The Modified LSD detector with the Priori Information

We use symbol vector instead of coded bits as a basic unit in the BCJR Algorithm. With this approach, we have added the dependency between contiguous symbol vectors. As mentioned, we use the LSD algorithm to reduce the required computational complexity. One problem with the LSD algorithm is that transmitted symbol vectors may not be included in the list L_LSD. If this does happen, the error rate of the TICM-T scheme will be dominated by those bits belonging to the symbol vectors. This kind of error cannot be corrected through iteration. We can enlarge the radius in the LSD algorithm to include more candidates. However, the computational complexity of the LSD will become higher. Here, we propose a method to alleviate this problem. From the modified BCJR algorithm in (2.42), we can calculate LLR of coded bits by

{ }

It is known that the LLR of a bit representing the probability of the bit being to one or zero.

Thus, if the absolute value of the LLR is large, we can the make decision on the bit. The larger the absolute value of the LLR, the more confident we can have for the decision. On the other hands, the more decisions we make, the less candidates we have to test in the LSD algorithm. As a result, we can enlarge the radius of the LSD without increasing computational complexity. For example, the LSD calculates the distance between the possible symbol vector and the received

vector.

with the Cholesky factorization, the distance can be calculated as

( ) ( )

²

This will form a tree structure and the distance can be calculated level-by-level. Now, we can rank LLRs and select corresponding top

C

_APP bits for detection, where 1≤

C

_APP≤

N

_bpt. Using

this method, the searching domain will be decreased from 2^Nbpt to 2^Nbpt−CAPP. Then, the radius of LSD,

r

_LSD, can be increased at the rest iterations without adding too many symbol vectors in the list. At the beginning of a decoding iteration, the LSD detector will find a new L_LSD with its increased

r

_LSD.

3.4 Simulation Results

In this section, we report simulation results to evaluate the performance of the proposed scheme. We consider two different systems with the same throughput, one with the conventional BICM scheme, and the other with the proposed TICM. The signal to noise ratio (SNR) is defined as the average received power per receive antenna divided by the average noise power. We use an IEEE 802.11n proposal released by TGn Sync in July 2005 [15] as our basic simulation platform.

An optional mode with K=56 (the channelization bandwidth 20 MHZ), and

N =4. The number

_T of receive antennas is assumed to be the same as that of transmit antennas.

The first system is built based on the IEEE802.11n proposal except for that the original CC encoder is replaced by the turbo encoder shown in Fig. 3-2. The two coded bit streams from two component encoder are interleaved and mapped to QAM symbols alternately. The code rate of the turbo encoder is 1/2 and

K

_RSC=3. We use the LSD detector and MIMO soft-bit demapper outlined in 2.7.2 to calculate LLRs of coded bits. The BCJR algorithm is used to exchange the extrinsic information between two component encoders during the iterative decoding process. We can view this as an inner iteration, since we can conduct turbo equalization and yield an outer iteration. In the outer interation, the extrinsic information generated at the decoder is fed back to the MIMO demapper to update soft information of coded bits. Since we have two feedback loops, there are many ways to conduct iterations. For simplicity, we let a complete cycle of iteration consist of one for turbo decoding, and one for turbo equalization. We call the system BICM-T.

The block diagram of the MIMO-OFDM transceiver with BICM-T is shown in Fig. 3-5 and Fig.

3-6.

Fig. 3-5: The block diagram of the MIMO-OFDM transmitter for BICM-T

remove GI

Fig. 3-6: The block diagram of the MIMO-OFDM receiver using the LSD for BCIM-T

The second system is also built based on the IEEE802.11n proposal. In addition to that the original CC encoder is replaced by the turbo encoder (shown in Fig. 3-2), but also the

bit-interleaving scheme is also replace by the tone-interleaving scheme proposed in Chapter 3.

Then, the tone-level BCJR method is used to exchange extrinsic information between two

component decoders, and calculate information bits probability. Here,

C

_APP is set to be 2 (and 4) at the third (fifth) iteration, and enlarge the radius of the LSD twice. As before, we call the system TICM-T.

We choose the channel-B (NLOS) with distance 6m, and the channel-D (NLOS) as our channel models, and a 4x4 system with 16-QAM transmission for comparison. Assume that the frequency offset and timing offset are perfectly compensated at the receiver. The PPDU length is set as 1000bytes; so there are 8000 information bits per frame. The preamble format for TICM-T and BICM-T is assumed to be the same as the original system. The standard per-tone channel estimation method (no smoothing) is used to estimate the MIMO channel. If the number of symbol vectors in L_LSD is less than a threshold (<300), the radius of the sphere is doubled ensuring that a proper iterative decoding.

Fig. 3-7 and Fig. 3-8 show simulation results for these two systems; one for channel–B and the other for channel-D. Note that we only use the estimated channel in simulations. As we can see, TICM-T outperforms BICM-T. If we let the target FER is 0.1, from Fig. 3-7, we can observe that TICM-T outperforms BICM-turbo about 1 dB in the first iteration. In the second and third iterations, TICM-T outperform BICM-T about 2.5 dB. Fig. 3-8 shows the results for channel-D.

The first iteration gap between TICM-T and BICM-T is still about 1dB, also. The second and third iteration gap is about 3 dB, slightly higher than that in channel-B. From the results, we can conclude that the TICM-T scheme is significantly better than the BICM-T scheme.

Fig. 3-7: Performance comparison of BICM-T, and TICM-T (20MHZ, 4X4 16-QAM, channel B, estimated-channel)

Fig. 3-8: Performance comparison of BICM-T, and TICM-T (20MHZ, 4X4 16-QAM, channel B, estimated-channel)

在文檔中 渦輪等化及渦輪碼在MIMO-OFDM系統上之實現 (頁 57-62)