Adaptive Modulation and Turbo Coding for 3GPP LTE Systems with Limited Feedback
Konstantinos Manolakis , M. A. Gutierrez-Estevez , Volker Jungnickel Technische Universität Berlin, Department of Telecommunication Systems, Berlin, Germany Fraunhofer Heinrich Hertz Institute, Berlin, Germany Email:
[email protected]
Abstract—Link adaptation is recognized as a powerful technique for enhancing spectral efficiency over wireless channels. While its theoretical aspects are well understood, it is not clear yet how to practically deal with limited feedback. In this paper, we study a frequency-selective link adaptation scheme for orthogonal frequency division multiplexing (OFDM). The modulation order is adjusted per resource block (smallest timefrequency unit assigned to a user), while a joint coding rate is used for all variable-length codewords, comprising resource blocks with different modulations. In order to meet the required coding rate, adaptive puncturing is applied after a fixed-rate Turbo encoder. Link adaptation is guided by an effective signal-tonoise ratio (SNR), which is calculated over several subcarriers by a mapping function. 3GPP LTE compliant link-layer simulations were performed for optimizing the SNR interface so that the spectral efficiency is maximized under a codeword error rate constraint and tradeoffs between feedback savings and spectral efficiency losses were elaborated. The result is a thoroughly tested link-layer abstraction for 3GPP LTE including adaptive modulation and bit-interleaved coding that can be also used for system-level simulations towards future mobile radio systems.
I. I NTRODUCTION Link adaptation is a key technology, required for using efficiently the available spectrum. Adapting the modulation order and power to the time-varying channel conditions was initially introduced in [1] and [2], before joint bit and power loading was investigated [3]. Since then, link adaptation has been extended into frequency domain and has become an essential feature for enhancing spectral efficiency in orthogonal frequency division multiplexing (OFDM) systems [4], [5]. Since the value of bit-interleaved coded modulation over fading channels was shown ( [6], [7]), a new generation of algorithms for joint adaptation of modulation and channel coding rate was developed ( [8], [9]). As each code has a different sensitivity to fading conditions, novel algorithms target maximizing the data rates under a codeword error rate (CWER) constraint [10]. Given a channel code, information theoretic analysis of the properties of bit-interleaved codewords leads to so-called effective signal-to-noise ratio (SNR) values, which capture the short-term channel fading. In OFDM, this metric is used for frequency-selective link adaptation. Various SNR interfaces and corresponding algorithms have been proposed and evaluated for adaptive modulation with Low-Density Parity-Check (LDPC) codes in [11] and [12] as well as with Turbo codes in [13] and [14], all of them for codewords with fixed lengths.
From a higher-level point of view, those interfaces also provide performance models, which predict the short-term CWER and are important for realistic system-layer simulations. An overview of existing link-layer abstraction models, also known as link-to-system interfaces, as well as a description of a system-level evaluation framework can be found in [15], [16]. In frequency division duplex (FDD) systems, channel quality indicator (CQI) is provided by the terminals to the base stations. Due to resource scarcity, CQI typically encapsulates compressed channel information. An overview of limited feedback schemes can be found in [17]. Adaptive bit-interleaved coded OFDM with limited feedback has been investigated in [18] and [19]. In [20], the impact of outdated CQI on link adaptation] has been evaluated and channel prediction gains have been shown. More recently, a machine-learning interface dealing with channel aging has been presented in [21]. In this work, we consider adaptive modulation and bitinterleaved Turbo coding following Third Generation Partnership Project (3GPP) Long Term Evolution (LTE) specifications [22]. A novel aspect of our work consists in using variable-length codewords, while large codewords are targeted in order to maximize coding gains. Look-up tables and exact model parameterization are provided for modulation and coding scheme (MCS) selection, explicitly for LTE and a given CWER constraint. The effective SNR is calculated over several resource blocks, while the tradeoff between feedback savings and spectral efficiency losses is evaluated by link-layer simulations over the spatial channel model extended (SCME). The rest of this paper is organized as follows. Section II presents adaptive modulation and coding for 3GPP LTE. In Section III, link-layer abstraction methods are discussed. In Section IV, link-layer simulations evaluate the spectral efficiency with the proposed link adaptation strategy and provide tradeoffs between feedback savings and performance losses. Conclusions are summarized in Section V. II. A DAPTIVE M ODULATION AND C ODING IN 3GPP LTE The system model of the single-link communication chain under study is shown in Fig. 1, where link adaptation is split into two parts: First, terminals calculate the effective SNR and provide CQI feedback, while the MCS is chosen at the base station. Fig. 2 shows the base station’s adaptive modulation and coding sub-system in more detail. The MCS is chosen from an LTE-specific look-up table (simulated with additive
978-1-4799-4482-8/14/$31.00 ©2014 IEEE
bits
Coding and interleaving
Transmitter
Symbol modulator
OFDM modulator
OFDM demodulator
MCS selection
Channel estimation
SNReff calculation
CQI feedback
Demod. and bits Decoding
Receiver
Fig. 1. Adaptive OFDM transmission in FDD mode: Using SNR values measured on subcarriers, terminals calculate the effective SNR and report it via CQI feedback to the base stations. Based on CQI index, the modulation and coding scheme (MCS) is chosen from a look-up table.
Segmentation
Turbo encoder
Rate matcher
Interleaver
Fig. 2. Coding and interleaving (first block in Fig. 1): Data segmentation into codewords of variable length, fixed-rate Turbo coding, rate matching and random bit-interleaving. Sub-system follows 3GPP LTE specification [22].
white Gaussian noise (AWGN) under a CWER constraint) and according to the provided CQI feedback. The procedure is in line with 3GPP LTE [22] and is repeated in every subframe. Before transmitting the user’s data, the bit stream is organized into segments, which lengths depend on the MCS and on the resources assigned to the user. Codewords (encoder output) fit within the frame, while at the same time building long codewords is targeted in order to maximize the coding gains. A cyclic redundancy check (CRC) is attached to the segments for detecting bit errors at the receiver, before they are passed to a Turbo encoder with a fixed "inner" rate of 1/3. In the next step, the "outer" coding rate is tuned to the final coding rate R, defined by the MCS. This is done by a circular buffer puncturing method, as described in [23]. A global coding rate R is calculated for all codewords through a weighted-mean of the local rates of each codeword, as given by the MCS on the Nrb resource blocks of the assigned spectrum: Nrb j=1 ηj rj . (1) R = Nrb j=1 ηj Here, ηj and rj denote the number of bits per symbol and the coding rate of the j th resource block, according to the assigned MCS. Finally, random interleaving is applied to the codewords and the so-called transport block is generated, before bits are mapped to complex-valued symbols and finally passed to the OFDM modulator. At the receiver, after OFDM demodulation, soft de-mapping returns the detected bits, which are de-interleaved and finally organized into the user’s packets. In parallel, the effective SNR values are calculated for the CQI feedback. The described adaptive modulation and coding mechanism has moderate system complexity due to following reasons: • Codeword length is taken from look-up tables so that codewords fit the LTE frame • Outer coding rate is taken from look-up tables • A single coding rate is applied for all codewords, simplifying receiver-side decoding
III. L INK - LAYER A BSTRACTION M ODELS In this Section, we explain how the effective SNR values are calculated. Based on pilot symbols, terminals estimate the broadband channel frequency response and the AWGN level, and provide an SNR vector to the link adaptation block. The channel on each subcarrier is used for taking advantage of interpolation gains between pilots. The effective SNR is calculated by nf SNRi 1 −1 f . (2) SNReff = α1 · f nf i=1 α2 The number of subcarriers per resource block is nf , while parameters 0 < α1 ≤ 1 and α2 ≥ 1 tune the model. In [13] an alternative ink adaptation interface has been proposed, which calculates the effective SNR as a weighted sum (0 < β ≤ 1) between expression (2) with α2 = 1 and the minimum SNR within the resource block (SNRmin ): nf 1 −1 SNReff = β · f f (SNRi ) + (1 − β) · SNRmin . nf i=1 (3) Regarding the mapping function f (x), using f (x) = log2 (1 + x),
(4)
leads to the so-called capacity effective SNR metric (CESM). The exponential mapping (EESM) uses f (x) = e−x ,
(5)
while logarithmic mapping (LESM) corresponds to f (x) = log10 (x).
(6)
Finally, the mutual information effective SNR mapping (MIESM) uses a mapping function, which depends on the particular coding gain. It is calculated by the mutual information of bit-interleaved codewords, as analyzed in [24] and exemplarily evaluated in [11]. A detailed description of the above link-to-system interfaces and of a system-level evaluation framework can be found in [15]. Discussion on link-layer abstraction models (2) and (3): Model (3) considers the minimum SNR within the resource block, which prevents detection errors in case of strong frequency-selective fading. Thus, it is suitable for Rayleigh
SNR on subcarriers
SNReff
CQI granularity
mobility, cell-ID, CWER
Inner link adaptation
Outer link adaptation
α2
α1
Interface compound
Fig. 3. Two-stage link adaptation: regarding expression (2), "inner" link adaptation sets parameter α2 , while "outer" long-term loop controls α1 .
fading or when SNReff is calculated over a wide spectrum. On the other hand, model (2) has two parameters, which offers higher flexibility. Parameter α2 can be understood as an "inner" scaling factor of the SNR input values. It can be tuned according to channel frequency selectivity, coding gain and modulation order. Parameter α1 is an "outer" scaling factor, which can have the role of an outer-loop control mechanism, which adjusts the model when the transmission conditions change. A two-stage link adaptation model, also driven by the CWER, is shown in Fig. 3. The outer loop can be activated when large-scale channel parameters change (e.g. assignment to a new base station) or when CQI errors exist due to mobility and the "inner" model is mismatched. IV. P ERFORMANCE E VALUATION Evaluation scenario and parameters: The evaluated system is shown in Fig. 1, with most relevant 3GPP LTE parameters listed in Table I. Data are transmitted over the urban macro SCME, which is here constant for the duration of one LTE subframe. Evaluation is performed over a statistically sufficient number of subframes, transmitted over independent SCME channel realizations. Without loss of generality, large-scale fading parameters have been disregarded and the mean channel power has been normalized to unity. The mean symbol power is set to Es = 1 and no power adaptation is applied. We consider one mobile user, to which the complete spectrum is assigned (10 MHz is the maximum spectrum per user in 3GPP LTE). Perfect channel knowledge is assumed at the receiver, which is used for calculation of the effective SNR values as well as for zero-forcing channel equalization. For link-layer abstraction we use model (2) with CESM (4), which approaches very well MIESM and is less complex [15]. As the channel is static during one subframe, we use α1 = 1. We investigate the role of α2 , also in combination with a variable number of resource blocks used for SNReff . As this frequency band can be larger than the channel coherence bandwidth, the role of α2 is to decrease the final SNReff value and prevent from errors due to model misalignments because of fading. MCS selection is based on look-up Table II, while SNR switching points have been taken from AWGN simulations for the MCS in 3GPP LTE, considering a 10% CWER constraint (red solid line in Fig. 7).
TABLE I 3GPP LTE S YSTEM PARAMETERS Parameter System bandwidth FFT/IFFT size No of data subcarriers Subcarrier spacing Subcarriers per resource block No of resource blocks OFDM symbols per subframe Cyclic prefix Subframe duration Modulation scheme Turbo (inner) coding rate Final (outer) coding rate Length of encoder input
Value 10 MHz 1024 600 15 kHz 12 50 14 160/144 samples 1 ms QPSK, 16QAM, 64QAM 1/3 0.17 - 0.91 40 - 6144 bits
TABLE II SNR S WITCHING P OINTS FOR MCS CQI 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Modulation QPSK QPSK QPSK QPSK QPSK QPSK QPSK 16QAM 16QAM 16QAM 16QAM 16QAM 64QAM 64QAM 64QAM 64QAM 64QAM
Coding rate 0.17 0.23 0.29 0.36 0.45 0.55 0.64 0.50 0.55 0.62 0.72 0.80 0.64 0.68 0.76 0.82 0.91
SNR [dB] < -3.4 -3.4 -2.3 -1.4 -0.4 0.8 2.7 5.3 6.8 7.5 8.5 10.0 11.4 14.0 14.5 15.8 17.1 19.8
The mean spectral efficiency is evaluated by CLTE =
K 1 (1 − CWERk ) ηk Rk , K
(7)
k=1
and is measured in (bits/s/Hz). Here, CWERk ∈ {0, 1}, ηk ∈ {0, 2, 4, 6} and rk denote the CWER, the number of bits per symbol and the coding rate of the k th of totally K transmitted resource blocks, respectively. Note that Rk (1) is the same for all resource blocks within the subframe and that (7) does not consider the overhead due to pilots and cyclic prefix. Simulation results: Fig. 4 depicts the maximum achieved spectral efficiency over the mean SNR, given a 10% CWER constraint. For each curve, the effective SNR is calculated over a number of resource blocks between 1 and 50. It has been used α1 = 1, while α2 has been evaluated and optimized in the range 1 to 18 in steps of 0.5. From the α2 values, the ones maximizing the spectral efficiency were determined and are shown in Fig. 5. When calculating one CQI value per resource block, α2 = 1 is the optimal value, as the channel is almost frequency-flat.
5
4
Spectral Efficieny [bits/s/Hz]
3.5
90 80 Spectral efficiency (% of maximum)
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100 CQI / 1 RB CQI / 2 RB CQI / 3 RB CQI / 6 RB CQI / 10 RB CQI / 25 RB CQI / 50 RB
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Fig. 4. Spectral efficiency over mean SNR for varying CQI granularity, one value per 1 up to 50 resource blocks (RB). Model (2) with CESM (4) is used, with α1 = 1 and optimized α2 (see Fig. 5) for a 10% CWER constraint.
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40 50 60 Feedback savings (%)
70
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Fig. 6. Mean spectral efficiency over feedback savings, averaged over for SNR between 8 and 24 dB. CESM with α1 = 1 and α2 (Fig. 5) is used.
Spectral efficiency is averaged over an SNR interval between 8 and 24 dB. As observed, 50% of the feedback can be saved with an average cost of around 10% in spectral efficiency. When only one CQI value is reported (98% feedback savings), the spectral efficiency lies slightly above 30% of its maximum.
18
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0
CQI / 1 RB CQI / 2 RB CQI / 3 RB CQI / 6 RB CQI / 10 RB CQI / 25 RB CQI / 50 RB
Parameter α2
12
Fig. 7 illustrates the spectral efficiency for CQI per resource block (same curve as blue line in Fig. 4) next to the Shannon spectral efficiency (refers to ergodic capacity over all subcarriers and for uniform power allocation), defined as Es · |H|2 CSCME = E log2 1 + . (9) σn2
10
8
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2
0
0
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10 SNR [dB]
15
20
Fig. 5. Evaluation of α2 over mean SNR for varying CQI granularity, one value per 1 up to 50 resource blocks (RB). Model (2) with CESM (4) is used, with α1 = 1 and under a 10% CWER constraint.
However, calculating the effective SNR over a larger frequency band, α2 needs to be adjusted, so that the target CWER is not exceeded. This mapping targets (and achieves) a lower spectral efficiency but is needed for avoiding errors. Some curves in Fig. 5 do not fall monotonously, because of switching of modulation scheme between CQI value 7 and 8. This is also reflected by a step in the AWGN spectral efficiency curve, shown with red solid line in Fig. 7. Fig. 6 evaluates the achieved spectral efficiency (CLTE ) as a percentage of the maximum value CLTE,max : cLTE,% =
CLTE CLTE,max
· 100%.
(8)
The x-axis corresponds to the feedback savings, with respect to the maximum feedback, i.e. one CQI value per resource block.
Expression (9) has been evaluated for the SCME, where H denotes the channel on an OFDM subcarrier, and is shown with blue dashed line. As observed, the gap between the achieved and the Shannon spectral efficiency is around 4 dB. The MCS switching points were obtained by AWGN spectral efficiency, illustrated in Fig. 7 with red solid line. The well-known AWGN Shannon capacity Es (10) CAWGN = log2 1 + 2 σn is shown with red dashed line. As observed, losses due to channel coding redundancy of about 2.5 dB can be observed. Note
that because of the Jensen’s inequality and as E |H|2 = 1, it holds CSCME ≤ CAWGN . Discussion and open issues: In order to interpret correctly the results of this work, following facts and limitations need to be considered: • Spectral efficiency (7) does not consider overhead due to pilot symbols and cyclic prefix. • Parameter α2 has been optimized for a static scenario. For time-varying channels, 0 < α1 ≤ 1 needs to be used.
R EFERENCES
8 i) C
, AWGN
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Fig. 7. Bounds and practically achieved spectral efficiency over mean SNR: i) LTE for AWGN; ii) Shannon limit for AWGN; iii) LTE for CQI per resource block for SCME, see Fig. 4; iv) Shannon (ergodic) for SCME.
•
•
•
Variable codeword lengths (and coding gains) make MCS selection more difficult. Codeword lengths also depend on the available resources, also a source of uncertainty. One user has the full spectrum, no scheduling gains exist and deep fading channels are not excluded. In this context, performance should be seen as a lower bound. Adapting the coding rate per codeword or even further per resource block could possibly enhance performance (not shorter codewords fitting in one resource block, as this would limit the coding gains). Information bits need to be allocated in frequency given the local coding rates. V. C ONCLUSION
We presented a frequency-selective link adaptation scheme for OFDM-based 3GPP LTE systems, where modulation is adjusted per resource block, while a global coding rate is used. The encoding chain includes a fixed-rate Turbo encoder with variable-length codewords, a rate matcher and a channel interleaver. The link-abstraction interface has been parametrized to the channel and transmission scenario, considering a codeword error rate constraint of 10%. Link-layer evaluation of the scheme showed that the achieved spectral efficiency lies about 4 dB from the Shannon (ergodic) level. It was also found that feedback can be reduced to the half with around a price of 10% in spectral efficiency. At the same time, saving 90% of feedback still guarantees a spectral efficiency over 50% of the maximum. As a reference we provide the exact mapping charts and parametrization of our model for 3GPP LTE, for variable feedback savings. ACKNOWLEDGMENT This work has been co-funded by the Deutsche Forschungsgemeinschaft (DFG) under project CoMP impairments (JU 2793/3-1). The authors would also like to thank Prof. Adam Wolisz and Dr. Peter Jung from the Technische Universität Berlin for their valuable comments.
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