Fast Fourier Transform Architecture Research Articles

Optimized power and speed of Split-Radix, Radix-4 and Radix-2 FFT structures

Fast Fourier transform (FFT) is a fundamental building block for digital signal processing applications where high processing speed is crucial. Resource utilization in implementing FFT structures can be minimized by optimizing the performance of multipliers and adders used within the design. FFTs are also widely used in various machine learning algorithms. To achieve increased processor efficiency and reduced resource utilization, we propose a hardware design for Radix-2, Radix-4, and Split-Radix FFT architectures that utilizes a novel parallel prefix adder. This design offers lower power consumption, smaller chip area, and faster operation compared to existing architectures. Our performance analysis focuses on metrics such as power consumption, clock speed, and hardware complexity for Radix-2, Radix-4, and Split-Radix FFT algorithms implemented with the proposed adder. We compare these metrics using our proposed arithmetic structure against existing adder designs. The results indicate that the Split-Radix FFT architecture achieves lower power consumption and smaller chip area compared to Radix-4 and Radix-2 methods. Additionally, the Split-Radix FFT exhibits a higher clock speed. Therefore, based on these findings, the Split-Radix algorithm appears to be a compelling choice for implementation on field-programmable gate arrays due to its high speed and lower power consumption.

Area–time–energy efficient architecture of CBNS‐based fast Fourier transform

AbstractA new approach for implementing the fast Fourier transform (FFT) using complex binary number system (CBNS) is presented in this paper. The advantage of using CBNS is that instead of processing the real and imaginary parts of a complex number separately, we can process both as a single entity. A total of four FFT architectures have been developed, which are 16‐, 64‐, 256‐, and 1024‐point FFT architectures. The proposed FFT is designed using Verilog‐HDL and implemented using a Virtex‐7 field‐programmable gate array (FPGA). The maximum clock rate achieved by the proposed FPGA‐based design is 376.1 MHz. The FPGA resource utilization of the FFT is less than the state‐of‐the‐art FFT designs. An application‐specific integrated circuit (ASIC) for the FFT is also designed. The normalized energy per FFT of the proposed ASIC is 0.14 nJ, and the normalized area per FFT of the ASIC is 1.08 mm2 which is less than other existing designs.

Low-Power Very-Large-Scale Integration Implementation of Fault-Tolerant Parallel Real Fast Fourier Transform Architectures Using Error Correction Codes and Algorithm-Based Fault-Tolerant Techniques

As technology advances, electronic circuits are more vulnerable to errors. Soft errors are one among them that causes the degradation of a circuit’s reliability. In many applications, protecting critical modules is of main concern. One such module is Fast Fourier Transform (FFT). Real FFT (RFFT) is a memory-based FFT architecture. RFFT architecture can be optimized by its processing element through employing several types of adder and multipliers and an optimized memory usage. It has been seen that various blocks operate simultaneously in many applications. For the protection of parallel FFTs using conventional Error Correction Codes (ECCs), algorithmic-based fault tolerance (ABFT) techniques like Parseval checks and its combination are seen. In this brief, the protection schemes are applied to the single RAM-based parallel RFFTs and dual RAM-based parallel RFFTs. This work is implemented on platforms such as field programmable gate arrays (FPGAs) using Verilog HDL and on application-specific integrated circuit (ASIC) using a cadence encounter digital IC implementation tool. The synthesis results, including LUTs, slices registers, LUT–Flip-Flop pairs, and the frequency of two types of protected parallel RFFTs, are analyzed, along with the existing FFTs. The two proposed architectures with the combined protection scheme Parity-SOS-ECC present an 88% and 33% reduction in area overhead when compared to the existing parallel RFFTs. The performance metrics like area, power, delay, and power delay product (PDP) in an ASIC of 45 nm and 90 nm technology are evaluated, and the proposed single RAM-based parallel RFFTs architecture presents a 62.93% and 57.56% improvement of PDP in 45 nm technology and a 67.20% and 60.31% improvement of PDP in 90 nm technology compared to the dual RAM-based parallel RFFTs and the existing architecture, respectively.

Memory-Based FFT Architecture With Optimized Number of Multiplexers and Memory Usage

This brief presents a new P-parallel radix-2 memory-based fast Fourier transform (FFT) architecture. The aim of this work is to reduce the number of multiplexers and achieve an efficient memory usage. One advantage of the proposed architecture is that it only needs permutation circuits after the memories, which reduces the multiplexer usage to only one multiplexer per parallel branch. Another advantage is that the architecture calculates the same permutation based on the perfect shuffle at each iteration. Thus, the shuffling circuits do not need to be configured for different iterations. In fact, all the memories require the same read and write addresses, which simplifies the control even further and allows to merge the memories. Along with the hardware efficiency, conflict-free memory access is fulfilled by a circular counter. The FFT has been implemented on a field programmable gate array. Compared to previous approaches, the proposed architecture has the least number of multiplexers and achieves very low area usage.

VLSI Implementation of Integrated Massive MIMO Systems (IMMS) for N-point FFT/IFFT Processor

The 5G technologies and OFDM introduce a substantial element of latency in the baseband Massive MIMO system. To declaim the low delay demand of multiple input and multiple outputs, a Fast Fourier Transform (FFT) and also consequent implementation was proposed. The main idea of this proposed system is to utilize the VLSI chip routing technology and reduce computations, processing time, and low latency. This proposed system is to reduce the number of computational complexities in the downlink and reorder the uplink. In OFDM implementation, the chip area of FFTs and IFFTs is occupied by memories, and these memories can be extracted using registers or RAM. An efficient data programming approach for memories and butterflies has been developed using embedded VLSI technology with multiple inputs and outputs (MIMO), known as mass embedded MIMO systems. Using this proposed scheme (Integrated Massive MIMO), N point FFT/IFFT processor design achieves a better throughput and lowest latency than for single-input pipelined FFT or IFFT architectures. In an N-point FFT/IFFT, the introduced scheme using VLSI Technology leads to more reduction in the latency. This N-point FFT/IFFT implementation is named “Integrated Massive MIMO Systems” (IMMS).

Energy Efficient Design of Fast Fourier Transform using Reversible Logic

Digital computation using reversible logic has gained significant research interest in recent years. It promises energy-efficient digital systems due to its information lossless characteristics. A thorough physical design of computationally intensive circuits is essential to analyze the true potential of this developing paradigm. This paper presents a reversible logic implementation of the Fast Fourier Transform (FFT) algorithm as a relevant design case. The proposed architecture’s hierarchical design is based on a reversible standard cell approach. CMOS 0.35μm technology is used for the pass transistor design as well as the full custom layout. Post layout simulations and technology design rule checks are used to validate all design units. The reversible design of an 8-point FFT with 8-bit quantization occupies 0.768 mm2 area and consumes 6.5 mW power at 10 MHz frequency and 3.3 V supply voltage. The major functional units of proposed FFT architecture demonstrate a considerable power saving as compared to their various existing implementations.

Efficient FPGA architecture to implement non-separable fast Fourier transform for image and video applications

ABSTRACT Fast Fourier Transform (FFT) is widely used in image and video processing applications to convert the respective image or video frames into transform domain that is very helpful to extract the accurate features of that image or video frame for various real-time applications. In this paper, efficient non-separable 8-point FFT architecture (DIT-FFT) is proposed that is implemented on Spartan-6 (xc6slx45-3csg324) FPGA. The proposed architecture consists of Data Format Conversion, Addition, Subtraction, Multiplier Equivalent and D-FF blocks, respectively. The non-separable equations of 8-point DIT-FFT are derived from the respective Butterfly Diagram that is then implemented using basic logic gates, which optimises the hardware utilisations with the help of Complex Conjugate property. The constant multiplications present in the non-separable DIT-FFT equations are implemented through Adders and Shifters presents in Multiplier Equivalent block which further optimises the overall hardware utilisations. Moreover, the Q-format are used to increase the data accuracy of the architecture. The comparison results show that the proposed architecture is better than existing in different prospectives.

High-Speed Continuous Wavelet Transform Processor for Vital Signal Measurement Using Frequency-Modulated Continuous Wave Radar

This paper proposes a high-speed continuous wavelet transform (CWT) processor to analyze vital signals extracted from a frequency-modulated continuous wave (FMCW) radar sensor. The proposed CWT processor consists of a fast Fourier transform (FFT) module, complex multiplier module, and inverse FFT (IFFT) module. For high-throughput processing, the FFT and IFFT modules are designed with the pipeline FFT architecture of radix-2 single-path delay feedback (R2SDF) and mixed-radix multipath delay commutator (MRMDC) architecture, respectively. In addition, the IFFT module and the complex multiplier module perform a four-channel operation to reduce the processing time from repeated operations. Simultaneously, the MRMDC IFFT module minimizes the circuit area by reducing the number of non-trivial multipliers by using a mixed-radix algorithm. In addition, the proposed CWT processor can support variable lengths of 8, 16, 32, 64, 128, 256, 512, and 1024 to analyze various vital signals. The proposed CWT processor was implemented in a field-programmable gate array (FPGA) device and verified through the measurement of heartbeat and respiration from an FMCW radar sensor. Experimental results showed that the proposed CWT processor can reduce the processing time by 48.4-fold and 40.7-fold compared to MATLAB software with Intel i7 CPU. Moreover, it can be confirmed that the proposed CWT processor can reduce the processing time by 73.3% compared to previous FPGA-based implementations.

STQCA-FFT: A fast fourier transform architecture using stack-type QCA approach with power and delay reduction

Quantum-dot Cellular Automata (QCA) is a novel and fast-growing nanotechnology that is used to build VLSI circuits. This paradigm has proven to be the fastest among various other technologies. In this paper, a novel Fast Fourier Transform architecture has been implemented using QCA. As FFT is a frequently used algorithm in signal processing applications, the architecture of the FFT has to be optimized in terms of area, power, and delay. An innovative method has been introduced to implement FFT using QCA named Stack-Type Quantum-dot Cellular Automata (STQCA). This novel architecture reduces the area by half that of conventional approaches. The proposed FFT layout yields better performance, with number of quantum cells and size as, 32,534 and 87.23 µm2 respectively. The latency between input and output is about 0.116 ns which is quite low. The layout's power dissipation has also been extracted using the QCADesignerE-2.2 tool, which is merely 17.12nW. To summarize, the proposed module show a reduction of 65% in delay and 99% in power dissipation.

Hardware Chip Performance of CORDIC Based OFDM Transceiver for Wireless Communication

The fourth-generation (4G) and fifth-generation (5G) wireless communication systems use the orthogonal frequency division multiplexing (OFDM) modulation techniques and subcarrier allocations. The OFDM modulator and demodulator have inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT) respectively. The biggest challenge in IFFT/FFT processor is the computation of imaginary and real values. CORDIC has been proved one of the best rotation algorithms for logarithmic, trigonometric, and complex calculations. The proposed work focuses on the OFDM transceiver hardware chip implementation, in which 8-point to 1024-point IFFT and FFT are used to compute the operations in transmitter and receiver respectively. The coordinate rotation digital computer (CORDIC) algorithm has read-only memory (ROM)-based architecture to store FFT twiddle factors and their angle generators. The address generation unit is required to fetch the data and write the results into the memory in the appropriate sequence. CORDIC provides low memory, delay, and optimized hardware on the field-programmable gate array (FPGA) in comparison to normal FFT architecture for the OFDM system. The comparative performance of the FFT and CORDIC-FFT based OFDM transceiver chip is estimated using FPGA parameters: slices, flip-flops, lookup table (LUTs), frequency, power, and delay. The design is developed using integrated synthesis environment (ISE) Xilinx version 14.7 software, synthesized using very-high-speed integrated circuit hardware description language (VHDL), and tested on Virtex-5 FPGA.

Design and Implementation of AGU based FFT Pipeline Architecture

Present it is most needful task to get various applications with parallel computations by using a Fast Fourier Transform (FFT) and the derived outputs should be in regular format. This can be achieved by using an advanced technique called Multipath delay commutator (MDC) Pipelining FFT processor and this processor will be capable to perform the computation of a different data streams at a time. In this paper the design and implementation of AGU based Pipelined FFT architecture is done Caluclation of a butterfly is done within 2 cycles by the instructions proposed. A Data Processing Unit (DPU) is employed in this pipeline architecture and supports the instructions & an FFT Adress Generation Unit (FAGU) caluclates butterfly input & output data adresses automatically. The DPU proposed sysyem requires less area compared to commericial DSP chips. Futhermore, the proposed FAGU reduces the number of FFT computation cycles. The FFT design architecture will have real data paths. With various FFT sizes, different radix & various parallesim levels, the FFT can be mapped to the pipeline architecture. The most attractive feature of the pipelined FFT architecture is it consists of bit reversal operation so it requires little number of registers and better throughput.

FPGA Implementation of an Efficient FFT Processor for FMCW Radar Signal Processing

This paper presents the design and implementation results of an efficient fast Fourier transform (FFT) processor for frequency-modulated continuous wave (FMCW) radar signal processing. The proposed FFT processor is designed with a memory-based FFT architecture and supports variable lengths from 64 to 4096. Moreover, it is designed with a floating-point operator to prevent the performance degradation of fixed-point operators. FMCW radar signal processing requires windowing operations to increase the target detection rate by reducing clutter side lobes, magnitude calculation operations based on the FFT results to detect the target, and accumulation operations to improve the detection performance of the target. In addition, in some applications such as the measurement of vital signs, the phase of the FFT result has to be calculated. In general, only the FFT is implemented in the hardware, and the other FMCW radar signal processing is performed in the software. The proposed FFT processor implements not only the FFT, but also windowing, accumulation, and magnitude/phase calculations in the hardware. Therefore, compared with a processor implementing only the FFT, the proposed FFT processor uses 1.69 times the hardware resources but achieves an execution time 7.32 times shorter.

Exploring the CORDIC Algorithm and Clock-Gating for Power-Efficient Fast Fourier Transform Hardware Architectures

This work explores hardware-oriented optimizations for the CORDIC (COordinate Rotation Digital Computer) algorithm investigating the power-efficiency improvements employing N-point Fast Fourier Transform (FFT) hardware architectures. We introduced three hardware-oriented optimizations for the CORDIC: (a) improving the signal extension, (b) removing the angle accumulation and (c) eliminating the redundancies in the iterations, both unnecessary when processing the FFT processing. Fully sequential FFT architectures of 32, 64, 128, and 256 points were synthesized employing ST 65 nm standard cell libraries. The results show up to 38% of power savings on average when using our best CORDIC optimization proposal to the FFT architecture comparing to the explicit multiply-based butterfly version. Moreover, when combining our best CORDIC optimization with the clock-gating technique, the power savings rises to 78.5% on average for N-point FFT.

A novel parallel prefix adder for optimized Radix-2 FFT processor

The Fast Fourier Transform (FFT) is the basic building block for DSP applications where high processing speed is the critical requirement. Resource utilization and the number of computational stages in Radix-2 FFT structure implementation can be minimized by improving the performance of utilized multiplier and adder blocks. This work proposes a hardware design of an efficient Radix-2 FFT architecture using optimized multiplier and novel Parallel prefix (PP) adder. The designed FFT architecture results in low power and area with an increase in operation speed in comparison to the existing architectures. Our proposed Radix 2 FFT implementation results in 18.218 ns (6.030 ns logic delay and 12.118 ns router delay) in comparison with 24.003 ns delay for Wallace multiplier using Kogge Stone PP adder (M1P1), 24.162 ns delay for Wallace multiplier using Brent Kung PP adder (M2P2), 24.889 ns delay for Wallace multiplier using Landner Fischer PP adder (M3P3) and 22.827 ns delay for Wallace multiplier using Han Carlson PP adder (M4P4) algorithm. The proposed adder and hence the FFT processor can be used in different applications where high speed, low power, and less area is required. The novel PP architecture results in a 20.19% improvement in comparison with other state-of-art techniques.

The Constant Multiplier FFT

In this paper, we present a new fast Fourier transform (FFT) hardware architecture called constant multiplier (CM) FFT. Whereas rotators in previous architectures must rotate among several different angles, the CM FFT exploits the use of constant multipliers to calculate the rotations. The paper explores the 4-parallel and 8-parallel radix-2 CM FFT, which calculates the FFT entirely by using constant multipliers. Later, radices 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> are presented, with emphasis in radix-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> and radix-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> as the best alternatives. Experimental results for a 1024-point radix-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> CM FFT show that the proposed approach reduces the number of block random-access memories (BRAM) and digital signal processing (DSP) slices with respect to previous approaches, while achieving the highest clock frequency for a 4-parallel FFT architecture on field-programmable gate arrays (FPGAs) reported so far.

Design optimisation of multiplier‐free parallel pipelined FFT on field programmable gate array

Fast Fourier transform (FFT) is utilised to minimise the complexity of discrete Fourier transform by converting signals from frequency domain to time domain and conversely. Digital signal processing systems like image processing, general filtering, sonar, spread-spectrum communications and convolutions use this FFT operations. Radix-2 decimation in frequency (R2DIF) method is designed to execute an efficient FFT architecture in this study. Each and every state of the FFT stores the input and output the data using the R2DIF method. Also, the complex twiddle factors in FFT are replaced by the proposed uniform Montgomery algorithm. This technique simply performs the shift-add method instead of the multiplication process which also enhances the convergence of the calculation. So, the FFT implementation is done with the help of the proposed method which reduces the usage of chips in the process. Based on this approach, it performs the operation of FFT from 16 points to 1024 points and the performance of this proposed method is compared with existing approaches. Moreover, it does not require expensive dedicated functional blocks and uses only distributed logic resources. The simulation is carried out by the Xilinx platform using Verilog coding. The proposed design outperforms conventional methods in terms of less usage power and high speed.

Hardware chip performance analysis of different FFT architecture

ABSTRACT The Fast Fourier Transform (FFT) is one of the most important algorithm used in digital signal processing (DSP) and digital communication applications to compute fast operations. FFT and IFFT is widely used in modulation and demodulation schemes such as Orthogonal Frequency Division Multiplexing (OFDM), TV broadcasting (DVD), Digital radio broadcasting (DVB) etc. The different FFT processor architectures are used for several applications. The Xilinx ISE tool has FFT Core, which can be directly used for several applications. FFT support four types of architectures: Radix-2 lite burst I/O, Radix-2 burst I/O, Radix-4 burst I/O and Pipelined I/O. The research article focuses on the hardware chip performance analysis of the variable length FFT processor architectures on Field Programmable Gate Array (FPGA) platform using VHDL programming in which FFT length varies from 8 point to 65,536 point. The input data stream is considered of 8-bit, 16-bit and 32-bit. The estimated hardware chip performance parameters are DSP Slices and block RAM. The timing parameter are transform cycles and frequency. It is estimated that radix-2 lite burst I/O performs better in terms of hardware resource utilisation on FPGA and pipelined hardware architecture performs better in terms of transform cycles in comparison to other FFT architectures. The decoded 1024-point FFT signal is observed in Xilinx ISE software integrated Chipscope Pro-Analyzer. The analysis predicts about the best-suited FFT hardware architecture when the designer is going to design the hardware chip on FPGA platform for several applications.

Area and power‐efficient variable‐length fast Fourier transform for MR‐OFDM physical layer of IEEE 802.15.4‐g

The authors present a novel 16/32/64/128-point single-path delay feedback pipeline fast Fourier transform (FFT) architecture targeting the multi-rate and multi-regional orthogonal frequency division multiplexing (MR-OFDM) physical layer of IEEE 802.15.4-g. The proposed FFT architecture employs a mixed-radix algorithm to significantly reduce the number of complex multipliers. It utilises a configurable complex constant multiplier structure instead of a fixed constant multiplier to efficiently conduct W 32 , W 64 , and W 128 twiddle factor multiplication. A hardware-sharing mechanism has also been formulated to reduce the memory space requirements of the proposed 16/32/64/128-point FFT computation scheme. The proposed design is implemented in Xilinx Virtex-5 and Altera's field-programmable gate array devices. For the computation of 128-point FFT, the proposed mixed-radix FFT architecture significantly reduces the hardware cost in comparison with existing FFT architecture. The proposed FFT architecture is also implemented by adopting the 90 nm complementary metal-oxide-semiconductor technology with a supply voltage of 1 V. Post-synthesis results reveal that the design is efficient in terms of gate count and power consumption, compared to earlier reported designs. The proposed variable-length FFT architecture gate count is 22.3K and consumes 3.832 mW, while the word-length is 12-bits and can be efficiently useful for the IEEE 802.15.4-g standard.

Selecting FFT Word Length for an OFDM Receiver That Supports Undersampling

In this paper, we focus on Orthogonal Frequency Division Multiplexing (OFDM) transceivers where undersampling is employed by the receiver Analog/Digital Converter (ADC) when sparse information is exchanged. Several Fast Fourier Transform (FFT) symmetry properties are exploited to allow the substitution of specific input values by others that have already been sampled by the ADC. Several architectures have been proposed in the literature for efficient FFT implementations in terms of power, speed and hardware resources. The FFT input/output values, twiddle factors, etc., are complex numbers with their real and imaginary parts being represented using fixed point format. A tradeoff has to be made between rounding error and complexity. The optimal minimum FFT word length is investigated by combining the undersampling and the rounding error. A configurable new FFT architecture has been developed in hardware description language to test the error model with various FFT sizes, word lengths and Quadrature Amplitude Modulations (QAM). A system designer can take into account the sparseness of the input data and define the desired rounding and undersampling error relation. Τhe developed error model would then predict the required word length and ADC resolution with average Root Mean Square Error (RMSE) less than 1.

PARALLEL PIPELINED MULTI RADIX VARIABLE LENGTH FAST FOURIER TRANSFORM ARCHITECTURE

There is an enormous demand for high speed data communication or high speed internet using Long Term Evolution (LTE) or LTE-Advanced communication methods. To achieve the high speed data rate in the receiver side, it is necessary to achieve high throughput in the Fast Fourier transform (FFT) architecture. Hence there is demand to improve the throughput of the FFT architectures used for high speed data communication. The FFT architecture is designed and optimized for LTE-A applications. However, the high throughput has been achieved by sacrificing hardware resources of the Field Programmable Gate Array (FPGA). Many fixed and variable length FFT processors are proposed by the researchers with improved performance focusing either on algorithmic modifications, novel architectural optimizations or radix selection. Among these FFT processors, the goal and main objectives of this paper are: 1. To design and implement a pipelined FFT architecture to give high throughput for LTE-A MIMO applications 2. To develop an intellectual property (IP) core for FFT computation with variable FFT size 3. To propose a parallel implementation to increase the performance of LTE-A baseband processing system. In an Orthogonal Frequency Division Multiplexing (OFDM) baseband communication system, FFT operation is one of the highest computationally serious tasks which directly influence the communication system performance factor. The baseband hardware has to be capable as well as efficient enough to calculate FFT in specific timing restrictions. Thus, the parallel pipelined multi radix Variable Length FFT architectures for LTE-A Multiple-Input-Multiple-Output (MIMO) applications have been designed. The proposed FFT architecture delivers a throughput of 550 MSPS at the maximum clock rate of 550 MHz. The proposed FFT support the FFT length of 64, 128, 256, 512, 1024 and 2048 for LTE-Advanced MIMO standard. The proposed FFT architecture has been implemented in Xilinx Artix-7 FPGA device and the performance metrics have been analysed. Even though the proposed FFT architecture consumes additional Block-RAMs (BRAM) and quite an amount of Xilinx-Xtreme Digital Signal Processor (DSP)/ DSP48 resources, the Power Delay Product (PDP) of the proposed FFT is excellent compared to the existing FFT architectures. The proposed multi radix mixed 2/3/5 parallel pipelined 2048 point FFT architectures exhibits very less latency of 11.382 µs at 550 MHz clock frequency compared to the existing system with the latency of 56.88 µs at 200 MHz clock frequency. Moreover, the designed FFT architecture utilizes 96 Xilinx Xtreme DSP blocks 25040 clock cycles to complete the FFT operation with an excellent throughput of 2200 MSPS with FFT computation time of 45.528 µs at the clock frequency of 550 MHz for the 4x4 MIMO- OFDM architecture. Therefore, the designed FFT provides high throughput rate in order to meet the modern wireless standard specifications. The proposed FFT architecture outperforms well in terms high throughput, low latency and better PDP with extra hardware as trade-off for both for Single FFT and for MIMO technology.