Canceling” [5] Toshiaki. K. “ Low-Complexity Systolic V-BLAST Architecture” IEEE Transactions on Wireless Communications, 2009