A number of study results demonstrated that the performance of the coded MIMO scheme can be highly enhanced by incorporating iterative decoding and detection scheme by exchanging soft information between the symbol detector and decoder. One of the critical problems of these iterative schemes is an exponential order of the complexity with increase of number of bits in a symbol and the number of antennas. In this paper, we present an efficient iterative detection and decoding scheme for MIMO systems with phase shift keying (PSK) modulation schemes and low density parity check (LDPC) codes. In order to reduce the complexity by the number of antennas, we adopt minimum mean square error (MMSE) based linear detection scheme with parallel interference cancellation. In addition, soft bit estimation is made only with a single distance calculation per bit, with approximating performance to the maximum likelihood detection 1.
There have been a number of research studies on the development of detection schemes for multi-input multi-output (MIMO) systems, in order to achieve a capacity approaching performance. The basic idea is to utilize a detector that maximizes the a posteriori probability (MAP) in order to achieve the best performance in combination with powerful forward error correction (FEC) coding scheme. In addition to the iterative soft decoding of the FEC scheme, re-utilization of the soft output fed-back into the symbol detection process made it possible to produce a capacity approaching performance [
Recently, a number of researches reported results on minimum mean square error (MMSE) based MIMO detection schemes with soft iterative processes, due to their reasonable performance and complexity trade-offs [
In this paper, we present an efficient linear MIMO detection scheme for a coded MIMO system, where phase shift keying (PSK) modulation schemes are used with low density parity check (LDPC) codes. In the proposed scheme, soft symbol values are first estimated by utilizing a PIC-MMSE filter, and then soft bit information (SBI) values are estimated only with a single distance estimation per bit. For this, we first normalize the detected symbol from the PIC-MMSE filtering process, and then map it to a specific region, so that SBI estimation can be made with a single distance calculation [
The remainder of this paper is organized as follows. Section II describes a MIMO system model with soft iterative detection and decoding (IDD), with an FEC scheme with soft iterative decoding process. Next, the operational prin- ciples of the PIC-MMSE MIMO detection for IDD are described. In Section III, we detail the SBI estimation process by describing mathematical formulas when the PIC-MMSE detector is employed with PSK modulation. Section IV de- monstrates the bit error rate (BER) performance and the complexity of the proposed methods are compared with the conventional schemes for the LDPC coded MIMO systems with PSK modulation schemes. Finally, conclusions are drawn in Section V.
Suppose the received symbol vector is represented as
where
The PIC-MMSE MIMO detector is performed as follows. First, with the a priori information,
where
The second step is PIC on the received symbol vector,
where
where
The third step is suppressing the NPI term in (4) using the MMSE filter in (5). Then, the filtered result for the
where
where
It is clear in (7) that the search process to find the solution of
It was reported that there were no performance degradation even if the a priori information from the channel decoder in (7) was neglected, for the systems using binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) [
With this simplification, the argument of
First, we consider that the constellation diagram can be divided into
With the above property, (9) can be generalized as
where
In addition,
where
linear-order for each independent layer without degrading the performance from the Max-approach.
Soft symbol value estimations specified in (2) and (3) require
By denoting
where
With this information, we simplify the expressions of
Then, we apply the same rule for the soft IDD scheme, and denote the iteration index inside the PIC-MMSE detector as
Equation (16) is then applied to QPSK, whereby QPSK can be decomposed into two independent BPSK. Then, expressions of the real and imaginary parts of the soft symbol values,
and accordingly, the
The expressions for the real and imaginary part of
where
where
We simulated the BER performance of the proposed methods over a Rayleigh fading channel. We used the LDPC code with an information length of 16,200 bits and a code rate of 1/2. The min-sum product algorithm with a correction factor was used [
Proposed/conventional | Proposed/conventional | |
1 | ||
2 | ||
3 | ||
4 |
In this paper, we proposed the symbol mapping technique for the PIC-MMSE based MIMO detection of PSK to reduce the complexity, resulting from the elimination of the search process to find the minima in the SBI estimation. To further reduce the computational complexity, we presented efficient method for PSK schemes to calculate the soft symbols in the PIC process. Simulation results showed that the proposed techniques reduced the complexity to nearly linear- order without degrading the BER performance.
Zhang, M.X. and Kim, S. (2017) Soft Iterative Linear Detection for LDPC Coded MIMO Scheme with PSK. Int. J. Communications, Network and System Sciences, 10, 148-156. https://doi.org/10.4236/ijcns.2017.108B016