Adaptive Modulation and Coding for Turbo Receivers in Space-Time BICM C´esar Hermosilla and Leszek Szczeci´nski Institut National de la Recherche Scientifique INRS-EMT Montreal, Canada {hermosil,leszek}@emt.inrs.ca Abstract— Adaptive modulation and coding (AMC) consists in adjusting the transmission parameters according to the channel state which affect the performance of the receiver. Practical implementation of the AMC is commonly done in scalar channels, where the signal to noise ratio characterizes sufficiently well the quality of the transmission. In this paper, we propose to use the AMC in matrix (MIMO) channels with the receiver employing the iterative (turbo) processing. Such solutions were not yet proposed in the literature due to the lack of appropriate performance evaluation tools. In the paper we employ the recently proposed method based on the so-called EXIT analysis, which was shown to predict accurately the performance of the turbo receivers. The numerical results obtained in the space-time bit-interleaved coded modulation MIMO transmission indicate that the throughput obtained exceeds considerably a non-adaptive transmission, and approaches the optimal water-filling solution.

I. I NTRODUCTION Transmission over wireless channels suffers, among many impairments, from the fading which imposes severe limits on the achievable data rates. To exploit efficiently the timevarying fading channel, the transmitter should adjust its modulation and coding rate [defining the so-called modulation and coding set (MCS)] on the basis of the channel state information (CSI), i.e., the set of parameters characterizing well the quality of the transmission. The main issue in such adaptive modulation and coding (AMC) schemes is to translate the CSI into a transmission-performance metric [1–3]. Commonly, the transmitter chooses the MCS depending on the signal to noise ratio (SNR), which defines the performance measured by the bit- or block error rates (BER/BLER). The AMC has been already adopted in practice, e.g., in the high speed downlink packet access (HSDPA) [4] or EDGE [5]. Independently of AMC, which palliates the effect of fading, a considerable effort was deployed to improve the performance of the receivers and make them robust against interference and/or noise. In particular, using the paradigm of iterative processing inspired by the vertiginous ascension of the socalled turbo codes [6], the iterative (i.e., turbo) receivers has been studied by many authors for interference-limited channels, yielding turbo equalizers [7, 8], turbo MIMO receivers [9, 10], or turbo MUD detectors [11]. In interference limited transmission the AMC becomes more cumbersome because the CSI cannot be reduced to a scalar Research supported by PROMPT Quebec

parameter such as the SNR, and is rather represented by the channel impulse response (in equalizers) or channel-matrix (in case of the MIMO transmission). Employing popular linearcombiner based receivers the performance evaluation is then not trivial but realizable (one can still use the SNR after the linear combining for the AMC). However, if iterative processing is applied, the number of iterations (limited by the available processing capabilities of the receiver) must be taken into account, which adds the new dimension quite difficult to analyze. Thus, it is not surprising that there is no work showing the AMC for the turbo-receivers1 . This is indeed a challenging problem because in order to have an operational AMC it is necessary to develop a suitable tool to characterize the behavior of iterative receivers for any channel state and number of iteration. Such tool, based on the EXIT method, derived from the EXIT charts [12], was recently proposed in [13], where the accurate evaluation of the BER of the iterative receivers with linear front-end was shown. The objective of this paper and its main contribution is, therefore, the demonstration that it is possible to implement the AMC when the receiver employs iterative processing. This was never shown before due to the lack of appropriate tools for the performance evaluation of such receivers. As a case under study we choose the so-called multipleinput multiple-output (MIMO) transceivers, where both the transmitter and the receiver are equipped with multiple antennas [14]. Such transceivers exploit the spatial dimension of the propagation environment and are believed to be a solution to the problem of increasingly scarce bandwidth in wireless transmission. We focus on the so-called space-time bit-interleaved coded modulation (S-T BICM) transmission [9, 10, 15] with pseudo-random interleaving of the data in time and space (among antennas), which offers a smooth transition between the robustness offered by the transmit diversity of the space-time codes [16] and the spectrally efficient transmission yield by pure spatial multiplexing [16]. Moreover, the S-T BICM allows to adjust modulation independently of the coding rate, which definitively is an asset for a flexible AMC system. The paper is organized as follows: in section II we introduce 1 Note that it is possible to use AMC in scalar channels when iterativelydecoded turbo-codes are used. But the reliability metrics calculated using the channel output are not affected by the iterations, therefore, such case should not be confused with turbo-receivers

1293 1-4244-0270-0/06/$20.00 (c)2006 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

η Transmitter

Channel H

+

MCS Adaptation

Receiver

MCS Selection

Fig. 2.

Model of transmission with AMC.

M1 [·]

c2

C,Π

. . .

Channel Estimation

Feedback Channel

Fig. 1.

c1

M2 [·]

cM

MM [·]

s1 s2 sM

S-T BICM transmitter based on vertical encoding.

Figure 1 shows the general system model where the receiver, using the estimated CSI, selects the most appropriate MCS and sends this information to the receiver via the feedback channel. The MIMO transmission is modeled as

focus on the functionality of the AMC when iterative receivers are used. The results in more realistic fading scenarios and the adaptation with outdated CSI (e.g., [18]) are under preparation. The above simplifications also ease the implementation through a block-fading model, i.e., the channel matrix H is assumed invariant during the transmission of the block of data, but independently varying among the transmissions of different blocks. The block-fading model makes meaningful the comparison with the quasi-ideal AMC obtained with socalled water-filling approach shown in Section IV. The CSI estimated at the receiver, and denoted by the pair N 0 ), is used to select the MCS, which should maximize (H, the expected throughput of the transmission calculated as

r(n) = Hs(n) + η(n)

T = β(1 − BLER),

the general system model. In section III the basics of EXIT analysis are presented and the principle of the AMC in MIMO S-T BICM transceivers is given. Section IV shows the numerical results and comparisons between the different systems proposed. Finally, we draw conclusions in Section V. II. S YSTEM M ODEL

(1) T

T

where the vector symbol s(n) = [s1 (n), . . . , sM (n)] ( denotes the transpose), is sent at time n through the N × M channel matrix H. Each element of H represents the channel gain between a pair of transmitting and receiving antennas. The observation vector r(n) = [r1 (n), . . . , rN (n)]T is corrupted by a zero mean noise vector η(n) with a covariance matrix E{η(n)η H (n)} = IN0 , where N0 is the power spectral density of the noise. The symbol (·)H denotes the conjugatetranspose operations, and I is the N × N unitary matrix. The signal sk (n), called also a data sub-stream is transmitted in blocks of length L, i.e., n = 1, . . . , L. Each element sk (n) is obtained via memoryless modulation, i.e., mapping of a codeword ck (n) = [ck,1 (n), . . . , ck,Bk (n)]T of length Bk into a constellation alphabet Ak = {αk,i : i = 1, . . . , 2Bk }, sk (n) = Mk [ck (n)]. Notice that every sub stream k can be mapped into a distinct constellation Ak . We assume that the bits ck,l (n) are independent for k = 1, . . . , M ; l = 1, . . . , B, and equiprobably drawn from the set {0, 1}. Consequently, the symbols sk (n) are independent and equiprobable. 2Bk Each constellation Ak has zero mean, i=1 αk,i = 0 , and B 2k |αk,i |2 = 1. has normalized energy 2−Bk i=1 L To obtain the sequence of codewords {ck (n)}n=1 the socalled Vertical Encoding (VE) is considered [14, 17], i.e., Q information bits are encoded with rate ρ by an encoder C, interleaved by Π, and then demultiplexed into M substreams, as depicted in Fig. 2. In what follows we assume that the receiver can instantaneously inform the transmitter about the selected MCS. This is also equivalent to saying that the channel is varying slowly enough so that the MCS selected during one transmission is valid for the subsequent one(s). We hasten to say, that in practice such conditions are difficult to meet but at this point we

(2)

is the estimated BLER and the nominal spectral where BLER efficiency of a an MCS is given by β=ρ

M

Bk .

(3)

k=1

Using the throughput as the performance measure is a reasonable choice when considering the AMC [19]. Clearly, the estimation of the BLER in (2) is the main challenge and its accuracy will determine how successful the operation of the AMC is. We do not consider the retransmissions, i.e., erroneous packets are considered lost and are taken care of by the higher layers of the communications system. A. Turbo Receiver At the receiver, whose model is shown in Fig. 3, the frontend (FE) receiver and the channel decoder exchange iteratively information on the coded bits ck,l (n) using logarithmic likelihood ratios (LLR) Λck,l (n) = ln

P(ck,l (n) = 1) , P(ck,l (n) = 0)

(4)

where P(·) denotes probability. The maximum aposteriori (MAP) decoder [20] implemented here with the max-log simplification [10] produces extrinsic LLRs Λex,D ck,l (n) for the coded bits ck,l (n), using the input (a priori) LLRs Λa,D ck,l (n). The obtained extrinsic LLRs are used, in turn, as a priori information by the FE receiver in the subsequent iteration. The decoder also delivers the LLRs corresponding to the information bits ΛD x (q), which are the final product of the turbo receiver: the sign of ΛD x (q) determines the estimate of the bit x(q).

1294 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

Front end Receiver

The FE receiver, considered here, is composed of a soft interference canceller (IC) “cleaning up the signal”, i.e., subtracting the estimates of the interfering symbols from the received data, a linear combiner (LC) suppressing the residual interference present in the “cleaned” signal, and a non-linear de-mapper M−1 [·], transforming the outputs of the linear combiner into the LLRs. The operations may be described as follows [9, 11, 21, 22]: rk (n) = r(n) − [HE{s(n)} − hk E{sk (n)}],

j=l

(7) where hk is the k-th column of matrix H, expectation E{·} is calculated using a priori LLRs Λack,l [21], Blb is the set of all codewords b = [b1 , . . . , bBk ] having the l-th bit bl set to b, µk = wkH hk , and variance of the interference and noise at the output yk (n) is given by σk2 (n) = wkH (HV(n)HH − vk (n)hk hH k + IN0 )wk .

. ..

r1 (n) r2 (n)

(8)

The weight wk of the LC are derived to minimize the mean square error (MMSE) between yk (n) and sk (n), which results in [11, 21, 22]

−1 ¯ H + (1 − v¯k )hk hH wk = HVH hk , (9) k + IκN0 L ¯ = diag(¯ where V v1 , . . . , v¯M ) and v¯k = L1 n=1 vk (n) is the 2 time-averaged variance vk (n) = E{|sk (n)| } − |E{sk (n)}|2 , which is computed from the a priori LLR. Thanks to such averaging the receiver is calculated once per data block and not for every time index n, which simplifies the implementation [21, 23]. We introduced also the regularizing factor κ to avoid undesirable degradation of the performance for high SNR2 ; in this study we used κ = 2. If channel estimation is employed, the CSI elements (H, N0 ) used in the above equations should be replaced with N 0 ). (H, III. A DAPTIVE M ODULATION AND C ODING FOR TURBO RECEIVERS

The performance evaluation of turbo receivers (in terms of the BER or the BLER) for given the CSI is far from trivial because the iterative processing is highly non-linear 2 We observed that for some channels H and for small value of N , 0 the iterative process tended to diverge with increased number of iterations. Although we have no precise explanation for this phenomenon, we noted that it can be remedied overestimating the value of the noise variance N0 . Such regularization approach is often used in the engineering practice for solving linear problems, e.g., [24].

rN (n)

y2 (n) LC

(ΓM ) yM (n)

Demux

R ) (Iout

M−1 1 [·] M−1 2 [·]

R (Iout,M ) Λex cM,l (n) M−1 M [·]

.. .

Π D (Iout ) ex,D Λc (m)

R ) (Iout,1 ex Λc1,l (n)

(Γ1 ) y1 (n)

R ) (Iin

Λac (m)

ΛacM,l (n)

(5)

yk (n) = wkH (n)rk (n) (6) Bk |µ M [b] − y (n)|2 k k k ex a − b Λ (n) Λck,l (n) = min0 j c k,j σk2 (n) b∈Bl j=1 j=l B k |µ M [b] − y (n)|2 k k k a − min1 − − bj Λck,j (n) , 2 σk (n) b∈Bl j=1

Λac1,l (n)

mux

D (Iin ) ex a,D Λc (m) Λc (m) SISO −1

Π

ΛD x (m)

decoder

Fig. 3. Baseband model of the Turbo receiver - parameters used to characterize the signals, cf. Section III-A, are shown in parenthesis.

and the closed-form description of its behavior is not possible. This is the main difficulty of applying the AMC with turbo receivers. Therefore, for tractability, some simplifications must be adopted. A. EXIT Analysis The most popular tool to describe the iterative process is based on the so-called extrinsic information transfer (EXIT) charts introduced in [12] to characterize the behavior of turbodecoders. Further, EXIT charts were also used to describe turbo equalizers [23], turbo MIMO receivers [13], and turbo MUD receivers [25]. In such approach the LLRs exchanged between two SISO devices are assumed to be realizations of ergodic stochastic white processes each well defined by its probability density functions. Further more, only one parameter of the pdf is taken into account - the mutual information between the extrinsic LLRs and the corresponding bits. Each of the devices, i.e., the FE receiver and the decoder, is then characterized by a non-linear scalar (EXIT) function. Thus, the behavior of the receiver or the decoder is described D,[j] D,[j] R,[j] R,[j] respectively by Iout = f D (Iin ), and Iout = f R (Iin ), [j] [j] where Iin and Iout are the input (a priori) and output information of the FE receiver and the decoder in the j-th iteration [(·)D and (·)R refer to the decoder and the FE receiver]. R,[j] D,[j−1] D,[j] R,[j] Since Iin = Iout and Iin = Iout , the behavior of the turbo receiver is described by the evolution of the MI throughout the iterative process. Further more, the MI can be related to the BER (or BLER), i.e., BER = f BER (I D ) and BLER = f BLER (I D ) [13], thus EXIT charts may be used to evaluate the performance of the iterative receiver. The functions describing each device are generally obtained by simulation. This is particularly troublesome when they depend on the channel conditions, which generally vary in time. For such cases, a more practical approach based on the EXIT analysis was proposed in [13], where the information transfer functions of the FE receiver is computed using the CSI (H, N0 ). The detailed description of the EXIT analysis goes beyond the scope of this paper. In what follow we will, therefore, give

1295 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

only a succinct description of the main principles, referring the reader to [13] for more details. The main idea of the EXIT analysis proposed in [13] relies on the parametrization of all signals involved in the iterative process and finding the non-linear functions relating the parameters at the input and the output of a particular device. Since the decoder’s EXIT function f D (·) may be found by off-line simulations, the main problem is to find efficiently R R and Iout [i.e. the EXIT function the relationship between Iin R f (·)] using solely the CSI (H, N0 ). This is done in the following series of steps for j = 1, . . . , Jmax R,[j]

Iin

[j] vk 2,[j] σ ¯k

D,[j−1]

= Iout = =

[j]

Γk = R,[j]

Iout,k = R,[j]

Iout = D,[j]

Iout =

(10)

R,[j] fσ (Iin ) [j] [j],H wk (HV HH [j],H |wk hk |2 2,[j] σ ¯k [j] R Gk (Γk , Iin )

1 M

M

R,[j]

Iout,k

k=1 D R,[j] f (Iout ),

(11) −

[j] v k hk hH k

+

[j] κIN0 )wk

(12) (13)

(14) (15) (16)

where Jmax is a predefined number of iterations, depending on the available processing capability of the receiver, and we D,[0] set Iout ≡ 0. The function fσ (·) relating the a-priori MI to the variance of the symbols is computed numerically off-line and further used to a) calculate the optimal receivers (9), and b) determine the strength of the interference and noise (12); the latter is used to calculate the signal to interference and noise ratio (SINR) (13). The function Gk (·) relating the LC’s output’s SINR to the MI at the output of the de-mapper must be obtained by off-line integration3 . Finally, (15) is the consequence of the LLRs multiplexing before they are passed to the decoder. The non-linear functional relationships fσ (·) and Gk (·) are stored in lookup tables and interpolated for the need of the R,[j] operations. So, once the CSI is available the MI Iout is obtained without any simulations and may be done on-line. The next step is to obtain an estimate of the BLER, which will be further used to calculate the estimated throughput of the transmission (2). Although it is possible to obtain the function it depends on the length of the data f BLER (·) by simulations, block Q = Lρ k Bk . This requires to find function f BLER (·) for each MCS, which would make the implementation more cumbersome: adding a new MCS would require new simulations. Therefore, we opted for a simplification noting that the function f BER (·) is almost independent of the block length (provided that the block is large enough). Once the BER is 3 Notice that in the case of no a priori information (i.e., I R = 0), in Bk Gk (·, 0) is equivalent to the capacity of a BICM system as presented in [26]

estimated using this function, the BLER can be approximated by [19] = 1 − (1 − BER) Q, BLER (17) which was found sufficiently precise in the framework of the presented approximations. Thanks to the simplification (17), only one function f BER (·) needs to be obtained for each coding rate ρ. B. Selecting the Modulation and Coding Set The sequence of steps leading to choosing the appropriate MCS is described as follows. N 0 ). 1) The CSI is estimated yielding (H, 2) Using (H, N0 ), the MI at the output of the decoder D,[J ] Iout max after a predetermined number of iterations Jmax is computed using (10)-(16) for each available MCS. D,[J ] 3) The output MI Iout max is translated into the BLER using (17) and the expected throughput estimate BLER is computed by (2). 4) The MCS providing the largest throughput is selected, and the index to the best MCS is sent over the feedback channel. In general, the transmitter is allowed to use Kρ different coding rates ρi , i = 1, . . . , Kρ and KA different modulations sets Ai , i = 1, . . . , KA . Two transmitter structure with different degrees of freedom and complexity of adaptation are considered. • Per transmission modulation control (PTMC). In this transmission scheme the modulation used at each of the antennas are identical Ak ≡ A so there is KA · Kρ different MCS. • Per antenna modulation control (PAMC). In this transmission scheme the modulation at each antenna may be different so there is (KA )M · Kρ . Clearly, for the PAMC, the complexity of MCS selection grows rapidly with the number of transmitting antennas M. C. System of reference and water-filling To have the idea about how far the performance of the analyzed AMC falls from possibly ideal transmission, we consider here the so-called horizontal encoding transmission scheme, where the information bits are first demultiplexed into M sub streams and next each sub stream is separately encoded and interleaved to produce encoded sequence ck (n) [17]. This is shown schematically in Fig. 4. The HE transmission is followed by the perfect precoding, which allows the receiver to separate ideally the transmissions from all antennas. In such system, the transmitter first performs eigen- value/vectors decomposition of the matrix R = HH H, i.e., R = QΛQH , where the columns of Q are eigenvectors of R and Λ is a diagonal matrix whose elements are the eigenvalues of R. The receiver “sees” then the transmission through the composite channel H = HQ and applies matched filtering to

1296 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

. . .

s1

12

s2

s2

10

M1 [·]

C1 ,Π1 C2 ,Π2

s1

c2

M2 [·]

Precoding Q

cM CM ,ΠM

sM MM [·]

. . .

T [bits/channel use]

c1

sM

Fig. 4. Transmitter based on horizontal encoding for S-T BICM; precoding with the matrix Q is also applied to allow for perfect data separation at the transmitter.

8

AMC VE PTMC AMC VE PAMC AMC HE Waterfilling VE QPSK rate 1/4 VE 16QAM rate 1/4 VE QPSK rate 3/4 VE 16QAM rate 3/4

6 4 2

H

the data, i.e., y = H r which, after simple algebra yields independent transmissions: y = Λs + η, where the filtered noise is spatially white, i.e., E{ηη H } = ΛN0 . Since in such VE transmission scheme the modulation and the coding rate may vary for each antenna, there will be (KA · Kρ )M different MCS. To select the MCS we use the water-filling solution, i.e. not only MCS are independently chosen for each antenna but we allow also the power of each antenna to vary, which ultimately may require some of them to be switched off. Since there is no closed-form solution to such water-filling problem, we use the “greedy” algorithm proposed in [18], which increases the spectral efficiency of each transmission Bk ·ρk minimizing the distributed transmission power and maintaining the “target” BLER BLERt for each of the sub-streams. IV. N UMERICAL R ESULTS In this section we present numerical results obtained applying the proposed AMC in the PAMC and the PTMC systems comparing them to the HE system with water-filling adaptation; for the latter we use the target BLER, BLERt = 0.01, cf. [18]. For all the examples shown, we consider N = M = 4, L = 500, H is block-fading, and Rayleigh distributed. The iterative receivers are allowed to perform Jmax = 5 iterations. There are KA = 2 constellations Ai : 4-QAM and 16-QAM, and Kρ = 2 code rates; we use convolutional codes: ρ1 = 1/4 with generator polynomials {5777}8 and ρ2 = 3/4 obtained by puncturing [according to [27]] of the code with generator polynomials {57}8 . Thus, for the VE PTMC, the VE PAMC, and for HE there are, respectively 4, 32, and 256 different MCS. Figure 5 shows the throughput obtained in PTMC and PAMC scenarios compared with the throughput obtained using fixed MCS in PTMC. The throughput is evaluated as Nbl 1 βi Pi , T = Nbl i=1

(18)

where Nbl is the number of transmitted blocks (we used Nbl = 10000), Pi is binary variable indicating if the i-th block is error-free (Pi = 1) or contains errors (Pi = 0), and βi is the nominal spectral efficiency in the transmission of the i-th block, cf. (3).

0 0

5

10

1 N0 [dB]

15

20

25

Fig. 5. Throughput for the AMC in 4 × 4 MIMO VE transmission over Rayleigh fading channel; the receiver carries out Jmax = 5 iterations; perfect CSI information is available. For comparison, the MIMO HE with waterfilling adaptation and the throughput of non-adaptive MIMO VE transmissions for each available MCS are also shown. .

We observe that the PTMC transmission/adaptation scheme maintains the throughput greater then each of the MCS considered individually. This is what should be expected from well operating AMC system because N10 is the average SNR, thus for some channel realizations H, the AMC system can switch to a low or high spectral efficiency MCS so as the throughput is always maximized. The advantage of slightly more complex PAMC over the PTMC is well seen in the SNR range 13-20[dB], where no MCS of the PTMC may ensure high throughput and the PAMC is able to take advantage of the flexibility of the modulation adaptation per antenna. The reference throughput obtained for the HE with waterfilling offers undeniable advantage of more than 1.2[bit/channel use] over PAMC. It is particularly useful for low SNR range. In this region, the MCS (ρ = 14 and A 4QAM) with lowest spectral efficiency is performing poorly, because, unlike in the HE transmitter, the power adaptation is not allowed for. Of course, the advantage offered by the HE transmitted with precoding must be paid by increased bandwidth of the feedback channel as it has to carry a sufficiently accurate representation of the eigenvectors Q and eigenvalues Λ. On the other hand, in PAMC and PTMC only the index to a particular MCS must be sent over the feedback channel. In Fig. 6 we show the results obtained when the channel is estimated using 48 pilot symbols (i.e., roughly 10% of the total payload). Although the throughput curves are affected in all studied cases, we may appreciate that the HE transmission with waterfilling seems to be more sensitive to the channel estimation errors than the VE with PAMC and the throughput loss of the latter with respect to the former is consistently less than 0.8[bit/channel use]. The results shown do not take into account the throughput loss due to pilot symbols to not hinder the very effect of the channel estimation errors, so the curves from Fig. 6 and Fig. 5 may be directly compared. Finally, we note that for very high SNR, the throughput

1297 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

12

T [bits/channel use]

10

AMC VE PTMC AMC VE PAMC AMC HE Waterfilling

8 6 4 2 0 0

5

10

1 N0 [dB]

15

20

25

Fig. 6. Throughput for the AMC in 4 × 4 MIMO VE transmission over Rayleigh fading channel; the receiver carries out Jmax = 5 iterations; the CSI is estimated using 48 pilot symbols. The results for MIMO HE with waterfilling adaptation are shown. .

obtained with the HE transmission and water-filling adaptation is slightly lower than the one obtained by PAMC. This is quite surprising, but we note that the AMC we propose, maximizes directly the throughput while the water-filling solution is based on maintaining the target BLER. Thus, discrepancy of few percent may be expected. V. C ONCLUSIONS In this paper we have presented a method allowing for implementation of the AMC when the turbo receiver are employed. The performance evaluation of the receiver, being the critical issue of the AMC, is carried out using the so-called EXIT analysis. The functionality of the AMC is demonstrated using example of the space-time MIMO transmission. The numerical results demonstrate that the performance evaluation tool is efficient for adaptation to time-varying conditions. Two different structure of the transmitter are analyzed, differing in the way the modulation may be adapted. The results indicate that adjusting the modulation independently for each antenna and using a single channel encoder provides very promising results only slightly worse than those of the reference system, which is much more difficult to adapt and requires the complete knowledge of the system model. The latter assumption requires heavy transmission load for the feedback channel. Moreover, the benefit of the water-filling over S-T BICM may be diluted by inaccurate and/or outdated CSI. This is the subject of the ongoing research. R EFERENCES [1] A. Goldsmith and S.-G. Chua, “Adaptive coded modulation for fading channels,” IEEE Trans. Commun., vol. 46, no. 5, pp. 595–602, May 1998. [2] S. Catreux, V. Erceg, D. Gesbert, and J. R.W. Heath, “Adaptive modulation and MIMO coding for broadband wireless data networks,” IEEE Commun. Mag., vol. 40, no. 6, p. 108, June 2002.

[3] V. Lau and S. Maric, “Variable rate adaptive modulation for DS-CDMA,” IEEE Trans. Commun., vol. 47, no. 4, p. 577, Apr. 1999. [4] 3GPP, “High speed downlink packet access: UE radio transmission and reception,” 3GPP, Tech. Rep. V1.3.0 Release 5, February 2003, TSG RAN WG4 Meeting 26. [5] 3GPP, “Digital cellular telecommunications system (phase 2+); GSM/EDGE radio access network (GERAN) overall description; stage 2,” ETSI, Tech. Rep. [6] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near shannon limit errorcorrecting coding and decoding: Turbo codes,” in Proceedings of ICC 93, May 93, pp. 1064 –1070. [7] C. Douillard, M. J´ez´equel, C. Berrou, and A. Picart, “Iterative correction of intersymbol interference: Turbo equalization,” European Transactions on Telecommunications, vol. 6, no. 5, Sept. 1995. [8] R. Koetter, A. C. Singer, and M. T¨uchler, “Turbo equalization,” IEEE Signal Processing Mag., vol. 21, no. 1, pp. 67–80, Jan. 2004. [9] M. Sellathurai and S. Haykin, “Turbo-BLAST for high speed wireless communications,” in WCNC’2000 IEEE Wireless Commun. and Networking Conf., Sept. 2000, pp. 315–320. [10] B. Hochwald and S. ten Brink, “Achieving near-capacity on a multipleantenna channel,” IEEE Trans. Commun., vol. 51, no. 3, pp. 389–399, Mar. 2003. [11] X. Wang and H. V. Poor, “Iterative (turbo) soft interference cancellation and decoding for coded CDMA,” IEEE Trans. Commun., vol. 47, no. 7, pp. 1046 – 1061, July 1999. [12] S. ten Brink, “Convergence behaviour of iteratively decoded parallel concatenated codes,” IEEE Trans. Commun., vol. 49, no. 10, pp. 1727 –1737, Oct. 2001. [13] C. Hermosilla and L. Szczecinski, “Performance evaluation of linear turbo-receivers using analytical extrinsic information transfer functions,” EURASIP Journal on Applied Signal Processing, pp. 892–905, May 2005. [14] G. J. Foschini, D. Chizhik, M. J. Gans, C. Papadias, and R. Valenzuela, “Analysis and performance of some basic space-time architectures,” IEEE J. Select. Areas Commun., vol. 21, no. 3, pp. 303–320, Apr. 2003. [15] H. E. Gamal, “On the design of layered space-time systems for autocoding,” IEEE Trans. Commun., vol. 50, no. 9, pp. 1451–1461, Sept. 2002. [16] G. Foschini, D. Chizhik, M. Gans, C. Papadiasand, and R. Valenzuela, “Analysis and performance of some basic space-time architectures,” vol. 21, no. 3, pp. 303–320, Apr. 2003. [17] X. Li, H. Huang, G. J. Foschini, and R. A. Valenzuela, “Effects of iterative detection and decoding on the performance of BLAST,” in IEEE Global Telecommunication Conference GLOBECOM, Nov. 2000, pp. 1061–1066. [18] P. Xia, S. Zhou, and G. B. Giannakis, “Adaptive mimo-ofdm based on partial channel state information,” IEEE Trans. Signal Processing, vol. 52, no. 1, pp. 202 – 213, Jan. 2004. [19] Q. Liu, S. Zhou, and G. B. Giannakis, “Cross-layer combining of adaptive modulation and coding with truncated ARQ over wireless links,” IEEE Trans. Wireless Commun., 2004. [20] L.J.Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimum decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inform. Theory, vol. 20, pp. 284–287, Mar. 1974. [21] M. T¨uchler, R. Koetter, and A. C. Singer, “Turbo equalization: principles and new results,” IEEE Trans. Commun., vol. 50, no. 5, pp. 754–767, May 2002. [22] C. Hermosilla and L. Szczecinski, “Turbo receivers for narrow-band MIMO systems,” in IEEE ICASSP, vol. 4, Apr. 2003, pp. 421–424. [23] M. T¨uchler, R. Koetter, and A. C. Singer, “Minimum mean squared error equalisations using a priori information,” IEEE Trans. Signal Processing, vol. 50, no. 3, pp. 673–683, Mar. 2002. [24] J. Benesty, Y. Huang, and J. Chen, “A fast recursive algorithm for optimum sequential signal detection in a BLAST system,” IEEE Trans. Signal Processing, vol. 51, no. 7, pp. 1722 – 1730, July 2003. [25] K. Li and X. Wang, “EXIT chart analysis of turbo multiuser detection,” IEEE Trans. Wireless Commun., vol. 4, no. 1, pp. 300– 311, Jan. 2005. [26] G. Caire, G. Taricco, and E. Biglieri, “Bit interleaved coded modulation,” IEEE Trans. Inform. Theory, vol. 44, no. 3, pp. 927–946, May 1998. [27] Y. Yasuda, K. Kashiki, and Y. Hirata, “High rate punctured codes for soft decision Viterbi decoding,” IEEE Trans. Commun., vol. 32, no. 3, pp. 315–319, Mar. 1984.

1298 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

I. I NTRODUCTION Transmission over wireless channels suffers, among many impairments, from the fading which imposes severe limits on the achievable data rates. To exploit efficiently the timevarying fading channel, the transmitter should adjust its modulation and coding rate [defining the so-called modulation and coding set (MCS)] on the basis of the channel state information (CSI), i.e., the set of parameters characterizing well the quality of the transmission. The main issue in such adaptive modulation and coding (AMC) schemes is to translate the CSI into a transmission-performance metric [1–3]. Commonly, the transmitter chooses the MCS depending on the signal to noise ratio (SNR), which defines the performance measured by the bit- or block error rates (BER/BLER). The AMC has been already adopted in practice, e.g., in the high speed downlink packet access (HSDPA) [4] or EDGE [5]. Independently of AMC, which palliates the effect of fading, a considerable effort was deployed to improve the performance of the receivers and make them robust against interference and/or noise. In particular, using the paradigm of iterative processing inspired by the vertiginous ascension of the socalled turbo codes [6], the iterative (i.e., turbo) receivers has been studied by many authors for interference-limited channels, yielding turbo equalizers [7, 8], turbo MIMO receivers [9, 10], or turbo MUD detectors [11]. In interference limited transmission the AMC becomes more cumbersome because the CSI cannot be reduced to a scalar Research supported by PROMPT Quebec

parameter such as the SNR, and is rather represented by the channel impulse response (in equalizers) or channel-matrix (in case of the MIMO transmission). Employing popular linearcombiner based receivers the performance evaluation is then not trivial but realizable (one can still use the SNR after the linear combining for the AMC). However, if iterative processing is applied, the number of iterations (limited by the available processing capabilities of the receiver) must be taken into account, which adds the new dimension quite difficult to analyze. Thus, it is not surprising that there is no work showing the AMC for the turbo-receivers1 . This is indeed a challenging problem because in order to have an operational AMC it is necessary to develop a suitable tool to characterize the behavior of iterative receivers for any channel state and number of iteration. Such tool, based on the EXIT method, derived from the EXIT charts [12], was recently proposed in [13], where the accurate evaluation of the BER of the iterative receivers with linear front-end was shown. The objective of this paper and its main contribution is, therefore, the demonstration that it is possible to implement the AMC when the receiver employs iterative processing. This was never shown before due to the lack of appropriate tools for the performance evaluation of such receivers. As a case under study we choose the so-called multipleinput multiple-output (MIMO) transceivers, where both the transmitter and the receiver are equipped with multiple antennas [14]. Such transceivers exploit the spatial dimension of the propagation environment and are believed to be a solution to the problem of increasingly scarce bandwidth in wireless transmission. We focus on the so-called space-time bit-interleaved coded modulation (S-T BICM) transmission [9, 10, 15] with pseudo-random interleaving of the data in time and space (among antennas), which offers a smooth transition between the robustness offered by the transmit diversity of the space-time codes [16] and the spectrally efficient transmission yield by pure spatial multiplexing [16]. Moreover, the S-T BICM allows to adjust modulation independently of the coding rate, which definitively is an asset for a flexible AMC system. The paper is organized as follows: in section II we introduce 1 Note that it is possible to use AMC in scalar channels when iterativelydecoded turbo-codes are used. But the reliability metrics calculated using the channel output are not affected by the iterations, therefore, such case should not be confused with turbo-receivers

1293 1-4244-0270-0/06/$20.00 (c)2006 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

η Transmitter

Channel H

+

MCS Adaptation

Receiver

MCS Selection

Fig. 2.

Model of transmission with AMC.

M1 [·]

c2

C,Π

. . .

Channel Estimation

Feedback Channel

Fig. 1.

c1

M2 [·]

cM

MM [·]

s1 s2 sM

S-T BICM transmitter based on vertical encoding.

Figure 1 shows the general system model where the receiver, using the estimated CSI, selects the most appropriate MCS and sends this information to the receiver via the feedback channel. The MIMO transmission is modeled as

focus on the functionality of the AMC when iterative receivers are used. The results in more realistic fading scenarios and the adaptation with outdated CSI (e.g., [18]) are under preparation. The above simplifications also ease the implementation through a block-fading model, i.e., the channel matrix H is assumed invariant during the transmission of the block of data, but independently varying among the transmissions of different blocks. The block-fading model makes meaningful the comparison with the quasi-ideal AMC obtained with socalled water-filling approach shown in Section IV. The CSI estimated at the receiver, and denoted by the pair N 0 ), is used to select the MCS, which should maximize (H, the expected throughput of the transmission calculated as

r(n) = Hs(n) + η(n)

T = β(1 − BLER),

the general system model. In section III the basics of EXIT analysis are presented and the principle of the AMC in MIMO S-T BICM transceivers is given. Section IV shows the numerical results and comparisons between the different systems proposed. Finally, we draw conclusions in Section V. II. S YSTEM M ODEL

(1) T

T

where the vector symbol s(n) = [s1 (n), . . . , sM (n)] ( denotes the transpose), is sent at time n through the N × M channel matrix H. Each element of H represents the channel gain between a pair of transmitting and receiving antennas. The observation vector r(n) = [r1 (n), . . . , rN (n)]T is corrupted by a zero mean noise vector η(n) with a covariance matrix E{η(n)η H (n)} = IN0 , where N0 is the power spectral density of the noise. The symbol (·)H denotes the conjugatetranspose operations, and I is the N × N unitary matrix. The signal sk (n), called also a data sub-stream is transmitted in blocks of length L, i.e., n = 1, . . . , L. Each element sk (n) is obtained via memoryless modulation, i.e., mapping of a codeword ck (n) = [ck,1 (n), . . . , ck,Bk (n)]T of length Bk into a constellation alphabet Ak = {αk,i : i = 1, . . . , 2Bk }, sk (n) = Mk [ck (n)]. Notice that every sub stream k can be mapped into a distinct constellation Ak . We assume that the bits ck,l (n) are independent for k = 1, . . . , M ; l = 1, . . . , B, and equiprobably drawn from the set {0, 1}. Consequently, the symbols sk (n) are independent and equiprobable. 2Bk Each constellation Ak has zero mean, i=1 αk,i = 0 , and B 2k |αk,i |2 = 1. has normalized energy 2−Bk i=1 L To obtain the sequence of codewords {ck (n)}n=1 the socalled Vertical Encoding (VE) is considered [14, 17], i.e., Q information bits are encoded with rate ρ by an encoder C, interleaved by Π, and then demultiplexed into M substreams, as depicted in Fig. 2. In what follows we assume that the receiver can instantaneously inform the transmitter about the selected MCS. This is also equivalent to saying that the channel is varying slowly enough so that the MCS selected during one transmission is valid for the subsequent one(s). We hasten to say, that in practice such conditions are difficult to meet but at this point we

(2)

is the estimated BLER and the nominal spectral where BLER efficiency of a an MCS is given by β=ρ

M

Bk .

(3)

k=1

Using the throughput as the performance measure is a reasonable choice when considering the AMC [19]. Clearly, the estimation of the BLER in (2) is the main challenge and its accuracy will determine how successful the operation of the AMC is. We do not consider the retransmissions, i.e., erroneous packets are considered lost and are taken care of by the higher layers of the communications system. A. Turbo Receiver At the receiver, whose model is shown in Fig. 3, the frontend (FE) receiver and the channel decoder exchange iteratively information on the coded bits ck,l (n) using logarithmic likelihood ratios (LLR) Λck,l (n) = ln

P(ck,l (n) = 1) , P(ck,l (n) = 0)

(4)

where P(·) denotes probability. The maximum aposteriori (MAP) decoder [20] implemented here with the max-log simplification [10] produces extrinsic LLRs Λex,D ck,l (n) for the coded bits ck,l (n), using the input (a priori) LLRs Λa,D ck,l (n). The obtained extrinsic LLRs are used, in turn, as a priori information by the FE receiver in the subsequent iteration. The decoder also delivers the LLRs corresponding to the information bits ΛD x (q), which are the final product of the turbo receiver: the sign of ΛD x (q) determines the estimate of the bit x(q).

1294 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

Front end Receiver

The FE receiver, considered here, is composed of a soft interference canceller (IC) “cleaning up the signal”, i.e., subtracting the estimates of the interfering symbols from the received data, a linear combiner (LC) suppressing the residual interference present in the “cleaned” signal, and a non-linear de-mapper M−1 [·], transforming the outputs of the linear combiner into the LLRs. The operations may be described as follows [9, 11, 21, 22]: rk (n) = r(n) − [HE{s(n)} − hk E{sk (n)}],

j=l

(7) where hk is the k-th column of matrix H, expectation E{·} is calculated using a priori LLRs Λack,l [21], Blb is the set of all codewords b = [b1 , . . . , bBk ] having the l-th bit bl set to b, µk = wkH hk , and variance of the interference and noise at the output yk (n) is given by σk2 (n) = wkH (HV(n)HH − vk (n)hk hH k + IN0 )wk .

. ..

r1 (n) r2 (n)

(8)

The weight wk of the LC are derived to minimize the mean square error (MMSE) between yk (n) and sk (n), which results in [11, 21, 22]

−1 ¯ H + (1 − v¯k )hk hH wk = HVH hk , (9) k + IκN0 L ¯ = diag(¯ where V v1 , . . . , v¯M ) and v¯k = L1 n=1 vk (n) is the 2 time-averaged variance vk (n) = E{|sk (n)| } − |E{sk (n)}|2 , which is computed from the a priori LLR. Thanks to such averaging the receiver is calculated once per data block and not for every time index n, which simplifies the implementation [21, 23]. We introduced also the regularizing factor κ to avoid undesirable degradation of the performance for high SNR2 ; in this study we used κ = 2. If channel estimation is employed, the CSI elements (H, N0 ) used in the above equations should be replaced with N 0 ). (H, III. A DAPTIVE M ODULATION AND C ODING FOR TURBO RECEIVERS

The performance evaluation of turbo receivers (in terms of the BER or the BLER) for given the CSI is far from trivial because the iterative processing is highly non-linear 2 We observed that for some channels H and for small value of N , 0 the iterative process tended to diverge with increased number of iterations. Although we have no precise explanation for this phenomenon, we noted that it can be remedied overestimating the value of the noise variance N0 . Such regularization approach is often used in the engineering practice for solving linear problems, e.g., [24].

rN (n)

y2 (n) LC

(ΓM ) yM (n)

Demux

R ) (Iout

M−1 1 [·] M−1 2 [·]

R (Iout,M ) Λex cM,l (n) M−1 M [·]

.. .

Π D (Iout ) ex,D Λc (m)

R ) (Iout,1 ex Λc1,l (n)

(Γ1 ) y1 (n)

R ) (Iin

Λac (m)

ΛacM,l (n)

(5)

yk (n) = wkH (n)rk (n) (6) Bk |µ M [b] − y (n)|2 k k k ex a − b Λ (n) Λck,l (n) = min0 j c k,j σk2 (n) b∈Bl j=1 j=l B k |µ M [b] − y (n)|2 k k k a − min1 − − bj Λck,j (n) , 2 σk (n) b∈Bl j=1

Λac1,l (n)

mux

D (Iin ) ex a,D Λc (m) Λc (m) SISO −1

Π

ΛD x (m)

decoder

Fig. 3. Baseband model of the Turbo receiver - parameters used to characterize the signals, cf. Section III-A, are shown in parenthesis.

and the closed-form description of its behavior is not possible. This is the main difficulty of applying the AMC with turbo receivers. Therefore, for tractability, some simplifications must be adopted. A. EXIT Analysis The most popular tool to describe the iterative process is based on the so-called extrinsic information transfer (EXIT) charts introduced in [12] to characterize the behavior of turbodecoders. Further, EXIT charts were also used to describe turbo equalizers [23], turbo MIMO receivers [13], and turbo MUD receivers [25]. In such approach the LLRs exchanged between two SISO devices are assumed to be realizations of ergodic stochastic white processes each well defined by its probability density functions. Further more, only one parameter of the pdf is taken into account - the mutual information between the extrinsic LLRs and the corresponding bits. Each of the devices, i.e., the FE receiver and the decoder, is then characterized by a non-linear scalar (EXIT) function. Thus, the behavior of the receiver or the decoder is described D,[j] D,[j] R,[j] R,[j] respectively by Iout = f D (Iin ), and Iout = f R (Iin ), [j] [j] where Iin and Iout are the input (a priori) and output information of the FE receiver and the decoder in the j-th iteration [(·)D and (·)R refer to the decoder and the FE receiver]. R,[j] D,[j−1] D,[j] R,[j] Since Iin = Iout and Iin = Iout , the behavior of the turbo receiver is described by the evolution of the MI throughout the iterative process. Further more, the MI can be related to the BER (or BLER), i.e., BER = f BER (I D ) and BLER = f BLER (I D ) [13], thus EXIT charts may be used to evaluate the performance of the iterative receiver. The functions describing each device are generally obtained by simulation. This is particularly troublesome when they depend on the channel conditions, which generally vary in time. For such cases, a more practical approach based on the EXIT analysis was proposed in [13], where the information transfer functions of the FE receiver is computed using the CSI (H, N0 ). The detailed description of the EXIT analysis goes beyond the scope of this paper. In what follow we will, therefore, give

1295 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

only a succinct description of the main principles, referring the reader to [13] for more details. The main idea of the EXIT analysis proposed in [13] relies on the parametrization of all signals involved in the iterative process and finding the non-linear functions relating the parameters at the input and the output of a particular device. Since the decoder’s EXIT function f D (·) may be found by off-line simulations, the main problem is to find efficiently R R and Iout [i.e. the EXIT function the relationship between Iin R f (·)] using solely the CSI (H, N0 ). This is done in the following series of steps for j = 1, . . . , Jmax R,[j]

Iin

[j] vk 2,[j] σ ¯k

D,[j−1]

= Iout = =

[j]

Γk = R,[j]

Iout,k = R,[j]

Iout = D,[j]

Iout =

(10)

R,[j] fσ (Iin ) [j] [j],H wk (HV HH [j],H |wk hk |2 2,[j] σ ¯k [j] R Gk (Γk , Iin )

1 M

M

R,[j]

Iout,k

k=1 D R,[j] f (Iout ),

(11) −

[j] v k hk hH k

+

[j] κIN0 )wk

(12) (13)

(14) (15) (16)

where Jmax is a predefined number of iterations, depending on the available processing capability of the receiver, and we D,[0] set Iout ≡ 0. The function fσ (·) relating the a-priori MI to the variance of the symbols is computed numerically off-line and further used to a) calculate the optimal receivers (9), and b) determine the strength of the interference and noise (12); the latter is used to calculate the signal to interference and noise ratio (SINR) (13). The function Gk (·) relating the LC’s output’s SINR to the MI at the output of the de-mapper must be obtained by off-line integration3 . Finally, (15) is the consequence of the LLRs multiplexing before they are passed to the decoder. The non-linear functional relationships fσ (·) and Gk (·) are stored in lookup tables and interpolated for the need of the R,[j] operations. So, once the CSI is available the MI Iout is obtained without any simulations and may be done on-line. The next step is to obtain an estimate of the BLER, which will be further used to calculate the estimated throughput of the transmission (2). Although it is possible to obtain the function it depends on the length of the data f BLER (·) by simulations, block Q = Lρ k Bk . This requires to find function f BLER (·) for each MCS, which would make the implementation more cumbersome: adding a new MCS would require new simulations. Therefore, we opted for a simplification noting that the function f BER (·) is almost independent of the block length (provided that the block is large enough). Once the BER is 3 Notice that in the case of no a priori information (i.e., I R = 0), in Bk Gk (·, 0) is equivalent to the capacity of a BICM system as presented in [26]

estimated using this function, the BLER can be approximated by [19] = 1 − (1 − BER) Q, BLER (17) which was found sufficiently precise in the framework of the presented approximations. Thanks to the simplification (17), only one function f BER (·) needs to be obtained for each coding rate ρ. B. Selecting the Modulation and Coding Set The sequence of steps leading to choosing the appropriate MCS is described as follows. N 0 ). 1) The CSI is estimated yielding (H, 2) Using (H, N0 ), the MI at the output of the decoder D,[J ] Iout max after a predetermined number of iterations Jmax is computed using (10)-(16) for each available MCS. D,[J ] 3) The output MI Iout max is translated into the BLER using (17) and the expected throughput estimate BLER is computed by (2). 4) The MCS providing the largest throughput is selected, and the index to the best MCS is sent over the feedback channel. In general, the transmitter is allowed to use Kρ different coding rates ρi , i = 1, . . . , Kρ and KA different modulations sets Ai , i = 1, . . . , KA . Two transmitter structure with different degrees of freedom and complexity of adaptation are considered. • Per transmission modulation control (PTMC). In this transmission scheme the modulation used at each of the antennas are identical Ak ≡ A so there is KA · Kρ different MCS. • Per antenna modulation control (PAMC). In this transmission scheme the modulation at each antenna may be different so there is (KA )M · Kρ . Clearly, for the PAMC, the complexity of MCS selection grows rapidly with the number of transmitting antennas M. C. System of reference and water-filling To have the idea about how far the performance of the analyzed AMC falls from possibly ideal transmission, we consider here the so-called horizontal encoding transmission scheme, where the information bits are first demultiplexed into M sub streams and next each sub stream is separately encoded and interleaved to produce encoded sequence ck (n) [17]. This is shown schematically in Fig. 4. The HE transmission is followed by the perfect precoding, which allows the receiver to separate ideally the transmissions from all antennas. In such system, the transmitter first performs eigen- value/vectors decomposition of the matrix R = HH H, i.e., R = QΛQH , where the columns of Q are eigenvectors of R and Λ is a diagonal matrix whose elements are the eigenvalues of R. The receiver “sees” then the transmission through the composite channel H = HQ and applies matched filtering to

1296 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

. . .

s1

12

s2

s2

10

M1 [·]

C1 ,Π1 C2 ,Π2

s1

c2

M2 [·]

Precoding Q

cM CM ,ΠM

sM MM [·]

. . .

T [bits/channel use]

c1

sM

Fig. 4. Transmitter based on horizontal encoding for S-T BICM; precoding with the matrix Q is also applied to allow for perfect data separation at the transmitter.

8

AMC VE PTMC AMC VE PAMC AMC HE Waterfilling VE QPSK rate 1/4 VE 16QAM rate 1/4 VE QPSK rate 3/4 VE 16QAM rate 3/4

6 4 2

H

the data, i.e., y = H r which, after simple algebra yields independent transmissions: y = Λs + η, where the filtered noise is spatially white, i.e., E{ηη H } = ΛN0 . Since in such VE transmission scheme the modulation and the coding rate may vary for each antenna, there will be (KA · Kρ )M different MCS. To select the MCS we use the water-filling solution, i.e. not only MCS are independently chosen for each antenna but we allow also the power of each antenna to vary, which ultimately may require some of them to be switched off. Since there is no closed-form solution to such water-filling problem, we use the “greedy” algorithm proposed in [18], which increases the spectral efficiency of each transmission Bk ·ρk minimizing the distributed transmission power and maintaining the “target” BLER BLERt for each of the sub-streams. IV. N UMERICAL R ESULTS In this section we present numerical results obtained applying the proposed AMC in the PAMC and the PTMC systems comparing them to the HE system with water-filling adaptation; for the latter we use the target BLER, BLERt = 0.01, cf. [18]. For all the examples shown, we consider N = M = 4, L = 500, H is block-fading, and Rayleigh distributed. The iterative receivers are allowed to perform Jmax = 5 iterations. There are KA = 2 constellations Ai : 4-QAM and 16-QAM, and Kρ = 2 code rates; we use convolutional codes: ρ1 = 1/4 with generator polynomials {5777}8 and ρ2 = 3/4 obtained by puncturing [according to [27]] of the code with generator polynomials {57}8 . Thus, for the VE PTMC, the VE PAMC, and for HE there are, respectively 4, 32, and 256 different MCS. Figure 5 shows the throughput obtained in PTMC and PAMC scenarios compared with the throughput obtained using fixed MCS in PTMC. The throughput is evaluated as Nbl 1 βi Pi , T = Nbl i=1

(18)

where Nbl is the number of transmitted blocks (we used Nbl = 10000), Pi is binary variable indicating if the i-th block is error-free (Pi = 1) or contains errors (Pi = 0), and βi is the nominal spectral efficiency in the transmission of the i-th block, cf. (3).

0 0

5

10

1 N0 [dB]

15

20

25

Fig. 5. Throughput for the AMC in 4 × 4 MIMO VE transmission over Rayleigh fading channel; the receiver carries out Jmax = 5 iterations; perfect CSI information is available. For comparison, the MIMO HE with waterfilling adaptation and the throughput of non-adaptive MIMO VE transmissions for each available MCS are also shown. .

We observe that the PTMC transmission/adaptation scheme maintains the throughput greater then each of the MCS considered individually. This is what should be expected from well operating AMC system because N10 is the average SNR, thus for some channel realizations H, the AMC system can switch to a low or high spectral efficiency MCS so as the throughput is always maximized. The advantage of slightly more complex PAMC over the PTMC is well seen in the SNR range 13-20[dB], where no MCS of the PTMC may ensure high throughput and the PAMC is able to take advantage of the flexibility of the modulation adaptation per antenna. The reference throughput obtained for the HE with waterfilling offers undeniable advantage of more than 1.2[bit/channel use] over PAMC. It is particularly useful for low SNR range. In this region, the MCS (ρ = 14 and A 4QAM) with lowest spectral efficiency is performing poorly, because, unlike in the HE transmitter, the power adaptation is not allowed for. Of course, the advantage offered by the HE transmitted with precoding must be paid by increased bandwidth of the feedback channel as it has to carry a sufficiently accurate representation of the eigenvectors Q and eigenvalues Λ. On the other hand, in PAMC and PTMC only the index to a particular MCS must be sent over the feedback channel. In Fig. 6 we show the results obtained when the channel is estimated using 48 pilot symbols (i.e., roughly 10% of the total payload). Although the throughput curves are affected in all studied cases, we may appreciate that the HE transmission with waterfilling seems to be more sensitive to the channel estimation errors than the VE with PAMC and the throughput loss of the latter with respect to the former is consistently less than 0.8[bit/channel use]. The results shown do not take into account the throughput loss due to pilot symbols to not hinder the very effect of the channel estimation errors, so the curves from Fig. 6 and Fig. 5 may be directly compared. Finally, we note that for very high SNR, the throughput

1297 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.

12

T [bits/channel use]

10

AMC VE PTMC AMC VE PAMC AMC HE Waterfilling

8 6 4 2 0 0

5

10

1 N0 [dB]

15

20

25

Fig. 6. Throughput for the AMC in 4 × 4 MIMO VE transmission over Rayleigh fading channel; the receiver carries out Jmax = 5 iterations; the CSI is estimated using 48 pilot symbols. The results for MIMO HE with waterfilling adaptation are shown. .

obtained with the HE transmission and water-filling adaptation is slightly lower than the one obtained by PAMC. This is quite surprising, but we note that the AMC we propose, maximizes directly the throughput while the water-filling solution is based on maintaining the target BLER. Thus, discrepancy of few percent may be expected. V. C ONCLUSIONS In this paper we have presented a method allowing for implementation of the AMC when the turbo receiver are employed. The performance evaluation of the receiver, being the critical issue of the AMC, is carried out using the so-called EXIT analysis. The functionality of the AMC is demonstrated using example of the space-time MIMO transmission. The numerical results demonstrate that the performance evaluation tool is efficient for adaptation to time-varying conditions. Two different structure of the transmitter are analyzed, differing in the way the modulation may be adapted. The results indicate that adjusting the modulation independently for each antenna and using a single channel encoder provides very promising results only slightly worse than those of the reference system, which is much more difficult to adapt and requires the complete knowledge of the system model. The latter assumption requires heavy transmission load for the feedback channel. Moreover, the benefit of the water-filling over S-T BICM may be diluted by inaccurate and/or outdated CSI. This is the subject of the ongoing research. R EFERENCES [1] A. Goldsmith and S.-G. Chua, “Adaptive coded modulation for fading channels,” IEEE Trans. Commun., vol. 46, no. 5, pp. 595–602, May 1998. [2] S. Catreux, V. Erceg, D. Gesbert, and J. R.W. Heath, “Adaptive modulation and MIMO coding for broadband wireless data networks,” IEEE Commun. Mag., vol. 40, no. 6, p. 108, June 2002.

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1298 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2006 proceedings.