call the elements in x_k chips. Users are distinguished by their interleavers, hence the name Interleave Division Multiple Access (IDMA). The key principle of IDMA is that the interleavers π(k) should be different for different users. We assume that they are generated independently and randomly. These interleavers disperse the coded sequences so that the adjacent chips are approximately uncorrelated, which facilitates the simple chip-by-chip detection scheme [6]. Classical IDMA communication system is adopted as illustrated in Figure 1, which consists of an elementary signal estimator (ESE) and K singleuser a posteriori probability (APP) decoders (DECs). In our cases (DECs) are formed by despreaders.

The outputs of the ESE and DECs are extrinsic loglikelihood ratios (LLRs) about x_k(j) defined below as:

(1)

These a posteriori LLRs are further distinguished as e_ESE(x_k(j)) and e_DEC(x_k(j)), depending on whether they are generated by the ESE or DECs and channel coefficient h_k(j). A global turbo-type iterative process is then applied to process the LLRs, as detailed in [7]. The information bits for user k are first spread, then interleaved and transmitted over a channel. The received signal can be written as:

(2)

where is the j^th chip transmitted by user k, h_k(j) the time-varying coefficient for user k and n(j) are samples of an Additive White Gaussian Noise (AWGN) process with zero-mean and variance = N₀/2. When we assume quasi-static single-path channels, the coefficients h_k(j) of the channel are known from the receiver. In this case, the bit detection can be done by an ESE operation carried out a chip-by-chip manner. From (2) we define:

(3)

where is the distortion including interference plus noise in r(j) with respect to user-k. The mean and the variance functions are noted by E(.) and Var(.) respectively. can be approximated by a random Gaussian variable. A detailed derivation of the detection algorithm is given in [7,8]. Here we only list the algorithm:

1) Initialization set

(4)

2) Main operations

3) LLR generation

(5)

It can be verified that the above algorithm is an extremely simplified method. The cost per information bit per user increases linearly with the spreading length but is independent of the number of users K.

3. Joint Channel/Symbol Estimation

The classical iterative chip by chip algorithm is based on the assumption that the receiver has ideal channel state information (CSI). We now proceed to consider the channel estimation issue.

3.1. Channel Estimation

We investigate recursive estimation for IDMA systems without assuming channel knowledge over time-varying and quasi-static channels. The received signal, given by Equation (2) can be written as:

r(j) = h_k(j)∙x_k(j) + (6)

so the channel response at time j + 1 is done by:

h_k(j + 1) = h_k(j) + w_k(j + 1) j; k(7)

where h_k(j) is the state channel (the single path situationconsidered here is, of course, easily extended to multipath, via straightforward state-augmentation), w_k(j) is the zero mean, white Gaussian noise with covariance, and the noise covariance matrix Q(j) of the vector noise w(j) = [w₁(j), …, w_K(j)]. We assume that there is no inter-block interference. This allows independent processing of blocks. Let be the filtered state vector and P(j) be the (N × N) corresponding filtered error variance, where is the filtered error covariance matrix defined as

.

When a pilot embedding technique is used both with iterative joint channel estimation and multi-user detection [9,10], the transmitted signal from user k is the superposition of the data signal x_k and pilot p_k, where SA is the pilot length.

The received signals for pilot symbols at known locations, p_k = {p_k(l), p_k(z), …, p_k(SA)} is the pilot for user k.

Assuming that p_k are randomly and independently generated the initial estimate for our iterative algorithm is obtained using possible pilot symbols and deterministic estimator.

For pilot symbols, channel coefficients can be estimated in the usual linear Gaussian framework:

1) Step 1: Initialisation

{h_(0/–1); P_(0/–1) (initial mean, covariance)}.

2) Step 2: Prediction Prediction process for the filter is obtained using the evaluation equations of the mixed state vector

The error covariance prediction is given by:

(8)

3) Step 3: Filtering The states predicted by dynamic filters conditionally to j are updated using Kalman filter equations given by:

(9)

Where K(j) is the Kalman gain.

3.2. Combined Estimation, Detection and Decoding

The following is a brief outline of the function of each module in the iterative process. The lower part of Figure 1 shows the receiver structure under the assumption of known parameters of the channel h_k(j).

As channel variables are to be jointly estimated, we shall assume that channel is either static or slowly time-varying within a frame.

3.2.1. Pilot Symbols Processing

Pilot signals can be performed for finer estimation, during the inner decoder iterations and outer estimator/ decoder iterations.

1) time Varying Channel It requires computation of corrected channel coefficients for each chip. However, this is possible, after some iterative decoding system (local). In the following, we give the details of the detection system which iterates via the three modules.

a) Based on the pilot sequences and the a priori statistics of the time-varying channel; the channel estimator. j = 1, …, SA is updated as in A and h_k(j) will be equal to the last value estimated by the training pilot:

(10)

b) Based on the estimation of h_k(j) from the channel estimates, the IDMA system computes the extrinsic LLRs for x(j).

c) Based on the pilot symbols, and the estimation of symbols x_k(j), the channel estimator refines the data estimates {, k = 1, …, K and j = 1, …, J}.

For the next iteration, an estimate of the transmitted symbols and of the channel coefficient is used. A new estimated coefficient is calculated after full decoder/ estimator iterations. For the N^th iteration of the decoder, the LLR values of the transmitted bits are calculated on the base of the (L-1)^th iterated estimate; Where N = M × L, M is the number of estimation iterations, L the number of decoder iterations for each channel estimation. In order to reduce algorithmic complexity we use the ratio 1:5 between the number of inner iteration M and outer iteration L.

2) Static Channel We focus on the static channel case where the coefficients are assumed to be constant over the whole frame. This can be considered as a special case of the above general model. For this case, data matrix [K; J] reduces to a vector whose coefficient are simply given as and Q_j = 0 in Equation (8).

We assume, here, that the estimator is the last filtered value h_SA/SA and there is no change. But, of course, this estimator is valid only when we use a pilot sequence for estimating the vector channel coefficients. Otherwise iterative estimation is used instead.

3.2.2. Blind Case

In this case there is no bit information available for the iterative joint process discussed. According to the discussion above, we need to set up values h_k(j) that are updated, based on the feedbacks from the decoder in the iterative process. In the first iteration, we use the a priori information E(h_k(j)) j; k.

There are always decoder feedbacks available, and the channel coefficients are considered slowly varying during the time interval. Then the feedbacks from the decoder after the M next iterative decoding processes will be used in the next coefficient estimation.

The method of joint iterative turbo decoding and estimation is called turbo detection. Turbo detection allows decreasing the number of pilot symbols for estimation purposes and thus increases the user data rate for a given bandwidth. This method can be used to detect the symbols blindly. Such an iterative algorithm is shown in Figure 2.

4. Simulation Results

4.1. Static Channel

These results have been obtained with spreading codes length C = 8, K = 8 users, J = 2048 chips. Let us first test the effect of the estimation block on the receiver system. In Figure 3, we compare the performance of the IDMA algorithm, with different random values of h_k(j) for k = 1, …, K; j = 1, …, J; in two different cases:

• Without estimation block: the coefficients of the channel are fixed as h_k(j) = 1 k, j at the receiver and the algorithm in section 2 is applied.

• With blind estimation: the channel coefficients are blindly estimated, with three estimation iterations.

The Figure 3 illustrates the mean Bit Error Rate (BER) versus signal-to noise ratio (SNR = Eb = N0), where Eb is the mean user bit signal power.

4.2. Time-Varying Channel

Figure 4 shows the performance of the proposed iterative algorithm in time varying channels when = 0.001 (i.e. while subject to a random walk of ±25% over the whole frame) and give a comparison with the detection under perfect CSI at receiver side, for J = 256 × 8 chips and the performance exhibited by the iterative turbo receiver of Figure 2.

We illustrate, in Figure 5 the performance of the system under the same simulation conditions with = 0, 01. In Figure 6, the evolution of the BER for variable standard deviation from = 0.0001 to = 0.1 is illustrated, in the same simulation conditions than above. We observe good performance for = 0.0001 until = 0.001, and poor performance for > 0.01.

4.3. Trajectory Channel Variation

Figures 7 and 8 illustrate the evolution of estimated channel coefficients using the iterative algorithm with five pilot sequences (SA = 5) and without any pilot sequence, respectively and also provide the exact trajectory of coefficient h₄

5. Conclusion

In this paper we proposed low complexity iterative joint channel estimation, and decoding scheme for IDMA systems. This method has been developed to extract all the data/channel information through a two-level iteration algorithm. The proposed system inherits the low-complexity advantage of IDMA technique. In this paper, we have documented the performance trends exhibited by the proposed turbo detection receiver. The results obtained

show the efficacy of such methods even in blind case when the channel is unknown. Furthermore, we note that other techniques such as the Particle Filter method can be used to improve its effectiveness further.

REFERENCES