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**Comparison of different MIMO-OFDM signal detectors for LTE**

Master Thesis Seminar Presentation Student: SHAO Qiwen 69597A Supervisor: Olav Tirkkonen Aalto University School of electrical Engineering 21/11/2014

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**Contents 01 02 03 Motivations & Backgrounds Modeling & Simulation**

模板来自于 03 Results Analysis

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01 Motivations & Backgrounds

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Motivations Nowadays, it raises a higher demand of the transmission rate, transmission performance and data throughput. Not only use more spectrum resources, but also use more space resources. Multiple Input Multiple Output (MIMO) is used for signal transmission. Diversity is an effective technology. Time diversity, frequency diversity and space diversity. LTE is introduced and widely used nowadays. The key technologies of LTE are MIMO OFDM Signal detection algorithms are studied in this thesis. ZF, MMSE, ML, SD, QRM-MLD

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**Definitions We concentrate on BER performance of the detectors.**

In the same wireless transmission environment, what are the performances of these detectors? How does SD detector behave while the radius changes from small value to the value large enough compared to ML detector? How does QRM-MLD behave while the value of parameter M changes from 4 to 16 compared to ML detector? What are the performances of these detectors with a correlated MIMO channel? What is the performance of the detector while the MIMO-OFDM channel is correlated compared to if it is uncorrelated?

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**LTE For 3GPP LTE, there were many technological requirements [2]:**

Spectrum efficiency The downlink (DL) should be 3-4 times HSDPA for 2×2 MIMO antenna arrays The uplink (UL) should be 2-3 times E-DCH for 1×2 MIMO antenna arrays. Scalable bandwidth 1.4, 3, 5, 10, 15, 20 MHz should be possible. All carrier frequencies of IMT-2000 from 450 MHz to 2.6 GHz should be covered. The peak data rate in DL should be greater than 100Mb/s for 20MHz spectrum allocation in UL it should be greater than 50Mb/s for 20MHz spectrum allocation. The capacity 200 users for 5MHz and 400 users in large spectrum allocations. The latency requirement less than 100ms to establish U-plane in C-plane less than 10ms from UE to server in U-plane. The coverage requirements Full performance target for cell radius up to 5km Performance with slight degradation should be possible for cell radius up to 30km. Mobility requirements LTE is optimized for low speeds 0-15km/h but the connection should be maintained for speeds up to 350 or 500km/h. Handover time between 3G & 3G LTE in real time mode should be no more than 300ms and no more than 500ms in non- real time mode.

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**Spatial stream generator**

MIMO Channel estimator × × × × × × × × × × × × × × × × 𝑥 1 𝑦 1 Spatial stream generator Signal Detector × × × × × × × × 𝑥 N T ⋯ 𝑥 2 𝑥 1 × × × × 𝑥 2 𝑦 2 𝑥 N T ⋯ 𝑥 2 𝑥 1 × × × × … … × × × × × × × × × × × × 𝑥 𝑁 𝑇 𝑦 𝑁 𝑇 × × × × MIMO improves communications system performance by full use of space diversity. The data throughput and the spectrum utilization can grow exponentially. Multipath propagation would cause channel fading, which is harmful.

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OFDM S/P P/S IFFT FFT Add CP Remove CP D/A A/D Multipath Channel … OFDM is a multi-carrier modulation. Channel is divided into a number of orthogonal sub- channels. The high speed data signal is converted into parallel low speed sub-streams [3]. OFDM is effective against frequency selective fading and Inter Symbol Interference (ISI) [3]. Wireless data services are asymmetric, while using OFDM, the number of sub-channels can be adjusted flexibly to meet the different rate of downlink and uplink transmission [3]. OFDM can be jointly used with other access methods [6]. A major advantage of OFDM technology is that fast FFT/IFFT could be used for implementation [6].

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Channel Model In wireless transmission, the characteristics of the received signal changes because of [6] The distance between the two antennas The path(s) taken by the signal The environment (building and other objects) around the path The medium between the transmit antenna and the receive antenna is called the channel. The effects of the channel can be characterized by a linear response. There are three key components of the channel response [8] Path loss Shadowing Multipath Rayleigh distribution is the most common model used to describe the statistics of the receiving envelope of a time varying flat fading signal or the receiving envelope of an independent multipath components [8]. Rayleigh fading model is applicable to describe the wireless channels of built-up zone in city center [8]. We only concentrate on the multipath Rayleigh fading channel in this thesis.

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Spatial Correlation In practice, the channels between different antennas are often correlated. In urban cellular systems, the channel between the base station and the user is a multipath non-line-of-sight channel. The channel represents how the signal is reflected from the transmitter to the receiver. The received signal may be received from certain directions with strong spatial characteristics. The correlation between the received average signal gain and the angle of arrival (AoA) of a signal is the so called spatial correlation [9]. The existence of spatial correlation has been experimentally validated [10, 11]. In reference [6] it is assumed that the correlation matrices for the transmitter and receiver can be separated for the MIMO channel model of the correlation matrix model. The Kronecker model is introduced for modeling spatial correlation [10]. The correlation between the transmit antennas and receive antennas are assumed independent and separable.

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Signal Detection Signal detection technology is one of key technologies of LTE. Signal detection algorithms includes: Linear signal detection algorithms: ZF, MMSE, … Non-linear signal detection algorithms: ML, SD, QRM-MLD, … ML has the optimal BER performance. The current study focused on the signal detection algorithm is in two areas [6]: To enhance the performance of the linear detector. To reduce the complexity of maximum likelihood algorithm. QRM-MLD, SD algorithms are the algorithms to reduce the complexity of ML.

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Zero Forcing Linear signal detection only treats desired stream from target transmit antenna as signals and all other transmitted signals would be treat as interferences [6]. 𝐱 𝑍𝐹 = 𝐖 𝑍𝐹 𝐲=𝐱+ ( 𝐇 H 𝐇) −𝟏 𝐇 H 𝐳=𝐱+ 𝐳 𝒁𝑭 [6] Interference signals from other transmit antennas are minimized or nullified when detecting the signal from desired antenna [6]. Zero-Forcing detection is low complexity linear detection algorithm. The detector thus forces the interference to zero. It behaves as a linear filter separating different data streams to perform decoding independently on each stream, therefore eliminating the multi- stream interference [6]. The drawback of ZF detection is retarded BER performance due to noise enhancement [6].

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**Minimum Mean Square Error**

MMSE detector estimates the transmitted vector 𝐱 by applying the linear transformation to the received vector 𝐲. 𝐱 𝑀𝑀𝑆𝐸 = 𝐖 𝑀𝑀𝑆𝐸 𝐲= ( 𝐇 H 𝐇+ σ 𝒛 𝟐 𝐈) −𝟏 𝐇 H 𝐲= 𝐱 + ( 𝐇 H 𝐇+ σ 𝒛 𝟐 𝐈) −𝟏 𝐇 H 𝐳= 𝐱 + 𝐳 𝑀𝑀𝑆𝐸 [6] MMSE weight matrix 𝐖 𝑀𝑀𝑆𝐸 is to maximize the post-detection signal- to-interference plus noise ratio (SINR) [6]. MMSE receiver requires the statistical information of noise 𝜎 𝑧 2 . MMSE detectors balances the noise enhancement and multi-stream interference by minimizing the total error [6].

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Maximum Likelihood Maximum likelihood (ML) detection calculates the Euclidean distance between the received signal vector and the product of all possible transmitted signal vectors with the given channel 𝐇, and finds the one with the minimum distance. 𝐱 𝑀𝐿 = 𝑎𝑟𝑔 min 𝑥∈ 𝐶 𝑁 𝑇 𝐲−𝐇𝐱 [6] The ML method achieves the optimal performance as the maximum a posteriori (MAP) detection when all the transmitted vectors are equally likely [14]. Its complexity increases exponentially as modulation order and/or the number of transmit antennas increases [14].

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Sphere Decoding SD algorithm intends to find the transmitted signal vector with minimum ML metric, that is, to find the ML solution vector. However, it considers only a small set of vectors within a given sphere rather than all possible transmitted signal vectors [15, 16]. The main drawback of SD is that its complexity depends on SNR [15]. The sphere radius 𝑅 𝑆𝐷 will impact on the performance of SD detector as is indicated above. If the radius 𝑅 𝑆𝐷 is chosen too small, there would be no points inside the search area in the sphere and the algorithm would fail. Meanwhile, if the radius 𝑅 𝑆𝐷 is chosen too large, there would be too many points would be searched and the complexity would increase while the efficiency would decrease.

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QRM-MLD An approach for MIMO detection that applies QRM-MLD was proposed in [13]. QRM-MLD reduces the computational complexity compare with the computational complexity of ML detection in MIMO OFDM systems. Assuming that the number of the transmit and receive antennas are equal [6]. It searches all branches only for M retained nodes instead of all nodes. In a 2×2 MIMO system, for 16QAM, there are two branches, each branch has 16 nodes. It reduces the computation complexity from 16×16 to 𝑀×𝑀. The performance of BER of QRM-MLD depends on the parameter M. If M increases, its performance approaches the performance of ML detector while the complexity will also increases.

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02 Modeling & Simulation

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**Method Used Methods could be used:**

Theoretical analysis Simulation, e.g. Matlab Simulation Measurements in practice Due to complexity consideration and the same wireless propagation configuration, simulation method is chosen for the comparison of the detectors. It will helpful to better understand the signal detection algorithms as well as principle of MIMO-OFDM system.

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**System Modeling MIMO-OFDM is selected as the key technologies of LTE.**

S/P IFFT P/S Add CP Remove CP FFT Detector 16 QAM 𝑠 1 𝑠 2 𝑠 1 𝑠 2 𝑥 1 𝑥 2 𝑦 1 𝑦 2 MIMO-OFDM is selected as the key technologies of LTE. Multipath Rayleigh fading channel is selected and the channel is ideal. Spatial correlation is considered. AWGN is selected as the basic noise model. 16QAM is considered. Signal detectors: ZF, MMSE, ML, QRM-MLD, SD

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**Simulation Parameters**

Transmission Bandwidth 20 MHz MIMO antenna arrays 2×2 Data length 1200 Number of IFFT/FFT points 2048 Cyclic prefix length 144 Data modulation/Spreading 16QAM Symbol timing detection Ideal Multipath fading 6-taps Rayleigh fading Sample rate 30.72 MHz Spatial correlation Receiver: METRA Transmitter: METRA Macro Cell with 5° PAS Tap Channel A Channel B Doppler Spectrum Relative Delay (ns) Average Power (dB) 1 0.0 -2.5 Classic 2 310 -1.0 300 3 710 -9.0 8900 -12.8 4 1090 -10.0 12900 5 1730 -15.0 17100 -25.2 6 2510 -20.0 20000 -16.0

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03 Results Analysis

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Results

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**Results Analysis Figure 12 shows that in an uncorrelated scenario**

ZF detector has the worst BER performance while the ML detector has the optimal BER performance. As the way to reduce the complexity of ML detector, QRM-MLD and SD detector with low complexity (M=4 for QRM-MLD and the radius 𝑅 𝑆𝐷 is the half of the noise power respectively) have better BER performance than the basic linear detectors. While in a correlated scenario The comparison of BER performance is almost the same and the for a single detector, its BER degrades when in a correlated scenario.

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Results

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Results Analysis When the complexity of QRM-MLD or SD detector is increased (M=8 for QRM-MLD and the radius 𝑅 𝑆𝐷 is the twice of the noise power respectively), Figure 13 shows that QRM-MLD has a better BER performance than the basic linear signal detector as well as SD detector. ML detector always has the optimal BER performance. In a correlated scenario, the comparison of the BER performance of four different MIMO-OFDM detectors is relatively the same as in an uncorrelated scenario. Thus the BER of the detector degrades dramatically.

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Results

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Results Analysis QRM-MLD for different M values (we assumed the value of parameter M is M=4, M=8 and M=16 respectively) has been simulated simultaneously with ML detector and MMSE detector. Figure 5.3 shows that the greater the value of parameter M of QRM-MLD, the better the BER performance in the same spatial correlation scenario. When QRM-MLD has a low complexity (e.g. M=4), it has a lower BER than MMSE detector while it has the greatest complexity (M= 16 for the 16QAM constellation size), it has the same BER performance as the ML detector.

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Results

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Results Analysis SD for different radius 𝑅 𝑆𝐷 (half of the noise power, twice of the noise power and four times of the noise power plus one respectively) has been simulated simultaneously with ML detector and MMSE detector. Figure 5.4 shows that the greater the radius 𝑅 𝑆𝐷 , the better the BER performance in the same spatial correlation scenario. When SD detector has a low complexity (e.g. 𝑅 𝑆𝐷 is half of the noise power), it has a lower BER than MMSE detector while it has the greatest complexity ( 𝑅 𝑆𝐷 is equal to four times of the noise power plus one for a large enough value), it has the same BER performance as the ML detector.

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Conclusion MIMO technology can significantly increase channel capacity and spectrum efficiency. OFDM is an efficiency multi-carrier transmission technology as it can provide much higher spectrum utilization. Spatial correlation is studied. High spatial correlation means some spatial directions are statistically stronger than others [6]. 5 Signal detectors are studied. ML detector has the optimal BER performance. QRM-MLD algorithm and SD algorithm are the algorithms reduce the complexity of ML algorithm. Different M values of QRM-MLD for different complexity are studied. Different radius of SD for different complexity are studied. Basic linear detectors, e.g. ZF and MMSE have higher BER than ML detector, QRM-MLD and SD detector.

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