Incidencia de las influencias internas y externas identificadas sobre la decisión de

In this section, we evaluate the efficiency of the ACO based method in finding the optimal execution order. For demonstration purposes, the MIMO system is configured as follows. For channel coding and modulation at the transmitter, we adopt a rate1/3-PCCC that con- sists of two identical CCs with the generator polynomial_{{1, 15/13}}oand a Gray mapped

16 QAM modulation scheme. The codeword length Ncis set to6·103. Both the transmitter

and the receiver adopt two antennas, i.e.,Nt= Nr = 2. The 2× 2 MIMO fading channel is

frequency-flat, spatially uncorrelated but temporally correlated. The temporal correlation is described by the normalized maximum Doppler frequencyFD. The larger the value of

FD is, the faster the channel realization changes. When the normalized maximum Doppler

frequency FD equals 0.5, we have an i.i.d. fading channel. At the receiver, the latency

constraint on the processing time of the iterative decoding process is exemplarily set as Ttot = 14· Tii. The processing time of the outer iteration in the worst case is assumed to

be1.6 times higher than the processing time of the inner iteration, i.e., Toi,wst = 1.6· Tii.

Based on this setting, we can draw a tree graph to represent the execution order candidate set_Ssch, cf. the simple example in Fig. 6.2. By counting the number of leaf nodes in the tree

graph, we notice there are559 candidates in the setSsch. The task of the ACO based method

is to find the optimal execution order in_Ssch with respect to given channel statistics, i.e.,

the normalized maximum Doppler frequency and the SNR. Parameter Setting in the ACO based Method

The ACO based method is parameterized by the number of training iterationsNiter, the

thresholdNthrused for the condition check, and the number of ants M . In the following,

we examine their impacts on the performance of the ACO based method. For visualizing the variation of pheromone concentration on the up-to-date dominant path over training iterations, we adopt the following defined metric. At a step nodeo with out-degree two, the uncertainty of the stochastic decision made by an ant can be quantified by computing the entropyEo with respect to the pmf defined in (6.2). Averaging the entropies of the nodes

that have out-degree two and are involved in the up-to-date dominant path, the resulting value is denoted as Edom_{. A small E}dom _{implies the concentration of pheromone on the}

up-to-date dominant path is high. Therefore, when the parameters are properly chosen, Edom_{is expected to decrease over iterations until reaching a constant value.}

Fig. 6.4 shows the variation of Edom _{over iterations. With more ants, the ACO based}

method can converge at a faster rate. However, the complexity of each iteration increases with the number of ants. Another observation in Fig. 6.4 is that the final value of Edom

decreases as the number of antsM increases. Normalizing the low limit on the pheromone valueτminto one, the up limitτmaxincreases with the number of ants, see (6.4). As a measure

of the concentration of pheromone trails on the dominant path,Edom_{is therefore expected}

to be smaller for a largerM .

The threshold Nthr is used in the condition check unit in Fig. 6.3. According to the

description of the condition check unit given in Section 6.2.3, the number of training frames that are generated within each training iteration generally increases along withNthr. As a

result, the trial quality comparison amongM ants tends to be more reliable as the value of Nthr increases. By using different Nthr, the ACO based method (with M = 15 and

Niter = 200) converges to different solutions, which corresponds to different execution

orders. Fig. 6.5 depicts the FERs of these execution orders. When the thresholdNthris too

small, the ACO based method tends to find a suboptimal execution order.

In the following simulations, the ACO based method works withNiter= 200, M = 15

andNthr = 5.

Comparison with the ES and EXIT-function based Methods

Four channel scenarios are examined in Fig. 6.6. For each scenario, the normalized maxi- mum Doppler frequencyFD and the SNR(NtEs)/N0are jointly chosen to ensure an FER

of interest, i.e., 0.2%, is achievable. The ES, EXIT-function and ACO based methods are applied for identifying the optimal execution order with respect to each scenario. Let us simulate the performance of the execution orders identified by them, respectively. Fig. 6.6 depicts the achieved FERs and also the corresponding computational energy consumptions. As the ES based method is guaranteed to find the optimal execution order, the figures in Fig. 6.6 associated to “ES” are effectively baselines for the others. The ACO based method

20 40 60 80 100 120 140 160 180 200 0_.2 0_.4 0_.6 0_.8 1

Number of training iterations

E

dom

M = 10 M = 15 M = 20

Figure 6.4: Number of ants vs. number of training iterations;

normalized maximum Doppler frequencyFD = 5· 10−3and SNR(NtEs)/N0 = 8 dB.

1 3 5 7

10−3

10−2

Nthr

FER

Figure 6.5: Comparison among different choices of the thresholdNthr;

normalized maximum Doppler frequencyFD = 5· 10−3and SNR(NtEs)/N0 = 8 dB.

is near-optimal and evidently outperforms the EXIT-function based method. Moreover, Fig. 6.6(a) on the one hand shows a large FER gap between “EXIT” and “ACO”, particu- larly in fast fading channel scenarios. On the other hand, we observe from Fig. 6.6(b) that the execution order identified by the EXIT-function based method consumes nearly the same computational energy as that identified by the ACO based method. These two obser- vations indicate the importance of using a proper execution order at the receiver, as the energy efficiency is crucial to the receiver design.

TakingFD = 5· 10−2andFD = 5· 10−3 as two examples, Fig. 6.7 shows the perfor-

mance of the three methods at different SNRs. The EXIT-function based method performs particularly poor at high SNRs. This is because the EXIT-function is too optimistic in predicting the decoding performance when the codeword length is not sufficiently long. Furthermore, at a given SNR, the FER gap between “EXIT” and “ACO” reduces as the nor- malized maximum Doppler frequencyFD reduces. However, for targeting the same FER,

e.g., FER of10−3_{, the SNR gap between “EXIT” and “ACO” observed in Fig. 6.7(b) is nearly}

as large as that in Fig. 6.7(a). This means an appreciable SNR gain can still be achieved by following the optimal execution order in slow fading channels.

FD= 5·10−1, (NtEs)/N0= 5.9 dB FD= 5·10−2, (NtEs)/N0= 6.3 dB FD= 5·10−3, (NtEs)/N0= 8 dB FD= 5·10−4, (NtEs)/N0= 12.5 dB 10−3 10−2 10−1 100 Scenarios FER ES EXIT ACO

(a) Decoding Performance

FD= 5·10−1, (NtEs)/N0= 5.9 dB FD= 5·10−2, (NtEs)/N0= 6.3 dB FD= 5·10−3, (NtEs)/N0= 8 dB FD= 5·10−4, (NtEs)/N0= 12.5 dB 10 20 30 40 Scenarios Norm. Comput. Energy Comsum. ES EXIT ACO (b) Decoding Complexity

Figure 6.6: Comparison among the ES, EXIT-function and ACO based methods for identi- fying the optimal execution order under different channel statistics;

normalized computational energy consumption shown in the y-label is defined by normal- izing the computational energy consumption to the information bit sequence length.