## 1 Introduction  
Wireless communication systems face severe necessities in terms of transmission speed, technique capacity, reliability, and latency to meet the communication of new rising implementations such as Internet of Things (IoT), ultra-high description multimedia and virtual reality (VR) in the fifth generation (5G) [1, 2, 3]. Moreover, the development of wireless communication technique is limited to several harmful factors in the radio propagation environments, such as inter-symbol interference (ISI), multi-user interference (MUI), propagation attenuation, and multipath fading [4]. These damaging components cause various technological difficulties in the plan of reliable wireless communication systems. A heuristic approach to dealing with these design challenges is the use of a multi-antenna communication paradigm, which is of great interest in both academia and industry, because of obvious demonstration advantages of network capacity and service quality (QoS) [5]. The multi-input multi-output (MIMO) technique has been built by mounting multiple antennas to the transmitter and receiver terminals [6], which have proven to provide a range of improvements over single-input-single-output (SISO) systems [7]. However, Generalized Frequency Division Multiplexing (GFDM) waveform was recommended for the 5G air interface due to the nominal system complexity, suppression spectrum coordination, and lower peak-to-average-power ratio (PAPR), which provides higher power efficiency compared to OFDM [8]. The flexibility of the GFDM simplifies association with the single-carrier frequency domain equalizer (SC-FDE) and the filter bank multi-carrier (FBMC) systems [9]. The GFDM is based on modulation per subcarrier, where every subcarrier is single and independently modulated with multiple symbols. Subsequently, in this modulation scheme, the subcarrier is filtered through a circularly shifted prototype filter in the time and frequency regions. This filtering is intended to reduce the out-of-band emission (OOBE) residues and thus facilitates split-spectrum and dynamic spectrum distributions without causing serious interference to the GFDM system or other users. On the other hand, both ISI and inter-carrier interference (ICI) between sub-carriers may occur with such a filtering process. Fortunately, to obtain better performance than OFDM in several applications, used interference reduction techniques such as matched filter receiver with repetitive interference reduction, which is establish be effective, can be exploited well-designed receiving techniques [10]. In the challenge between the 5G waveform applicants, various modulation techniques were proposed. Some of the waveforms, for example; the FBMC system, which allows for simultaneous multiple access, focuses on providing a very low OOBE [11]. Other designs, such as windowed-OFDM (W-OFDM) [12] and filtered-OFDM (F-OFDM) [13], deal with the application complexity leading to several OFDM-based recommendations. In addition, GFDM was proposed as an alternative to OFDM to increase spectral efficiency by decreasing the cyclic prefix (CP) of OFDM [14]. However, due to the flexibility in adjusting dissimilar parameters such as subcarrier and subscript number, prototype pulse shape, and active subscript set, GFDM can be reconfigured to meet dissimilar necessities [15]. This flexibility performs the design and implementation of the combined multi-carrier frame based on the GFDM model. In this study, it is recommended to combine Walsh-Hadamard transform (WHT) [16] and Lifting Wavelet Transformation (LWT) [17] with GFDM waveform to increase the achievement of multi-carrier wireless telecommunication schemes using GFDM scheme. To examine the performance of the proposed WHT-LWT-GFDM waveform and to compare with waveforms such as conventional OFDM, GFDM and WHT-GFDM [18], using WHT, the computer simulation studies are performed over additive white Gaussian noise (AWGN) and frequency flat Rayleigh fading channels.