Adaptive Link Adaptation

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Adaptive Link Adaptation Fei Tang‡ Luc Deneire Marc Engels Marc Moonen¶ Interuniversity Microelectronics Center (IMEC) Kapeldreef 75, B-3001, Leuven, Belgium E-mail: [email protected]

Abstract—Link Adaptation (LA) can significantly increase the spectral theoretical possibility and gain of ALA, then verify the theoret- efficiency and render various levels of services, both of which are highly ical results by simulations. Using these results as a feedback, desirable for today’s high-speed communication systems. Although optimality can be ensured through careful designing for a fixed link con- we also device a simple and practical ALA update algorithm. figuration, due to changes of available power, data rate, and especially channel statistics, it is better to adapt the adaptation scheme per se in real II. SYSTEM MODEL AND CHARACTERIZATION PROCESS time. We term this technique as Adaptive Link Adaptation (ALA). Based on our previous work on a general optimal link adaptation scheme for a This section gives the framework of an adaptive system as certain configuration, we continue to investigate the problem of adapting well as the definitions of the most important system parameters the adaptation scheme online. This paper first recapitulates that general used in the optimization problem. For simplicity, we will only optimal link adaptation scheme, then gives the theoretic basis of ALA, treat ALA in the SISO, single carrier and single service case. and finally presents a simple yet working implementation of the update algorithm for ALA. Both theoretical and simulation results indicate the viability of ALA and an 18 dB gain can be achieved for the investigated A. Block Diagram of a SISO Adaptive System simple scenario. With low complexity, optimality, and generality, the proposed ALA provides a promising technique to substantially increase the The general structure of an SISO adaptive system is depicted spectral efficiency of practical communication systems. in Fig. 1. The receiver monitors the channel condition in real time and feeds it back to the transmitter. The transmitter de- cides whether to switch to a new mode of coding, modulation, I. INTRODUCTION spreading and power while ensuring a perceived quality of ser- To satisfy the ever-increasing demand for high-speed data vice. When doing this, under a given fixed bandwidth B, the services in today’s communication systems under bandwidth transmitter tries to maximize the throughput under the aver- and power constraints, we have to push the spectral efficiency age power constraint or vise versa. We address data services, to the extreme. In stead of designing the system according to which are insensitive to delay and can be of variable rate. As the (average) worst case, we can apply link adaptation to better a consequence, the perceived quality is related to the BER or utilize the instantaneous capacity as actual wireless channels the Frame Error Rate (FER) and we try to maintain a constant are time-varying and frequency-selective. Also as an important instantaneous BER or FER. by-product, an adaptive system can easily provide services of In practice, except for some reciprocal channels, in which different quality such as different BERs. the transmitter can also estimate the channel fading and inter- Link adaptation attracted a lot of attention recently. Some ference of the receiver side, the symbol by symbol adaptation previous papers [1], [2], [3], [4], [5] showed significant gains is hardly possible. We take a block by block adaptation ap- by using specific adaptive techniques. Currently a few ex- proach. The length of the block is the update period of the pre- isting and emerging wireless systems like IS-95B, WCDMA, dicted channel condition for the next block, which is mainly CDMA2000, HiperLAN/2 and (E)GPRS of GSM have already restricted by the feedback and processing delays. Actually, introduced some kind of rate adaptation [6]. However, pre- the channel condition may vary within one block. We use the vious work mostly focused on adaptive modulation and the channel quality q, which is average SINR-like to represent the flat-fading channel, and did not provide a general, yet practi- aggregated channel condition of the whole block. The SINR, cal and optimal adaptation scheme regardless of the underlying channel quality q, and signal quality qs are defined as: coding, modulation and channels. In most case while perfor- × α × α mance bounds are given, insight into how to do precise optimal = P p r = Es , SINR + + (1) switching between different working modes is seldom treated. N I N0 I0 Besides, these schemes are predetermined and fixed. If the channel changes, or power budget and data rate are changed, α × α q = F ( p r ), q = q × P, (2) the schemes are not appropriate anymore. aver N + I s In this paper, we address the problem of adapting the adaptation scheme on the fly. As a continuation of our previous work where P is the transmitted power, Es is the received symbol α on a general optimal link adaptation scheme [7], we present the energy, p is the fading component which we can track and predict and is constant within one block, αr is the residue fad- ‡ Also a Ph.D. Student at E.E. Dept., ESAT/INSYS, K.U.Leuven ing component which is too fast to predict and usually much ¶ Professor at E.E. Dept., ESAT/SISTA, K.U.Leuven smaller than component αp, N is the additive noise and I is the

Data Buffer

Data Adaptive Wide-band Demodulation Equalizer Buffer Techniques Fading Channel & Decoding Power

Tansmitter Channel Receiver

Fig. 1. Adaptive SISO System Model possible interference which has the same property as the addi- A. Optimal Adaptation Scheme tive noise, N and I are the power spectrum densities of the 0 0 The capacity of a time varying channel is maximized by noise and interference respectively, F is some kind of aver- aver performing “water pouring” filtering of power in the time do- age function which is used to extract only one value to repre- main [1]. However there is little loss in capacity when using sent the channel condition of the whole block. The channel is the constant power and variable rate strategy. But for practi- not restricted to be flat-fading. For non-flat-fading wideband cal coding and modulation schemes, the rates are discrete. So channels, the extended ones, including the equalizer, are used. we need power control to fill the “gap” between them. As indi- The channel does not have to be stationary, but first we will cated in [9], power adaptation can provide about 0.5bit/symbol assume that the distribution of channel quality p(q) is static. additional throughput. Therefore we choose the optimal vari- B. Characterization Process and Mode Selection able power and variable rate strategy. For a practical system, the simple water pouring filtering does not work since 1) the When there are several adaptive techniques like adaptive rates are discrete; 2) the performance of each mode has a dis- coding, adaptive modulation and spreading, a multitude of tance to channel capacity. However there is one necessary con- combinations among them exist. The characterization process dition for optimality learned from “water pouring”: allocate tries to extract from these candidate working modes the re- more bits when the channel condition is good. Therefore it is quired signal quality qs for the above block by block approach. easy to formulate the following optimization problem to max- For a target BER (FER), we try to find a required signal qual- imize throughput with an average power budget Pb: ity threshold th for each possible combination. Since we can α α only predict the p component and compensate it, r compo- N xi+1 nent still exists. Thus if we try to determine the threshold by f : min− ∑ R(i)p(q)dq, (5) x simulation, then the artificial channel for simulation should be i=1 xi the one with noise N, interference I and any uncompensated subject to fading component αr. The simplest case is that the fading is constant within one block. In this case, this artificial channel N xi+1 th(i) is AWGN. g : ∑ p(q)dq− P ≤ 0, (6) 1 q b A fair criterion to evaluate the performance of candidate i=1 xi modes is their respective spectrum efficiency. If we plot all candidate modes in the “Spectrum Efficiency R vs. Signal g ,···, + :0< x ≤ x ···x ≤ x + ···≤x . (7) Quality thresholds th” graph and link points to form the upper 2 N 1 1 2 i i 1 N outline of all points which is monotonously increasing, modes In this problem, different modes with rate R(i) correspond (M(i),i = 0,···,N) corresponding to the upper outline are the to different non-overlapping floating regions of the channel selected ones. And for th and R,wehave: quality q. We try to find the optimal boundaries xi between th(i) < th(i + 1), R(i) < R(i + 1), i = 0,···,N − 1, (3) them. From xi to xi+1 (i = 0,···,N − 1, xN+1 =+∞), the system works in mode i. Within each region, the power may be th(0)=0, R(0)=0. (4) adapted to maintain the signal quality constant at the threshold th(i). In order to fit into a general optimization format, III. ADAPTIVE LINK ADAPTATION we minimize the negative of the throughput. Before moving This section recapitulates the general optimal scheme pro- on, we give two important theorems [10]. Note that ∇ is the posed in [7], [8] and presents the theoretical basis of ALA. gradient operator.

1263 Theorem 1 (Kuhn-Tucker Theorem) Consider the constrained know the channel quality distribution or it’s not mathemati- optimization problem cally tractable. So we prefer to adapt the adaptation scheme per se on the ﬂy and this boils down to adapt the t parameter. min f (x), (8) x The ALA system is initialized with a t value based on known knowledge of the channel and will do the general link adapta- subject to tion. But it will update the adaptation scheme if the knowledge of the channel is not perfect or whenever the channel statistics, ( ) ≤ , = ,···, , ( )= , = ,···, . gi x 0 i 1 m h j x 0 j 1 l (9) required power or rate changes. This update process can be done iteratively. = { | ( )= } ( ∈ ) x is an interior point, I i gi x 0 , f and gi i I are dif- The actually used power is ferentiable continuously at x, vectors{∇gi(x),∇h j(x)|i ∈ I, j = ,···, } N 1 l are linearly uncorrelated. If x is a local optimal so- ci+1t th(i) lution, there exist non-negative w (i ∈ I) and v ( j = 1,···,l) P = ∑ p(q)dq. (13) i j q which statisfy i=1 cit

l Taking partial derivative of power P over t,wehave ∇ f (x) − ∑wi∇gi(x) − ∑ v j∇h j(x)=0. (10) ∈ = ∂P N th(i − 1) −th(i) i I j 1 = ∑ p(c t). (14) Theorem 2 (Global Optimality Theorem) If f and g (i ∈ I) ∂ i i t i=1 t are convex functions, h j( j = 1,···,l) are linear functions, and the Kuhn-Tucker condition is satisfied at x, x is a global solu- Thus we obtain the relationship of small variation of t and P at tion. the optimal point, i.e. Assuming g2,···,N+1 are not active, i.e. 2,···,N + 1 are not in I, applying the Kuhn-Tucker condition only with f and con- N th(i − 1) −th(i) t = sP, with s = 1/ ∑ p(c t). (15) traint g ,wehave∇ f = t∇g ,(t ≥ 0), we can get one local i 1 1 i=1 t minimum solution: Step size s is negative. It is reasonable, since a small decrease ( ) − ( − ) = , = th i th i 1 , = ,···, . of t from the optimal one will cause high rate modes to be used xi tci with ci ( ) − ( − ) i 1 N (11) R i R i 1 more frequently which translates into a small increase of actual used power. We use the method of steepest descent. 1) In With x and (3), we can verify that our initial assumption is i tracking mode, when t is near optimal, from (15), interestingly, satisfied. Indeed constraints g ,···, + are not active. Both the 2 N 1 we only need the discrete values of p(c t) i = 1,···,N, (not Hesse matrices ∇2 f and ∇2g are half positive definite, there- i 1 the whole distribution information) to calculate the step size fore f and g are convex functions. So a local minimum solu- 1 s, and arrive at the optimal t almost perfectly by adding t tion is also a global one. Substitute (11) into (6), and change to it. 2) When t is distant from the optimal one, we can not ≤ to equal, we can obtain the parameter t by solving this one- get the optimal one simply by adding t. However, we can variable equation: arrive at a local optimal point of t recursively as long as the step N size is negative and small enough. From the Global Optimality ci+1t th(i) ∑ p(q)dq = P . (12) Theorem, we know it is also a global one. q b i=1 cit Therefore, the ALA update algorithm works like just one So here, we prove that the determination of the optimal tap of of a classic adaptive LMS system, but with some dif- boundaries can be transformed into a one-dimensional prob- ferences. The actually used power block by block is first low- lem. The dual problem of minimizing the power under the passed to filter out the DC component. At iteration n, current average constant rate constraint can be obtained by switching used power Pn is subtracted from the budget power Pb and this (5) and (6). One important observation of (11) is that the op- error is multiplied by the step-size s to adapt t, and hence the adaptation scheme. As the above treatment, we can also build timal switching boundaries xi have a simple linear relationship regardless of channels, modulation and coding. And they are a ALA system for the dual problem with the constant average rate constraint. all proportional to t with a constant ci which is equal to the threshold error over rate error of neighboring modes. Discus- IV. NUMERICAL AND SIMULATION RESULTS sion of extensions to multicarrier, multiservice and MIMO systems can be found in [8], [11]. A. Setup For mathematical tractability, we assume the simplest sce- B. Update Algorithm of Adaptive Link Adaptation nario: M-QAM with constellation size of 2,4,16,64 is used; In reality, the channel is non-stationary and the statistics the channel is assumed to be Rayleigh or Ricean fading with may change over time. Even it does not change, we may not only additive white noise and different normalized Doppler

1264 8 8 Channel Capacity Capac−Rayleigh 7 Theotetical Optimal Scheme 7 Capac−Ricean k=0 dB Simu−F =0.1 d Capac−Ricean k=0 dB Simu−F =0.01 Capac−Ricean k=6 dB 6 d 6 Non−Adaptive BPSK Thput−Rayleigh Thput−Ricean k=0 dB 5 5 Thput−Ricean k=3 dB Thput−Ricean k=6 dB 4 4

3 3

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1 1 Spectral Efficiency (Throughput) (bps/Hz) Spectral Efficiency (Throughput) (bps/Hz)

0 0 5 10 15 20 25 4 6 8 10 12 14 16 18 20 22 24 Average SNR of Rayleigh Channel Average SNR

Fig. 2. Performance of Optimal Scheme and Non-Adaptive scheme Fig. 3. Performance in Ricean and Rayleigh Channels

1.5 Frequencies; budget power is normalized to one; for simplic- Rayleigh 1.4 Ricean k=0 dB ity, the block length is the symbol period; perfect knowledge of Ricean k=3 dB 1.3 channel quality, the SNR, is assumed. With target BER being Ricean k=6 dB 10−3, the rates and thresholds are summarized in Table I. 1.2 1.1 B. Performance of ALA 1

The performance of the general optimal LA scheme is sum- Parameter t 0.9 marized in Fig. 2 and Fig. 3. From Fig. 2, we observe a 0.8 18 dB gain when compared with non-adaptive BPSK in the 0.7 Rayleigh case. Simulation results also confirm the theoretical 0.6 performance curve under different Doppler Frequencies. As 0.5 we use the above simple scenario, the situation is reduced to 4 6 8 10 12 14 16 18 20 22 24 Average SNR that of [1]. Both results are comparable. Actually we do not need a common BER approximation as [1] did to derive the Fig. 4. Behavior of Parameter t optimal adaptation scheme. Instead, we use more accurately evaluated thresholds th values. Our result are slightly better than that of [1], about 0.1 to 0.3 more bps/Hz at various aver- stands for throughput while P for used power. The original age SNR values. average power is normalized to 1 (0 dB). In stead of quantifying the possible additional gain from For system 2, we can find from the curve of Ricean channel ALA, we try to find the possible loss in case of not adapting with k = 6 dB in Fig. 3, that the point with rate of 5.4015 corre- the scheme. But first we give the behavior of parameter t in sponds to average SNR of 22 dB, which equals to (19 + 3) dB. various Rayleigh and Ricean channel conditions in Fig. 4. (An So case 2 works optimally with the wrong t value and there is explanation of such a behavior can be found in [8].) Channel 1 no additional gain at all from adapting the adaptation scheme. (Rayleigh channel with average SNR of 7 dB) and channel 2 The same situation holds for the system 1. This is not surpris- (Ricean channel with Ricean factor k = 6 dB and average SNR ing since as long as the linear relationship between switching of 19 dB) are considered. There are two systems, system 1 and boundaries is hold, the scheme is always optimal. This ex- system 2, which have optimal adaptation schemes for channel 1 ample reiterates the importance of maintaining (11). However and channel 2 respectively. Table II summarize the numerical sticking to a wrong t value may severely violate the power bud- results before and after switching their t values. R in bps/Hz get or reduce the rate significantly.

TABLE I TABLE II RATE AND THRESHOLDS OF QAM NUMERICAL RESULTS OF SWITHING THE t VALUES Contellation Size 0 2 4 16 64 Orig. t Orig. R Switched R Switched P Rate R (bps/Hz) 0 1 2 4 6 System 1 0.6537 1.1276 0.3880 -7.25 dB Threshold th (dB) 0 7.04 10.80 16.70 22.70 System 2 1.4280 4.3468 5.4015 3dB

1265 V. A WORKING IMPLEMENTATION OF ALA 1.5 1.4 Again the above two channels in subsection IV-B are used for the simulation of ALA update algorithm. Channels begin 1.3 with their respective initial optimal t and are applied with the 1.2 counterpart channel model in simulation to iteratively update t. 1.1 However the direct implementation of ALA proposed in sub- 1 section III-B is not successful as the t value can not converge. 0.9

This problem is solved by using the following two tech- Parameter t Value 0.8 niques: 0.7 Modified Low-Pass filter One cause of the problem is the nor- mal low-pass filter. Since any change in the filtered power will 0.6 0.5 cause t to change and hence the adaptation scheme. And this 0 20 40 60 80 100 120 140 160 180 200 will substantially affect the subsequent used power and thus the Iteration Numbers filtered power. So the filtered power is fluctuating and the sys- Fig. 5. Convergence Characteristics of the ALA Implementation tem can easily be unstable. In order to estimate the DC component more reliably, we prefer to keep the adaptation scheme constant when doing this. So we choose to average a set of VI. CONCLUSION AND FUTURE WORK incoming block power Pbl, i.e. Based on a general optimal link adaptation framework, we ∑Sz 1 Pbl L propose a novel technique termed adaptive link adaptation. In- Pflt = , with Sz = . (16) Sz FDoppler sight into how to do precise mode switching is revealed and the feasibility of the ALA scheme is confirmed by a practical

Sz is normalized with Doppler Frequency FDoppler. This is rea- working implementation. Future work will try to improve the sonable as a fast changing channel corresponds to a small Sz. practical update algorithm by considering RLS-like approach. While in slow changing channels, a large Sz will eliminate pos- With low complexity, optimality and generality, the proposed sible false alarms of statistics changes. The L is introduced to ALA provides a promising technique to substantially increase guarantee that Pbl of L periods of FDoppler are collected. How- the spectral efficiency of communication systems. ever too large L will cause a slow system response. Using simulation as a feedback, a good compromise is L = 10. REFERENCES [1] Andrea J. Goldsmith and Soon-Ghee Chua, “Variable-rate variable- power MQAM for fading channels,” IEEE Trans. Commun., vol. 45, Variable Step Size Another cause is the fixed step size. If a no. 10, pp. 1218–30, Oct. 1997. system already works at the optimal parameter t, then the it- [2] Krishna Balachandran, Srinivas R. Kadaba, and Sanjiv Nanda, “Channel erative process should not alter the current value of t. This quality estimation and rate adaptation for cellular mobile radio,”IEEE J. Select. Areas Commun., vol. 17, no. 7, pp. 1244–56, July 1999. usually results in a very small step size s. So the convergence [3] Mohamed-Slim Alouini, Xiaoyi Tang, and Andrea J. Goldsmith, “An rate is very slow. Therefor we try to design a variable step size adaptive modulation scheme for simultaneous voice and data transmis- F sion over fading channels,” IEEE J. Select. Areas Commun., vol. 17, no. step defined as: 5, pp. 837–50, May 1999. [4] Dennis L. Goeckel, “Adaptive coding for time-varying channels using m IEEE Trans. Commun. Fstep = −β|P| . (17) outdated fading estimations,” , vol. 47, no. 6, pp. 844–55, June 1999. [5] Jeff M. Torrance and Lajos Hanzo, “Latency and networking aspects of When t is near the optimal point and P is small, the function adaptive modems over slow indoors Rayleigh fading channels,” IEEE absolute value is small. Otherwise it is large. So at iteration n, Trans. Veh. Technol., vol. 48, no. 4, pp. 1237–51, July 1999. [6] Sanjiv Nanda, Krishna Balachandran, and Sarath Kumar, “Adaptation t is updated as techniques in wireless packet data services,” IEEE Commun. Mag., vol. 38, no. 1, pp. 54–64, Jan. 2000. m+1 [7] Fei Tang, Luc Deneire, and Marc Engels, “On the optimal switching t = t − − β|P| . (18) n n 1 scheme of link adaptation,” in Proc. IEEE 22st Symposium on Informa- tion Theory in the BENELUX, May 2001, pp. 69–76. Considering implementation easiness, we choose m = 1 and a [8] Fei Tang, Luc Deneire, Marc Engels, and Marc Moonen, “A general op- . β timal switching scheme for link adaptation,” Proc. IEEE VTC FALL’01, very conservative value of 0 3 for to ensure stability. Oct. 2001, in press. Fig. 5 is the convergence characteristics of a system with [9] Cenk Köse and Dennis L. Goeckel, “On power adaptation in adaptive sigaling systems,” IEEE Trans. Commun., vol. 48, no. 11, pp. 1769–73, initial value of t for channel 1 while applied with channel 2. Nov. 2000. We see this practical implementation is working well. After [10] M. Avriel, Nonlinear Programming: Analysis and Methods, Prentice- 100 iterations, the relative error for t is less than 2%. Since we Hall, Englewood Cliffs, New Jersey, 1976. β [11] Fei Tang, Steven Thoen, Luc Deneire, and Marc Engels, “Adaptive use a very conservative value, there is no overshooting in the link adaptation for multicarrier systems,” Proc. IEEE ICWLHN’01, Dec. convergence process. 2001, in press.

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