Multipleinput multipleoutput (MIMO) system is considered to be one of the key technologies of LTE since it achieves requirements of high throughput and spectral efficiency. The semidefinite relaxation (SDR) detection for MIMO systems is an attractive alternative to the optimum maximum likelihood (ML) decoding because it is very computationally efficient. We propose a new SDR detector for 256QAM MIMO system and compare its performance with two other SDR detectors, namely, BCSDR detector and VASDR detector. The tightness and complexity of these three SDR detectors are analyzed. Both theoretical analysis and simulation results demonstrate that the proposed SDR can provide the best BLER performance among the three detectors, while the BCSDR detector and the VASDR detector provide identical BLER performance. Moreover, the BCSDR has the lowest computational complexity and the VASDR has the highest computational complexity, while the proposed SDR is in between.
Multipleinput multipleoutput (MIMO) system has been considered as a promising solution to provide high data rate and good quality of future wireless communications. In MIMO systems, detection algorithm is one of the major challenges due to its limitations of either unsatisfactory performance or high complexity. The maximum likelihood (ML) detection can provide the best blockerrorrate (BLER) performance, but its computational complexity is extremely high since it searches the vectors in the entire lattice space of the transmitted signals. Although equalizationbased detectors such as zeroforcing (ZF) decoding have very low complexity, they suffer from unacceptable degradations in BLER performance. Sphere decoding (SD) is able to provide the BLER performance of ML detection with less complexity by searching only a subset of the entire lattice space. Nevertheless, it has been proven that its expected complexity is still exponential [
The decoding algorithms based on semidefinite relaxation (SDR) approach have become more and more attractive simply because of the fact that semidefinite programming (SDP) problems can be efficiently solved in polynomial time [
In this paper, a new SDR detector is proposed for 256QAM system [
The system model for the MIMO transmission using
The complex transmission in (
Define a rank1 semidefinite matrix
It is easy to find that the ML detection problem given in (
It can be observed that the high complexity of the ML detection is due to the presence of the two nonconvex constraints (
The BCSDR problem (
It is worth noting that when constraint (
Substituting (
Since the first
Considering constraint (
Table
The value of

 




 




















By substituting (
Similar to the VASDR method, the first
As mentioned in Section
Firstly, we will demonstrate that the constraints of the BCSDR problem are equivalent to those of the VASDR problem. This equivalence has been considered in [
For each matrix
For any matrix
Now, we construct a semidefinite matrix
From (
From (
For each matrix
For any matrix
From (
From the perspective of geometry, it is easy to know that there should be vectors
From both Steps
Secondly, we will demonstrate that the constraints of proposed SDR problem are tighter than those of the BCSDR problem and also tighter than those of the VASDR due to the aforementioned equivalence. For this purpose, a new SDR problem is constructed given by
By comparing (
For each matrix
For any matrix
From (
Substituting (
From (
For each matrix
For any matrix
From (
Then, from (
From both Steps
Firstly, the BCSDR given in (
Computer simulations were conducted to evaluate the performance of these three SDR detectors. An uncoded MIMO system with independent Rayleigh fading channel was taken into account and the Sedumi toolbox within Matlab software was used to implement the SDR detection algorithms. Figures
The BLER performance of the SDR detectors for
The BLER performance of the SDR detectors for
The computational time of the SDR detectors for
The computational time of the SDR detectors for
In this paper, we proposed a SDR detector for 256QAM MIMO system and also reviewed two other SDR detectors, namely, BCSDR detector and VASDR detector. Then we analyzed the tightness and the complexity of these three SDR detectors. Both theoretical analysis and simulation results demonstrate that the proposed SDR can provide the best BLER performance among these three detectors, while the BCSDR detector and the VASDR detector provide exactly the same BLER performance. Moreover, the BCSDR has the lowest computational complexity and the VASDR has the highest computational complexity, while the proposed SDR is in between.
The authors declare that there is no conflict of interests regarding the publication of this paper.