Advanced Wireless Networks - 4G Technologies

118 ADAPTIVE AND RECONFIGURABLE LINK LAYER

where

¯

d = ∂ Rc = rT diag(YQTΠ) (4.28)

∂τe

is the drift of the average goodput from the ideal conditions due to the estimation delay. Replacing Q in Equation (4.28) it is easy to see that the explicit expression of d is:

4.1.13 Feedback process and acquisition errors

To identify a PHY mode, a control message with log2 M bits is used. The distance in bits among all pairs of codewords is given by the elements of a symmetric matrix having null elements on the diagonal, and defined by

n=1

where wi(n) is the nth bit of the ith codeword and denotes the modulo 2 bit-wise product of the codewords. The element of matrix H(f) is then given by:

where pe,r,f is the residual bit error probability in the feedback channel. Parameter pe,r,f is a function of channel coding gain and SINR through the bit error curve of the uncoded system for the given modulation, and is given by pe,r,f = pe(f)[Gc(γ )γ ].

One way of coding mode identifiers is adopting the Gray code. Assume that the message is transmitted always using the strongest mode, BPSK-1/2, in our case, but the error probability depends on the actual channel state. The error rate does depend on the state of the feedback channel. Under the assumption of symmetric channel, the channel state at control message transmission time is assumed to be the state of the direct channel τe before transmission time, i.e. the state at estimation time. Under this assumption, the delay in the adaptation chain is concentrated in the estimation delay model. With these assumptions, it is seen that the effect of feedback errors is negligible. Therefore, less relaxed assumptions on this feedback error model might not lead to very different results. In fact, as it is shown in Figure 4.8, in which the BER in the feedback channel pe(f) is assumed fixed and independent of the state of the direct channel, the impact is no longer negligible only for values of pe(f) so large as to be out of range in adaptive systems and often in communications systems in general.

4.2 ADAPTIVE TRANSMISSION IN AD HOC NETWORKS

The adaptive-transmission protocol described in this chapter is intended for mobile packet radio networks (PRNs), in which half-duplex radios employ direct-sequence spread spectrum (DS-SS). PRNs are examples of the ad hoc networks described in detail in Chapter 13. One of the key features of such networks is the lack of a fixed infrastructure or central controller to determine the power levels, code rates and other transmission parameters that

Figure 4.8 Sensitivity of average goodput to errors in the feedback channel. In this figure, the residual BER in the feedback channel is assumed fixed and independent of the state of the direct channel. The impact is no longer negligible only for values of pe,r,f so large to be out of range in adaptive systems and often in communications systems in general.

should be used by the terminals in the network. The adaptive-transmission protocol is a fully distributed protocol that determines the transmission parameters for a communication link from statistics obtained in the receiver on the link.

The receiver includes an automatic gain control (AGC) subsystem, one or more programmable matched filters (with different processing gain), a soft-decision decoder, and a subsystem that generates a postdetection signal quality (PDSQ) statistic. Three statistics, which can be derived in each receiver, are used to decide on the receiver configuration.

The PDSQ statistic is based on the output of the matched filter. It represents the desired signal level. In general this statistics can have high s(h) or low s(l) value. The symbolerror rate (SER) statistic is determined from an error count that is derived in the decoding subsystem. The error count can be obtained by re-encoding the information bits at the output of the decoder and comparing the encoded symbols with hard decisions that are based on the corresponding outputs of the matched filter. SER can have high e(h) or low e(l) value. The AGC statistic is an estimate of the total received power that indicates the level of interference and can have high i(h) or low i(l) value. Using a combination of the PDSQ, SER, and AGC statistics, the receiver selects the transmission parameters for the next packet, and it sends this information to the transmitter in an acknowledgment packet or as part of the exchange that occurs if a reservation protocol is used for channel access (e.g. in a clear-to-send message). The PDSQ, SER, and AGC statistics derived in the receiver

120 ADAPTIVE AND RECONFIGURABLE LINK LAYER

provide the only CSI that is available to the adaptive-transmission system. The transmission parameters that are adapted are the power level, spreading factor and code rate. As part of the design process for the adaptive transmission protocol, a set of thresholds, referred to as the adaptation thresholds, must be chosen. More details on statistics measurements and the threshold selection can be found in Block and Pursley [35]. The adaptive-transmission protocol uses the thresholds in conjunction with the AGC, PDSQ and SER statistics from past receptions to determine the transmission parameters for the next packet transmission.

A combination of measured values s( ) e( ) and i( ) is used in the adaptation algorithm to increase I ( ), decrease D( ) or not to change N ( ), the code rate R, power level S or processing gain G. NI( ), for example, represents the action ‘not change’ or ‘increase’ the parameter where ‘not change’ is the first choice that will be used in the first following packet. If the performance with the first choice is not satisfactory, the second choice will be used in the next transmission. Only one parameter is changed in the next transmission interval.

In general, the goal is to keep S low (save energy and minimize multiple access interference) and R high (minimize redundancy and maximize the throughput). High G would improve interference suppression but at the same time reduce the throughput for the fixed chip rate. Some examples of the control action given the measured statistics are:

(1)s(l), e(l), i(l) I(R), D(S), D(G)

(2)s(l), e(h), i(l) ND(R), NI(S), N(G)

(3)s(l), e(h), i(h) ND(R), NI(S), I(G)

Extension of the control rules to other combination of the measured statistics is straightforward.

The results shown in this section are for a communication system with binary differential phase-shift key (PSK) data modulation and binary DS-SS. Error correction is achieved with binary convolutional coding and soft-decision Viterbi decoding. Convolutional codes of rates 1/2 and 3/4 are available to the adaptive-transmission protocol. The code of rate 1/2 has constraint length 7 and minimum free distance 10.

For performance results, the spreading sequence is a maximal-length linear-feedback shift-register sequence of period 1023. An interfering signal, if present, uses a different m-sequence of length 1023. The spreading factors available to the adaptive-transmission protocol are 32, 64 and 128, and the number of information bits per packet is fixed at 1000. For the results, each simulation concludes after 50 000 packets are demodulated and decoded correctly. The sampling interval for the PDSQ statistic is t0 = Tc (chip interval).

The channel model incorporates range attenuation, shadow loss, MAI, and multipath propagation. Each of these four characteristics may be fixed or time-varying. For our purposes, a Markov channel is a communication channel for which at least one characteristic is time-varying, and each time-varying characteristic is modeled as a discrete-time Markov process. The Markov model for range attenuation is illustrated in Figure 4.9 [35], and the Markov model for the loss due to shadowing is illustrated in Figure 4.10. The model for the interference caused by other transmissions in the network consists of the two Markov chains, illustrated in Figure 4.11. Finally, each multipath component is modeled by the Markov chain in Figure 4.12. Each Markov chain may change states from one packet transmission to the next, but the state is assumed to be constant over the duration of the packet transmission.

Dmax

Dmax-1.5

Dmax-3

Dmax-4.5

•

•

•

Dmin+4.5

Dmin+3

Dmin+1.5

Dmin

Figure 4.9 Markov chain for range attenuation. All transition probabilities are p = 0.05.

Because a Markov channel is represented by one or more finite-state Markov chains, each of which has multiple states, it is actually a collection of a number of different channels. Such a collection is referred to as a channel class. The channel class denoted by C1 consists of the collection of all channels for which there is no shadow loss, multipath or MAI. For class C1, the only channel characteristic that has multiple states is the range loss, which takes values from Dmin to Dmax in steps of 1.5 dB, as illustrated in Figure 4.9. The values for

Dmin and Dmax for class C1 are 89 and 137 dB, respectively. Each of the other five channel classes also has multiple states for the range loss, but the values for Dmin and Dmax are different (see Table 4.2). The transmitter has six power levels arranged in steps of 6 dB.

In the model, the minimum power level provides an SNR of Ec/N0 = 0 dB at the receiver if the propagation loss is 90 dB. The parameter Ec is the received energy per chip for the desired signal. The value 0 dB is referred to as the reference value for Ec/N0, and 90 dB is the reference value for the propagation loss. If the chip rate is 16 Mchips/s, Ec/N0 = 0 dB gives S/N0 ≈ 72 dB, where S is the received power for the desired signal. If the transmitter uses its maximum power level and the propagation loss is 137 dB, the maximum value for class, then the SNR at the receiver is Ec/N0 = −17 dB. The maximum power level is 30 dB above the minimum power level, and the maximum propagation loss is 47 dB greater than its reference level, so Ec/N0 is 17 dB less than its reference value. Class C2 has variable shadow loss in addition to variable range attenuation. Each state is identified by its corresponding shadow loss, Si , 0 ≤ i ≤ 2, as illustrated in Figure 4.10. The value of S0 is 0 dB, and the values of S1 and S2 for class C2 are 10 and 20 dB, respectively, as shown in Table 4.2. Shadow losses of 20 dB or more have been observed in urban environments (see Chapter 3). The transition probability from Si state to Sj is denoted by Pi j . The values of the transition probabilities are also given in Table 4.2.

Notice that Dmax, the maximum range loss, is reduced from 137 to 117 dB in going from class C1 to class C2. The reason for this is to have the same maximum value for the total propagation loss for the two classes. In this way, the same set of transmitter power levels is appropriate for both classes. If we were to keep the maximum range attenuation at 137 dB and allow a maximum shadow loss of 20 dB, then the maximum transmitter power would have to be increased by 20 dB to provide the same SNR for the worst channel in the class. Because the minimum power level should remain the same in order to provide the same SNR for the best channel in the class, either the step size or the number of steps would have to be increased. It is more meaningful to keep the transmitter capability the same for different channel classes.

Channel class C3 has intermittent MAI. The strength and spreading factor for the interference are governed by the Markov chains illustrated in Figure 4.11, where Ec,i denotes the energy per chip for the interference signal. The model for the interfering signal includes the use of a rate- 12 code, so the spreading factor determines the duration of the interference.

124 ADAPTIVE AND RECONFIGURABLE LINK LAYER

The maximum range attenuation is adjusted so that the maximum transmitter power can provide an adequate packet-error probability for the worst channel in the class, which corresponds to the maximum MAI and a range attenuation of 129 dB, the value of Dmax shown in Table 4.2.

Multipath is present in channel class C4 in addition to the primary signal. The strengths of the different multipath components relative to the primary component are controlled by independent Markov chains, each having the form shown in Figure 4.12.

The delays of the multipath components relative to the primary component are chosen randomly and without replacement from the set {nTc; 1 ≤ n ≤ 150} (i.e. no two components have the same delay). The adaptive protocol is compared with a protocol that has fixed transmission parameters and a protocol with perfect CSI (channel state information). As the name implies, the latter protocol is always told the state of the channel for previous packet receptions, and so it is a model for an adaptive-transmission protocol that is perfect in its channel measurements and estimates of the channel state. Note that perfect knowledge of the past states does not imply perfect knowledge of the channel state for the next transmission, thus, the results for the protocol with perfect CSI do not provide an upper bound on the performance of adaptive-transmission protocol. The protocol with perfect CSI chooses the transmission parameters according to the channel state that was in effect during the most recent reception.

Each of the three protocols attempts to maximize the throughput efficiency, subject to constraints on the packet-error probability. The throughput efficiency, a measure of the throughput per unit energy, is defined as the ratio of the number of packets successfully received to the total energy expended. The constraint on average packet-error probability is PE ≤ 0.05. In some circumstances, the protocols may be able to improve the throughput efficiency by tolerating large numbers of errors in very poor channel conditions, while still meeting the constraint on PE. However, this is unfair, in the sense that the protocol would not provide an average packet-error probability of 0.05 over a time interval in which the channel state was very poor. To avoid this, it is required that each protocol adapt the parameters in order to provide a packet-error probability of 0.05 or less for each channel in the class. Note that meeting the latter constraint does not ensure that the former constraint is also met. For example, after a change in channel state, the error rate may be high until the protocol has adapted all parameters to the new state. The performance comparisons are for two scenarios. In the first scenario, each of the three transmission protocols knows the channel class but not the current channel state. The protocol with perfect CSI is told the state of the channel for the previous transmission, but the other two protocols are not given any information about the previous channel state. Each protocol chooses its transmission parameters in the best way for the given channel class. For example, the protocol with fixed transmission parameters uses the minimum power level, minimum spreading factor, and maximum code rate that provide the required packet-error probability for the worst channel in the given class. Similarly, the adaptive-transmission protocol uses the adaptation thresholds that are best suited for the given class.

In Figure 4.13, the throughput efficiency of each protocol is shown for each class. As expected, the protocol with fixed transmission parameters performs substantially worse than the protocols that adapt the transmission parameters. The protocol with perfect CSI has slightly better performance than adaptive-transmission protocol for classes C3, C4, and C5. For the remaining classes, the two protocols give nearly the same performance. Even though classes C1 and C2 have the same worst-case propagation loss, the results in Figure 4.13

since: (1) without proper error protection of the header, it would be of no help to apply any error control on the user data; and (2) the MAC header is also part of the data link layer. More discussion on adaptive frame length and coding can be found in References [36–39]. Three error-control schemes (referred to as FEC1, FEC2 and FEC3) are considered depending on: (1) how many RS code segments are used for each packet; and (2) how a packet with uncorrectable errors is retransmitted. The computation complexity of an error-control scheme is closely related to battery power consumption. Encoding/decoding processes with RS codes are known to consume substantial battery power. In this chapter we use the central processing unit (CPU) time for encoding/decoding of an RS codec implementation as the measure of computational complexity. While the actual complexity of the RS code will depend on a particular implementation, it is believed that the CPU time measurement can be a good reference. The three schemes are compared in terms of throughput performance and computation complexity.

4.3.1 RS codes

For the error control of user data, (N , K , q) RS codes over GF(q) are used, in which the codeword size N ≤ q − 1 and the number of information symbols K < N . A q-ary symbol is mapped to b bits, so q = 2b. RS codes are known to have the maximum error-correction capability for given redundancy, i.e. a maximum distance separable (MDS) code. For an (N , K , q) MDS code, the minimum distance dmin is determined as dmin = N − K + 1, where the error correction capability t = (dmin − 1)/2 = (N − K )/2, i.e. any combination of t symbol errors within N symbols can be corrected. The code rate rc is defined as rc = K/N . One can easily see that the more parity symbols (i.e. larger N − K ), the better error-correction capability. RS codes are also known to be efficient for handling bursty errors. For example, with (N , K , 2b) RS code with the error correction capability t, as many as bt bit errors can be corrected in the best case when all of b bits in each of bt-bit symbols are erroneous (i.e. bursty errors). However, only t bit errors can be corrected in the worst case when only one bit in each of tb bit symbols is erroneous (i.e. nonbursty errors). Originally, the codeword size of (N, K , q) RS code is determined to be q − 1. However, a shorter codeword can be obtained via code shortening. For example, given an (N , K , q) code, K − s information symbols are appended by s zero symbols. These K symbols are then encoded to make an N symbol-long codeword. By deleting all s zero symbols from the codeword, we can obtain (N − s, K − s) code. For decoding this shortened code, the original (N, K ) decoder can still be used by appending zero symbols between K − s information symbols and N − K parity symbols. Shortened RS codes are also MDS codes. Code shortening is especially useful for transmitting information with less than K symbols.

4.3.2 PHY and MAC frame structures

In this segment parameters of the popular WaveLAN modem are used. PHY and MAC overheads of the WaveLAN are shown in Figure 4.16 [40]. In WaveLAN, no error-correction coding is implemented; only the CRC code for error detection is used. In this section the MAC frame structure is modified as shown in Figure 4.17 for error-control schemes. First, the MAC header size is increased by one byte. This additional byte is used to give the