1 Lousy Processing Increases Energy Eiciency in Massive MIMO Systems Sara Gunnarsson, Micaela Bortas, Yanxiang Huang, Cheng-Ming Chen, Liesbet Van der Perre and Ove Edors Department o EIT, Lund University, Lund, Sweden Department o ESAT, KU Leuven, Leuven, Belgium imec, Leuven, Belgium Contact author: sara.gunnarsson@eit.lth.se Abstract Massive MIMO (MaMIMO) is a key technology or 5G wireless communication, enabling large increase in both spectral and energy eiciency at the same time. Beore it can be deployed, it is important to ind eicient implementation strategies. Because o the many antennas, an essential part o decreasing complexity, and urther improving energy eiciency, is optimization o the digital signal processing (DSP) in the perantenna unctions. Assuming an orthogonal requency-division multiplexing (OFDM) based MaMIMO system, this paper explores coarse quantization in the per-antenna digital transmit ilters and inverse ast Fourier transorms (IFFTs) and evaluates it in terms o perormance and complexity savings. Results show that DSP complexity can be greatly reduced per-antenna, and thereore signiicant power savings can be achieved, with limited perormance degradation. More speciically, when going towards MaMIMO and thereore increasing the number o antennas rom to, it is possible to reduce the complexity in each transmit ilter by 55%. Also, when using bits to represent the input signal and bits or the ilter coeicients, this results in an SNR degradation o less than.5 db compared to loating-point perormance. Consequently, we conclude that the overall system energy greatly beneits rom lousy per-antenna processing. Index Terms Massive MIMO, energy eiciency, digital signal processing, low accuracy, quantization I. INTRODUCTION Global mobile data traic is continuously increasing as the use and applications o wireless communication spreads more and more. The number o users and communicating devices ollows the same trend. At the same time, energy consumption or networks is increasing aster than the total worldwide electricity use. To be able to meet these challenges, a technology that can provide higher spectral eiciency, at the same time as being energy eicient, is needed. Massive MIMO (MaMIMO) is one o the most attractive technologies or ulilling the 5G requirements, since it can provide increased spectral eiciency while still enabling more energy eicient solutions. By using spatial multiplexing in a time-division duplex (TDD) mode, great capacity can be achieved in these systems [1]. Furthermore, the array gain and linear processing results in energy savings in the overall system. It has also been validated that MaMIMO works in a wide variety o situations in real-lie testbed experiments, achieving 97 1 53 373 /17/$31. c 17 IEEE a world record in spectral eiciency []. For these reasons, MaMIMO has become a clear candidate when standardizing 5G. What is yet to be progressed beore it can be deployed, are eicient implementation solutions. The basic idea, which MaMIMO is built on, is to use a large number o antennas relative to the number o active terminals. As proposed, the number o antennas will be into the hundreds. Since the per-antenna processing in the base stations is dominating the complexity in the digital signal processing (DSP) part, it is essential to investigate the perantenna unctions when developing energy eicient solutions. We address MaMIMO systems based on OFDM where, more speciically, the complexity in the per-antenna unctions is dominated by the transmit ilter and IFFT [3]. One way to make MaMIMO more energy eicient is to reduce complexity and resolution in the system. For example this can be done by utilizing error-prone digital hardware [], or by lowering the accuracy at the end o the digital transmit chain. It has been shown that a MaMIMO system can operate correctly with only or 3 bits with an SNR degradation as small as 1 db [5]. This paper demonstrates that with MaMIMO array gain, not only the power ampliier (PA) power, but also the digital complexity or each antenna can be reduced. We explore and evaluate perormance as well as calculate complexity savings, when complexity in the per-antenna unctions is reduced by lowering processing accuracy. The ocus is on the inal quantization implementations, combined with the power perspective in terms o complexity. We start with quantizing the signal in combination with quantization o either ilter coeicients or IFFT twiddle actors. Finally, the eect o this quantization is evaluated in terms o perormance and complexity savings per antenna-chain when increasing the number o antennas. Section II describes the system model and presents the scenario o the simulations. Section III elaborates on the complexity analysis which is later applied in comparisons. Section IV presents the quantization perormed in the transmit ilter and IFFT, ollowed by results and evaluation o the perormance including numbers or possible complexity savings, when increasing the number o antennas. Finally, Section V presents the conclusions.
Fig. 1. The MaMIMO downlink system model, with K single-antenna users served by M base station antennas. Transmit chain signals are quantized to n st bits internally in the IFFT and n s bits on the transmit ilter input. Twiddle actors in the IFFT are represented by n t bits and ilter coeicients by n bits. II. SYSTEM MODEL A MaMIMO system consisting o a base station with M antennas and K single-antenna users is considered. Throughout this work, the cases with, 3, or 1 antennas and users are usually considered. The dierent combinations will be stated as K M. The system is working in TDD mode and perect knowledge o channel state inormation (CSI) is assumed. Similar to 3GPP Long-term Evolution (LTE), the bandwidth is MHz and o subcarriers are used or data transmission, divided into resource blocks []. The structure o the system model can be seen in Fig. 1. The ocus is on the downlink scenario since it is usually more power consuming because o the higher traic load. The system starts with signal processing or the K users, including data generation and symbol mapping (not explicitly shown in the igure). The modulation ocused on is -QAM, in order to explore how a case that normally requires very accurate processing responds to coarse quantization. Channel coding is not included in the simulations unless explicitly speciied. Following the per-user processing is a MaMIMO precoder using zero-orcing (ZF). Ater that comes the per-antenna processing or the M antennas, which is the main ocus o this work. This process includes OFDM modulation, i.e an IFFT, upsampling and iltering. Ater passing the Rayleigh-ading channel, where each antenna to antenna link is generated independently with a power delay proile (PDP) according to ITU Pedestrian A [7], there is independent data detection or each one o the K users. III. COMPLEXITY ANALYSIS To assess the energy consumption o the digital processing, the arithmetic complexity o the transmit ilter and IFFT is used. While the complexity o DSP is oten assessed in terms o giga-operations per second (GOPS), a more in-depth study was pursued in order to quantiy the eect o coarse quantization. Thereore, the relevant relationships are derived, depending on the word lengths, or the required adders and multipliers needed to implement IFFTs and transmit ilters. The resulting complexity, C, in the IFFT and transmit ilter can be calculated in terms o number o additions and multiplications being made during the respective operation. The complexity calculations below are based on the Ladner- Fischer high-speed adder [], whose complexity is C adder = n log (n) or a maximum n bit input and the Baugh-Wooley high-speed multiplier [9], whose complexity is or n 1 and n bit inputs. A. Complexity o IFFT C multiplier = n 1 n Following LTE, a -point IFFT is implemented. The total number o butterly units is log () stages butterlies per stage. Each butterly has adders and multipliers, because o its complex nature. Apart rom the arithmetic complexity, the data transers (memories and registers) also contribute to the complexity o the processing []. Thereore, the IFFT complexity is multiplied with an overhead actor o and inally the IFFT complexity per sample is estimated as C IFFT = n st log (n st ) + n st n t, (1) where n st is the number o bits used to represent the signal internally and n t is the number o bits used to represent the twiddle actor. In the IFFT implemented in the system model, the same internal representation is used through all the stages. B. Complexity o transmit ilter The transmit ilter used in the simulations has roll-o actor.5, ilter span and upsampling actor. The 1 taps, resulting in adders and multipliers, are used to calculate each output sample. Since processing is in the complex baseband, both real and imaginary parts o the signal needs processing, resulting in the actor o. Given this, the ilter complexity per sample is estimated as C ilter = (n + n s ) log (n + n s ) + n n s, () where n s is the number o bits used or the input signal and n is the number o bits used or the ilter coeicients. The internal representation o the transmit ilter is n s + n + x,
3 where x comes rom the increased dynamic range when adding contributions rom all ilter taps. For the most pessimistic case, x would be log (1) = 5. In this paper, a more realistic case is considered where x is calculated rom the ilter coeicients. IV. COARSE QUANTIZATION: EXPLORATION AND ASSESSMENT In order to reduce the complexity in the per-antenna processing, coarse quantization in the IFFT and transmit ilter was perormed respectively, while assuming ull precision or the unction not in ocus. The complexity o these unctions scales with the number o antennas, and thereore, it can result in a signiicant portion o the overall complexity in the DSP. By simulating uncoded perormance and comparing against a target BER, or various combinations o IFFT and transmit ilter quantizations, the quantization combinations that deliver required perormance are ound. The presented curves show the shortest word lengths meeting, or exceeding, the BER perormance requirement. Speciically, when ocusing on the corner points, the optimum in terms o complexity per antenna or that speciic unction, which is needed to achieve the targeted perormance, can be ound. The number o bits or internal representation o the signal is used in plots or the IFFT, while the number o bits or representing the input signal is used in plots or the transmit ilter. This because the internal representation is the same through all the stages in the IFFT, while the internal representation in the transmit ilter will vary depending on the word length o the ilter coeicients. A. Perormance analysis o IFFT For a chosen Additive White Gaussian Noise (AWGN) SNR value at 1 db and a target BER o 3, quantization or the internally represented signal and twiddle actor was perormed. The BER 3, which is reached at SNR 1 db or the system when using loating point, was chosen as a reasonable BER which with relatively low-complex channel coding can be improved to suicient perormance. The results were assessed based on simulations or our dierent combinations o K M with an uncoded -QAM signal. The graphs in Fig. represent the minimum required bits in the IFFT or dierent combinations o K M. What can be seen is that graphs corresponding to the cases with 3, and 1 base station antennas respectively are overlapping, which indicates that an increase o the number o antennas relative the number o users no longer compensates or the loss o accuracy caused by the quantization. The minimum required number o bits or these numbers o antennas are or the twiddle actor and 15 or the internally represented signal. Comparing these three cases to the case, it can be seen that processing with lower resolution per antenna is possible when the number o antennas increases. Using calculations rom Section III, the IFFT complexity contour lines are included in the graph, in order to improve the comparison between the dierent options in terms o complexity per antenna-chain. Complexity is, quite naturally, lowest in the bottom let corner o the igure and grows with Number o bits, n st 1 19 1 17 15 13 13 1 9 15 x x3 x1 1 7 9 11 1 13 Number o bits, n, representing the twiddle actor t Fig.. IFFT quantization with users and between and 1 base station antennas. Number o internal signal representation bits n st and twiddle actor bits n t needed in the IFFT to achieve an uncoded target BER o 3 at 1 db SNR using -QAM. IFFT complexity contour lines based on Eq. (1) are dashed and grey. 1 1 x x3 x1 Fig. 3. Transmit ilter quantization with users and between and 1 base station antennas. Number o input signal bits n s and ilter coeicient bits n needed in the transmit ilter to achieve an uncoded target BER o 3 at 1 db SNR using -QAM. Filter complexity contour lines based on Eq. () are dashed and grey. the number o bits. While there is only one corner point or larger number o antennas, making it clear which option delivers the lowest IFFT complexity per antenna, the contour plot is helpul or the case, where it can be seen that the two corner points have roughly the same IFFT complexity per antenna. When increasing the number o base station antennas rom to 3 or above, the IFFT complexity can be reduced by 9% in each antenna. B. Perormance analysis o transmit ilter Input signal and ilter coeicient quantizations or the transmit ilter are investigated using the same BER perormance requirement and SNR as or the IFFT. The resulting graphs are shown in Fig. 3. Similar to the IFFT analysis, the complexity contour lines, calculated rom the relationship derived in Section III, are included to make it possible to ind the least complex quantization combinations ulilling perormance requirements.
-QAM, SNR = 1 db,, uncoded 1 x x 3x 1 - -3-5 1 1 Fig.. Filter quantization with base station antennas and between and 3 users. Number o input signal bits n s and ilter coeicient bits n needed in the transmit ilter to achieve an uncoded target BER o 3 at 1 db SNR using -QAM. Filter complexity contour lines based on Eq. () are dashed and grey. Fig. 5. Filter quantization with users, base station antennas and varying target BER. Number o input signal bits n s and ilter coeicient bits n needed in the transmit ilter to achieve uncoded target BERs o, 3 and 5 at 1 db SNR using -QAM. Filter complexity contour lines based on Eq. () are dashed and grey. The cases with and 1 antennas are almost overlapping and or the case with 3 antennas only a ew more bits are needed. For the case with antennas the number o needed bits is signiicantly larger, which also was the case or the IFFT in Fig.. Using only antennas is not large enough to beneit rom the law o large numbers to the same extent as the other cases. The system load per antenna is high and the number o antennas is too low or coarse quantization eects to eectively average out. A more speciic example, when increasing the number o base station antennas rom to, it is possible to reduce the ilter complexity in each transmit ilter by 55%. Comparing results or the transmit ilter to the ones or the IFFT, one dierence is that the number o required bits in the transmit ilter is lower compared to the IFFT. For the case with antennas the corner points with the same complexity are (, ) and (5, 5) or ilter coeicients and input signal respectively. This gives, or the latter case, an internal representation in the transmit ilter o 5+5+3=13 bits at most. Comparing this to the IFFT, where bits or the twiddle actor and 15 bits or the signal (same as the internal representation) was required, the conclusion is that, when increasing the number o antennas, it is possible to push the low accuracy processing in each transmit ilter urther than in each IFFT. With the observation that the low accuracy processing in the transmit ilter could be pushed more than the IFFT, urther assessment was made or the transmit ilter. Fig. shows the quantization when the number o antennas is ixed to and the number o users is varying between and 3. With antennas and these various system loads the outcome is similar, although a ew more bits are required or higher system loads. Further investigations included the number o required bits or the input signal and ilter coeicients with a ixed combination o antennas and users, but with varying target BER. In Fig. 5, it can be seen that or three dierent target BERs,, 3 and 5, there are only small dierences. When BER -1 - -3 - -QAM, n s = 5 and n = 5, Uncoded Code rate = 3/ -5 - -5 5 15 SNR Fig.. Uncoded and LDPC coded perormance. The corner point simulated with an uncoded -QAM signal and with LDPC coding, code rate 3/, respectively. There are antennas and users and the corner point quantization values are n s = 5 and n = 5 bits. comparing these curves, it can be concluded that in order to achieve the two better BERs, only one or two more bits are needed, in comparison to the worst BER. Further on, one corner point rom the case was chosen or additional evaluation o perormance and thereore simulated or a range o SNR values. The chosen corner point was 5 bits representing the input signal and 5 bits representing the ilter coeicients. The results o this perormance evaluation, as seen in Fig., is starting to show an error loor or higher SNR values. Usually in communication systems, channel coding is applied and the same corner point was thereore simulated with LDPC coding, using block size 7 bits and code rate 3/. Fig. also shows that when adding LDPC coding the required SNR can be signiicantly lower while achieving the same BERs, at the cost o higher complexity in the per-user processing, which is scaling with K. Evaluating the potential perormance loss caused by quantization in the transmit ilter gives the results shown in Fig. 7, which compares the case using loating-point to dierent ixed-
5 BER - -3 - -QAM,, uncoded n s = 5 and n = 5 n s = and n = Floating point ACKNOWLEDGMENT The research leading to these results has received unding rom the European Union Seventh Framework Programme (FP7/7-13) under grant agreement no 19 (MAM- MOET). We would also like to thank the Erasmus program or the scholarship received while conducting the research and S. Pollin s lab or taking care o us during our stay in Leuven. -5-5 15 SNR Fig. 7. Comparison between the loating point case and two dierent quantization combinations, the corner point n s = 5 and n = 5 bits and the case with n s = and n = bits. There are antennas and users and the signal is uncoded with the constellation -QAM. point combinations. Both the case with the corner point and the case when the number o bits used to represent the input signal and ilter coeicients are both increased rom 5 to bits, in order to also have a perormance closer to the loating-point case to compare with, is visualized. At a BER o 3 there is an SNR degradation o less than.5 db, or the latter ixedpoint combination, compared to when using loating-point. Even or these numbers with quite ew bits, great perormance is achievable but with the possibility to reduce the complexity per antenna due to the larger total amount o antennas. Also, there are possibilities or even greater complexity savings i optimizing the IFFT and transmit ilter internally. V. CONCLUSION This paper ocused on simpliied DSP or MaMIMO systems, exploiting the large number o antenna signals to reduce the processing accuracy in each antenna and hence, power consumption o the processing. We investigated the perormance and calculated complexity savings when coarsely quantizing the IFFTs and transmit ilters, in order to decrease the complexity in the per-antenna unctions and thereby, the overall DSP complexity. The results show that it is possible to push the transmit ilter more than the IFFT, requiring only bits or the input signal and bits or the ilter coeicients in order to get a perormance close to the loating-point case. For a BER o 3, this resulted in an SNR degradation o less than.5 db, despite using a sensitive -QAM constellation. A complexity analysis was also made showing that when increasing the number o antennas rom to 3 or above, complexity savings o 9% were possible or each IFFT. Similarly, an increment o the number o antennas rom to, resulted in a possibility to reduce the complexity in each transmit ilter by 55%. I optimizing the IFFT and transmit ilter internally, even greater complexity savings would be possible. These results show that, when increasing the number o base station antennas, it is possible to reduce the complexity per antenna by lowering the accuracy, having a signiicant impact on power consumption in MaMIMO systems. REFERENCES [1] E. G. Larsson, F. Tuvesson, O. Edors, and T. L. Marzetta, Massive MIMO or next generation wireless systems, IEEE Commun. Mag., vol. 5, no., pp. 1 195, Feb.. [] A. Nordrum, 5G researchers set new world record or spectrum eiciency, IEEE Spectrum, [Online]. Available: http://spectrum.ieee.org/tech-talk/telecom/wireless/5g-researchersachieve-new-spectrum-eiciency-record, May. [3] C. Desset, B. Debaillie, and F. Louagie, A lexible and uture-proo power model or cellular base stations, in 15 IEEE 1st Vehicular Technology Conerence (VTC Spring), May 15. [] Y. Huang, C. Desset, A. Bourdoux, W. Dehaene, and L. Van der Perre, Massive MIMO processing at the semiconductors edge: Exploiting the system and circuit margins or power savings, in 17 IEEE International Conerence on Acoustics, Speech and Signal Processing (ICASSP), Mar. 17. [5] C. Desset and L. Van der Perre, Validation o low-accuracy quantization in massive MIMO and constellation EVM analysis, in 15 European Conerence on Networks and Communications (EuCNC), Jun. 15. [] E. Dahlman, S. Parkvall, J. Sköld, and P. Beming, 3G Evolution - HSPA and LTE or Mobile Broadband, nd ed. Elsevier Ltd.,. [7] S. Steania, I. Touik, and M. Baker, LTE - The UMTS Long Term Evolution: From theory to practice, nd ed. John Wiley & Sons Ltd., 11. [] R. E. Lander and M. J. Fischer, Parallel preix computation, Journal o the Association or Computing Machinery, vol. 7, no., pp. 31 3, Oct. 19. [9] C. R. Baugh and B. A. Wooley, A two s complement parallel array multiplication algorithm, IEEE Trans. Comput., vol. C-, no. 1, pp. 5 7, Dec. 1973. [] C. Desset, B. Debaillie, and F. Louagie, Modeling the hardware power consumption o large scale antenna systems, in IEEE Online Conerence on Green Communications (OnlineGreencomm), Nov..