MUD approach

The aperiodic nature of the long codes employed in this work usually pre- cludes the use of linear multiuser detection schemes like MMSE detector and decorrelator, etc. due to high computational complexity. Therefore, only the nonlinear parallel interference cancellation scheme is considered here. The inner decoding scheme combined with interference cancellation is depicted in Fig. 10.5. Interference cancellation with hard and soft deci- sion feedback will be discussed next.

10.3.2.1 Hard decision interference cancellation

Hard decision interference cancellation (HDIC) is performed by estimating the transmitted signals in parallel for all the users, and then subtracting the estimated signals of the interfering users from the received signal r to form a new signal vector rHDIC

k,l for demodulation of the signal transmitted

from the lth _{path of user k. Mathematically, it is expressed as}

rHDIC_k,l = r− ˆAˆh+ ˆakˆhk,l (10.17)

where r_{∈ C}Nk_{denote the received signal vector due to the transmission of}

the jth _{symbol from the k}th _{user’s l}th _{path, it contains N}

k chips (usually

Nk > N due to multipath delay spread). The vector rHDICk,l ∈ CNk is its

interference canceled version after subtracting the contributions from all the other users and the same user’s other paths using hard decision feedback. The vector ˆAˆh represents the estimated contribution from all the users calculated by using the data matrix ˆAand channel vector ˆhestimated at

the previous iteration. The vector ˆakˆhk,lis the estimated contribution from

the lth _{path of user k.}

The derivation of Lc is the same as in Section 10.3.1 except rk,l is

replaced by rHDIC

k,l , the delay compensated and MAI and ISI canceled

version of the received vector due to the transmission of the jth _symbol

from the kth _{user’s l}th _{path. The MAI and ISI are estimated by mak-}

ing tentative hard decisions on the output from the outer decoder, i.e., ˆ

uk[nl] = sgn{Π(λ(uk[nl]; O))} (see Fig. 10.1) for all k. Then we go through

block encoding and spreading to produce an estimate of the transmitted chip sequence ˆsk, which is used for both interference cancellation and chan-

nel estimation. Channel estimation was treated in Chapter 5.

In the ideal situation, the MAI from other users and ISI from the same user’s other paths are canceled. Going through the same procedure as shown in (10.12) – (10.16), we come up with the same channel reliability value Lc = 4/N0. However, the mechanisms for deriving rk,l and rHDICk,l

are different (single user and MUD approach, respectively) which result in different y and L vectors used in equations (10.10) – (10.11) for computing LLR values.

It should be noted that the inner decoding can be accomplished with- out extrinsic information. In this case, L(wi; yi) = Lcy for all i in equa-

tion (10.10) and (10.11). The switch in Fig. 10.1 is turned off. The perfor- mance can still be improved at each iteration without extrinsic information because we get better estimate of the channel ˆhkand transmitted sequence

ˆsk (better cancellation) as the iteration proceeds.

10.3.2.2 Soft decision interference cancellation

To reduce the likelihood of error propagation, we can use soft informa- tion L(sk) instead of hard decision on sk for interference cancellation and

channel estimation. When soft IC is used, the iterative decoding scheme illustrated in Fig. 10.1 should be modified accordingly. Fig. 10.6 shows the revised version.

In [21, 22], interference cancellation and channel estimation using soft information were proposed, which is, however, not directly applicable in our scenario, because we do not have the soft estimates for all the inner code bits, but only for the systematic bits. To derive the LLR value of sk, we feed λ(u0k[nl]) = Π{λ(uk[nl]; O)} into a soft inner encoder which

computes λ(wp_ik(j)), the LLRs for codeword bits wp_ik(j), then spread them to derive L(sk). The design of the soft encoder (modulator) was introduced

in Section 9.2.4. With soft estimate of sk, we can derive the cancellation

residual after soft cancellation as

rSDIC_k,l = r_{− E[A|r]ˆh + E[a}k|r]ˆhk,l (10.18)

10.4 Numerical Results 181 PSfrag replacements − − Soft SISO Inner Decoder Encoder Decision SISO Outer Decoder Spreader λ(u0_{k [}n_{l ];}I) λ(u0_{k [}n l ];I) λ(u0_{k [}n_{l ];}O) _λ (uk[nl ];I) λ_(uk[n_{l ];}O) λ(bk[l]; I) λ_{(bk[l]; O)}

Π

Π

Π

Figure 10.6: Iterative decoding with soft IC and CE.

with Ck and compensating with path delays.

We need estimates of the complex channel gains to do maximum ratio combining as discussed in Section 10.3.1 and 10.3.2. Both hard and soft versions of the ML estimator are described in the previous chapter, and are not repeated here.

10.4

Numerical Results

Different approaches are evaluated numerically with computer simulations. The simulation parameter setting is the same as in Section 9.4.

Fig. 10.7 shows the results of iterative decoding for single user system with conventional approach (no interference cancellation is needed in this case). The gain by applying extrinsic information to the inner decoding is 1.3 dB at BER of 10−5_{and 0.8 dB at BER of 10}−3 _{when compared against}

non-extrinsic feedback case, which is more than the 0.6 dB gain reported in [71] for AWGN channel. If the approximation in (10.11) is used for inner decoding and the operation max∗ _{is replaced by max in (10.1) – (10.6) for}

the outer decoding, the performance loss is noticeable in low SNR region, and gradually becomes smaller as SNR increases. To study the behavior of each algorithm, the number of iterations is usually set to 7 (except in Fig. 10.15 and 10.16), since it is observed that almost all the algorithms would converge after 5 or 6 iterations.

We need to stress the fact that the interleaving design is essential for the system performance. To find out the optimum interleaver for the system in question, we pass the block size of 4620 code bits through different block in- terleavers, which exhibit large discrepancies in the results as demonstrated in Fig. 10.8. The interleavers of size 66_{× 70 and 44 × 105 in general work} better than others for the studied system. When the algorithm converges at the 6th_{or 7}th_{iteration, the former one attains the best performance. Al-}

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 10−5 10−4 10−3 10−2 10−1

100 single user system, M = 8, N = 64, L = 3, fdT = 0.01, 7−iteration

Bit error rate

Signal to Noise Ratio E

b/N0 [dB]

without extrinsic info maxlog extrinsic info logmap extrinsic info

Figure 10.7:Performance of iterative decoding for single user system.

10−4 10−3 10−2 10−1 100 M = 8, N = 64, E b/N0 = 6dB, fdT = 0.01, L = 3, K = 12, c=1.3/K

Bit error rate

size of block interleaver

PSfrag replacements

1 × 4620 11 × 420 22 × 210 44 × 105 66 × 70 105 × 44 210 × 22 420 × 11

Figure 10.8: Performance of different block interleavers on 7-stage HDIC aided iterative decoding with extrinsic information.

10.5 Correction/Adaptation of Extrinsic Information 183