## 2 FFT Design Considerations
### Kernel-Based FFT for Multiple Standards  
Most MIMO-OFDM standards have variable FFT lengths and stream levels, and thus, the corresponding MDC or MDF FFT designs generally employ a reconfigurable structure to support various FFT operation modes specified at the aimed specification [7; 20; 22]. In addition, considerable research has been conducted on advanced restructure schemes for multimode FFT processors that support multiple MIMO-OFDM standards [28; 29]. For such multimode/multistandard MIMO-OFDM FFT applications, the aforementioned studies have employed tailored reconfiguration methods to enable multimode FFT operations based on their individual MDC/MDF structures. Therefore,  
Figure 4: Block diagram of conventional \(M\)-path MDF FFT architecture for \(M\)-stream MIMO-OFDM.  
Figure 3: Block diagram of conventional \(M\)-path MDC fast Fourier transform (FFT) architecture for M-stream MIMO-OFDM.  
the aforementioned approaches lack the design flexibility and convenience to develop the multistandard MIMO-OFDM FFT architecture.  
However, among the mainstream MIMO-OFDM standards (WiFi, LTE, and 5G applications), 1- to 4-stream 128/64-point FFT is implemented with a base operation mode [20; 21; 22; 23; 25; 26; 27; 28]. This is one approach, using which a common optimized four-stream 128/64-point FFT kernel can be developed as a base module to construct specified \(M\)-stream \(N\)-point FFT/IFFT processors. For example, in the MDF FFT architecture, Figure 5 presents the aforementioned scheme. Considering \(M\)-stream \(N\)-point FFT computation (\(M>4\); \(N>128\), and \(N\) is to the power of 2), each \(N\)-point FFT can be performed using \(N^{\prime}\)-point FFT in conjunction with 128-point FFT based on the radix-\(N^{\prime}\)/128 FFT algorithm, where \(N^{\prime}\) is equal to \(N\)/128, and \(M\)-stream FFT can be implemented in \(\lceil M/4\rceil\) sets of four-stream FFT; \(\lceil\cdot\rceil\) denotes a ceiling operation. Figure 5 shows a four-stream 128/64-point FFT kernel prepared first as a common base module. This kernel module was further integrated with a front four-stream \(N^{\prime}\)-point FFT computation unit to complete a set of four-stream \(N\)-point FFT. Such configuration (FFT kernel and \(N^{\prime}\)-point FFT unit) can be extended to \(\lceil M/4\rceil\) sets, and complete \(M\)-stream \(N\)-point FFT operations can be implemented. For hardware modularization, kernel-based FFT configurations are more efficient and flexible when applied to scalable \(M\)-stream \(N\)-point FFTs for multiple MIMO-OFDM standards. Figure 5 presents a configuration which can be further modified and extended to integrate a conventional FFT kernel with MDC or memory-based units for target FFT computation. Considering four-path 128/64-point FFT kernel designs, employing the available FFT processors, which can perform the same FFT specification, is an efficient approach [21; 25]. Nevertheless, for system optimization, specific development of a hardware-efficient FFT kernel as a common module can be advantageous. In this study, the target FFT kernel module was designed using a modified MDF structure as support. In addition to the original four-stream 128/64-point FFT operations, the proposed FFT kernel used GI duration to enable five- and six-stream FFT operations, and thereby enhance the overall throughput with an improved area efficiency. The concept for GI utilization for the FFT design has been mentioned in [31] for the purpose of improving the operation latency. In our design, we further utilized the GI in common with a resource-sharing scheme to increase the operation throughput. The details of the proposed design are discussed in Sections 3 and 4.