Simulation results

Computer simulations are conducted to evaluate the proposed signalling schemes in terms of rSD. This ratio indicates the portion required for signalling bits in relation to the

number of transmitted data bits. The underlying adaptive OFDM system is described in Appendix A.

Signalling overhead for a fixed packet size

We consider a constant data rate of rD = 24 Mpbs standardized as one possible trans-

mission mode in IEEE 802.11a and a typical packet size of K = 10 OFDM data symbols, which gives a fixed number of BK = 960 data bits. In the standard, there is a 12-bits long LEN GT H field in physical layer convergence procedure (PLCP) header which in- dicates how many octets will be transmitted. The value K is determined based on the value of the LEN GT H field and the current data rate. In general, K depends on the used application, e.g. in real-time applications K is typically a small value.

For Huffman coding and the memory based signalling schemes, L_BX,Ng depends on the underlying channel state and the system SNR in addition. Consequently, rSD is variable.

In Figure 3.6, the cumulative distribution function of rSD is plotted. The cumulative

probability PSS(rSD) = P r(rSD ≤ rSD,0) with rSD,0 as a ratio of interest, is interpreted as

the probability with which an overhead represented by rSD,0resulting from some signalling

scheme X is sufficient for the signalling. We consider a typical SNR value of 20 dB and the channel model as well as the applied channel estimation algorithm given in Appendix A.

The signalling schemes in Section 3.2.1 are based on uniformly distributed symbols Pb_i1,b_i2,··· ,b_iNg. The signalling overhead LBU,Ng is therefore constant. These signalling

schemes result in a constant rSD. Any value lower than the corresponding rSD leads to

3.4 Performance comparison 33 0.020 0.04 0.06 0.08 0.1 0.12 0.14 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Signalling bits to data bits ratio (rSD)

C u m u la ti v e d is tr ib u ti o n fu n ct io n PS S Ng= 1 Ng= 2 Ng= 3 Huffman Ng= 1 Huffman Ng= 2 Huffman Ng= 3

Time st. dep. Huffman Ng= 1

Time st. dep. Huffman Ng= 2

Time st. dep. Huffman Ng= 3

Freq st. dep. Huffman Ng= 1

Freq st. dep. Huffman Ng= 2

Freq st. dep. Huffman Ng= 3

Figure 3.6: Signalling overhead of proposed signalling schemes in terms of rSD versus PSS

PSS = 1. The relation between rSD and PSS is described by a step function with transition

at exactly rSD. For Ng = 1, 2 and 3, the ratio is determined to rSD = 0.15, 0.125 and

0.1167 respectively.

Once the symbol probabilities Pb_i1,b_i2,_{··· ,biNg} are available, Huffman coding schemes can

be applied. The signalling overheads are also simulated for Ng = 1, 2 and 3. For Ng = 1,

a probability of PSS = 0.9 is achieved if rSD = 0.1 is ensured, while increasing Ng to

2 and 3, rSD can be reduced to 0.083 and 0.08 respectively, for the same probability of

PSS = 0.9. As shown in Figure 3.6, if rSD = 0.1 is allowed and Ng ≥ 2, a probability

of PSS ≈ 1 is possible compared to the signalling schemes above, a reduction of ∆rSD =

0.125_{− 0.1 = 0.025 is achieved, which corresponds to a net reduction of signalling bits of} ∆ ¯L_BH,2 = ∆rSDBK = 24 bits.

The signalling schemes, which utilize the frequency-domain memory effect, are also sim- ulated. The required signalling overhead L_BF,Ng is compromised of two contributions. The first contribution results from the initial symbol Z0, which is encoded by Huffman

coding scheme. The second contribution arises from the state-dependent symbols Znf

with nf ≥ 1, which are encoded based on the state-dependent Huffman coding scheme

rSD = 0.08, 0.07 and 0.065 are required respectively to reach a probability of PSS = 0.9.

Comparing with the Huffman coding without utilizing memory, for Ng = 3, a reduc-

tion in the overhead of ∆rSD = 0.08 − 0.065 = 0.015 is possible giving a net reduc-

tion in signalling bits of ∆L_BF,3 = ∆rSDBK = 14.4 bits. Furthermore, if a signalling

overhead of rSD = 0.08 is provided, a probability of PSS ≈ 1 can be achieved for both

Ng = 2 and 3 as confirmed in Figure 3.6. A comparison with the Huffman coding with

Ng = 3 gives ∆rSD = 0.1 − 0.08 = 0.02 corresponding to ∆L_BF,3 = 19.2 bits. Com-

pared to the coding schemes based on a uniformly distributed source, a reduction of ∆rSD = 0.1167− 0.08 = 0.0367 is achieved corresponding to ∆L′_BF,3 = 35.23 bits.

The signalling schemes based on the time-domain memory are simulated too. Just to show the potential of overhead reduction, only the steady-state signalling overhead is evaluated, which is slightly lower than the actually required overhead due to the overhead of the initial bit-loading vector b0. The more vectors bks are encoded, the smaller is the

contribution of b0. In the practice, however, due to the problem of catastrophic error

propagation, the number of packets using the time-domain state-dependent signalling scheme has to be limited.

For Ng = 1, 2 and 3, the probability of PSS = 0.9 corresponds to an overhead of rSD =

0.056, 0.038 and 0.032 respectively. For Ng = 3, a comparison of this signalling method

with the methods based on the frequency-domain memory combined with state-dependent Huffman coding and the Huffman coding scheme results in a reduction of ∆rSD = 0.065−

0.032 = 0.033 and 0.08− 0.032 = 0.048 respectively, which corresponds to a reduction in net signalling bits of ∆L_BT,3 = 31.68 and 46.08 bits. For Ng = 1, rSD = 0.06 gives

approximately PSS ≈ 1, while for Ng = 2 and 3, rSD can be reduced to around 0.045 for

a probability of PSS ≈ 1. This indicates that for each 100 data bits around 4.5 signalling

bits are required in the steady state if the bit-loading vector bks is encoded by the time-

domain state-dependent Huffman coding scheme, while the signalling method based on the uniformly distributed source model would require 0.1167_{× 100 = 11.67 bits.}

Signalling overhead for variable packet sizes

We have developed several signalling schemes, which utilized different information-theo retical properties of a common source. Some schemes result in an overhead LX,Ng inde-

pendent on K, e.g. schemes without considering time-domain memory effect. However, LX,Ng based on the time-domain state-dependent Huffman coding schemes varies with

K, as K impacts the time-domain correlation between consecutive bit-loading vectors. Intuitively, rSD decreases with increasing K implying that large packet size causes low

signalling overhead. From the standpoint of reducing signalling overhead, large K is de- sired. But in the practical system design K is limited due to time variance of the channel

3.4 Performance comparison 35

and synchronization impairments.

10 20 30 40 50 60 70 80 100 150 200 10−3 10−2 10−1 100 Frame size K rSD

Trivial coding scheme Ng= 3

Huffman coding scheme Ng= 3

Time st. dep. Huffman Ng= 3

Freq st. dep. Huffman Ng= 3

Trivial coding scheme Ng= 1

Figure 3.7: rSD versus K for SNR = 20 dB and PSS= 0.9

Here, we investigate the dependence of rSD on K for some signalling schemes, which is

plotted in Figure 3.7. For the signalling schemes with variable signalling overhead, we consider a probability of PSS = 0.9 and a system SNR of 20 dB. The K-independent sig-

nalling schemes results in overheads, which decrease linearly in the log-log representation at the same slope. For small K values the Huffman coding based signalling scheme using the knowledge of the symbol probabilities Pb1,··· ,bNg achieves a remarkable reduction in

signalling overhead, while for large K this reduction plays an unremarkable role in view of the error proprogation problem and implementation complexity. The further exploita- tion of frequency-domain memory effect results in a further reduction as confirmed in Figure 3.7. A high potential in reducing the overhead is achieved by the time-domain state-dependent Huffman coding, especially for small and middle packet size (K ≤ 50). With increasing K, the time-domain correlation decrease more and more giving the fact that the decreasing slope becomes more flat and the overhead approaches that of other signalling schemes. If K is increased to certain value, it would require more signalling overhead than the frequency-domain correlation based signalling schemes. For sufficiently large K, this method will even degrade to Huffman coding based signalling scheme since the time-domain correlation will disappear completely.

PER of adaptive modulation with explicit signalling

The potential benefit of adaptive modulation in terms of packet error ratio (PER) im- provement was demonstrated in Section 2.2.2. There, it was assumed that the adapted modulation schemes were perfectly synchronized between the transmitter and the re- ceiver. We have to evaluate the PER under the realistic condition that the adapted modulation schemes have to be explicitly signalled. As mentioned, the PER performance will be certainly degraded to some extend. Simulations were conducted to quantify this degradation for the proposed signalling schemes. To avoid repetition, these simulation results will be shown in Chapter 5.

Compared to the system with fixed modulation, a system improvement is achieved if the system with adaptive modulation and explicit signalling shows a better PER performance. To avoid repetition, the performance evaluation in terms of PER will be provided in chapter 5, where all system scenarios are compared with each other: namely adaptive modulation with perfect knowledge about the adapted modulation at the receiver, explicit signalling, automatic modulation classification and fixed modulation. To ensure a fair comparison, the net data rate has to be constant for all scenarios.