Single-tone and multi-tone transmissions in the narrowband Internet of Things (NB-IoT) uplink system can be accomplished by employing different orthogonal basis. In this paper, we develop an uplink NB-IoT baseband system model and derive the corresponding analytical signal model based on the discrete cosine transform type-I (DCT-I) domain. Basically, the circular convolution and channel matrix diagonalization issues for designing DCT-based systems are addressed without exploiting any redundancy (a prefix and a suffix sequences, and zero-padding (ZP)) into each transmitted data symbol blocks. In our proposed DCT-I based transceiver, we employ a standard cyclic prefix (CP) and apply discrete Fourier transform (DFT) and inverse DFT (IDFT) operations directly to make the channel matrix circulant and diagonal, resulting in the use of one-tap frequency-domain channel equalizer without incorporating extra front-end prefilter at the receiver. Furthermore, we propose novel least squares (LS) and linear minimum mean square error (LMMSE) channel estimators by considering the energy concentration and spectral compaction properties of DCT-I for the uplink NB-IoT system. The expressions for the DCT-I domain LS and LMMSE estimators are derived for channel frequency response estimation and mean square error computation. Finally, the viability of the proposed CP-DCT-I-NB-IoT uplink system, as well as the channel estimators, are tested compared with the standardized CP-DFT-NB-IoT and ZP-DCT type-2 even based single-carrier frequency-division multiple access (SC-FDMA) systems through rigorous computer simulations.

窄带物联网（NB-IoT）上行链路系统中的单音和多音传输可以通过采用不同的正交基来实现。在本文中，我们开发了上行链路 NB-IoT 基带系统模型，并基于离散余弦变换类型 I (DCT-I) 域推导出相应的分析信号模型。基本上，用于设计基于 DCT 的系统的循环卷积和信道矩阵对角化问题得到解决，而无需在每个传输的数据符号块中使用任何冗余（前缀和后缀序列以及零填充 (ZP)）。在我们提出的基于 DCT-I 的收发器中，我们采用标准循环前缀 (CP) 并直接应用离散傅立叶变换 (DFT) 和逆 DFT (IDFT) 操作来使信道矩阵循环和对角线，导致使用一键式频域信道均衡器，而无需在接收器处并入额外的前端前置滤波器。此外，我们通过考虑上行链路 NB-IoT 系统的 DCT-I 的能量集中和频谱压缩特性，提出了新颖的最小二乘法 (LS) 和线性最小均方误差 (LMMSE) 信道估计器。DCT-I 域 LS 和 LMMSE 估计器的表达式是为信道频率响应估计和均方误差计算推导出来的。最后，将所提出的 CP-DCT-I-NB-IoT 上行链路系统以及信道估计器的可行性与标准化的 CP-DFT-NB-IoT 和 ZP-DCT type-2 甚至基于单载频分多址 (SC-FDMA) 系统通过严格的计算机模拟。