Abstract — This paper is described intra-cell interference in case of multiuser access based on single-carrier frequency division multiple access signals (SC-FDMA), which is used in LTE networks for uplink control channel and virtual multiple-input multiple-output (V-MIMO) mode. It is shown the reason of intra-cell interference and performance degradation. Also it is discussed a gradient based solution for user alignment to minimize the interference. Keywords — interference, LTE, SC-FDMA, Gauss- Newton, optimization, SIR, mitigation. I. INTRODUCTION N the LTE uplink, SC-FDMA using discrete Fourier transform (DFT) precoded orthogonal frequency division multiple access was adopted for its prioritization of wide area coverage provisioning due to its low peak-to- average power ratio (PAPR) feature [1]. Multiple accesses for different terminals are multiplexed using orthogonal code division multiple access within the same resource block, in the same sub-frame [1]. An orthogonal multiplexing is achieved using orthogonal sequences, which are generated by cyclic-shifting the original constant amplitude zero auto-correlation (CAZAC) sequence [2]. This is based on the fact that cross-correlation is quite low among cyclic shifted CAZAC sequences. However, it was reported that orthogonal properties is destroyed due to the increasing inter-code interference, when the delay times of delayed paths approach the cyclic shift interval [3]. There are defined two type of inter-code interference caused by frequency offset and time offset [4]. Frequency offset is limited by requirements for terminal and has less influence on performance than both Doppler shift and time offset. Time offset has more significant influence on intra- cell interference appearance. II. INTERFERENCE AND POWER LEAKAGE The multiuser access and time offset introduce an error [4]. It is clear that different users interact in the propagation channel. CAZAC sequence is used for user separation on the receiver side. Multiuser access model is defined as: 訓噺屈 待 桑 待 隈 待 隙 待 髪デ 屈 槌 桑 槌 隈 槌 隙 槌 町貸怠 槌退怠 髪櫛 (1) For each antenna element 券噺な┼軽. Here 訓樺翁 懲 – Mikhail Maksimov (maksimovm@mail.ru) and Nikolai Merezhin (nmerejin@mail.ru) are with the department of Fundamentals of Radio Engineering, Southern Federal University, Taganrog, Russia. Vladimir Lyashev (lyashev@ieee.org) is research fellow of Southern Federal University and with Russian Research Center, Huawei Technologies Co. Ltd., Moscow, Russia. received signal, 桑 槌 樺翁 懲抜懲 – time offset matrix, which is defined by shifted window for symbol selection, 隈 槌 樺翁 懲 – vector of CAZAC sequence for terminal 圏; 隙 槌 is modulated symbol and 屈 槌 樺翁 懲抜懲 is diagonal channel matrix in frequency domain; 計 – number of sub-carriers, 軽 – number of antennas on the receiver (we assume single transmit antenna for each terminal), 芸 – number of users, 櫛 – Gaussian noise. Let us always call UE0 is desired terminal, and the others UEs are interferers. Consider orthogonal properties for 隈 槌 , we can obtain the signal for every user on each antenna element: 桁 待 噺隈 待 張 訓噺隈 待 張 屈 待 桑 待 隈 待 隙 待 髪 髪デ 隈 待 張 屈 槌 桑 槌 隈 槌 隙 槌 町貸怠 槌退怠 髪隈 待 張 櫛 . (2) Let us define the sum in (2) as intra-cell interference. If the matrix 範屈 槌 桑 槌 飯 is identity one, then we haven’t the interference, because of CAZAC sequence orthogonality 隈 待 張 隈 槌貯待 岩ど, otherwise it is not true. The orthogonality is lost, because of time offset by fading channel and synchronization: delay spread in the channel 屈 and synchronization error 桑. Let us define matrix 桑 in frequency domain 劇 槌 岫倦┸ 倦岻 噺 結 貸 鉄肺答禰 忍 入 畷 縄 沈 , (3) つ建 槌 – absolute accuracy of propagation delay estimation by synchronization sequence or sounding signal (劇 聴 is sampling period). As we have mentioned before, there are two reasons for time offset: synchronization error and channel spread, so we can define equivalent time offset matrix 桑 風 槌 噺屈 槌 桑 槌 . Thus, according (2) with normalization by coefficient 】隈 待 張 屈 待 桑 待 隈 待 】 we can write down power of each user 鯨 寞 槌 噺鋪 隈 轍 那 桑 風 忍 隈 忍 隈 轍 那 桑 風 轍 隈 轍 鋪 態 鯨 槌 , (4) where 鯨 槌 is transmitted power of user 圏, and 鯨 寞 槌 is power of desired user (圏噺ど) or leakage power of interferers into the desired channel. Thus, signal to interference ratio 5+4 岫単岻 噺鋪 隈 轍 妬 桑 風 轍 隈 轍 隈 轍 妬 桑 風 桃 隈 桃 鋪 態 託 轍 託 桃 ┻ (5) If time offset matrices for different users are close each other, then we can evaluate 桑 風 by algorithm proposed in [4] or by some other way and makes opposite shift of window for symbol selection (compensation of time offset). However, in practice, time offset matrix is different for different users that means we cannot compensate time offset according (1), because of nonlinear problem. Some nonlinear optimization methods are discussed in the next section. Non-Linear Optimization Scheme for Non-Orthogonal Multiuser Access Vladimir Lyashev, Member, IEEE, Mikhail Maksimov, Nikolai Merezhin I 44pf Vgngeqoowpkecvkqpu hqtwo VGNHQT 4236 Ugtdkc. Dgnitcfg. Pqxgodgt 47/49. 42360 ;9:/3/69;;/83;3/91361&53022 Æ4236 KGGG 581