Subject : Wireless and Cellular Communication (18EC81)

MODULE-4

TEXT BOOKS

Text Books:

1. “FUNDAMENTALS OF LTE”, Arunabha Ghosh, Jan Zhang, Jefferey Andrews, Riaz Mohammed, Pearson education (Formerly Prentice Hall, Communications Engg. and Emerging Technologies) ISBN-13: 978-0-13-703311-9.
2. “Introduction to Wireless Telecommunications Systems and Network”, Gary Mullet, First Edition, Cengaga learning India Pvt Ltd., 2006, ISBN-13: 978-81-315-0559-5.

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Reference Books:

1. “Wireless Communications: Principles and Practice” Theodore Rappaport, 2^nd Edition, Prentice Hall Communications engineering and emerging Technologies Series, 2002, ISBN 0-13-042232-0.
2. “LTE for UMTS Evolution to LTE-Advanced” Harri Holma and Antti Toskala, Second Edition - 2011, John Wiley & Sons, Ltd. Print ISBN: 9780470660003.2

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Key Enabling Technologies and Features of LTE

A brief introduction to some of the key enabling technologies used in the LTE design

1. Orthogonal Frequency Division Multiplexing (OFDM)
2. SC-FDE and SC-FDMA
3. Channel Dependent Multi-user Resource Scheduling
4. Multi-antenna Techniques
5. IP-Based Flat Network Architecture

���1.Orthogonal Frequency Division Multiplexing (OFDM)�

• One of the key differences between existing 3G systems and LTE is the use of Orthogonal Frequency Division Multiplexing (OFDM) as the underlying modulation technology.
• Widely deployed 3G systems such as UMTS(Universal Mobile Telecommunication System) and CDMA2000 are based on Code Division Multiple Access (CDMA) technology.
• CDMA works by spreading a narrow band signal over a wider bandwidth to achieve interference resistance and performs remarkably well for low data rate communications such as voice, where a large number of users can be multiplexed to achieve high system capacity.
• For high-speed applications, CDMA becomes untenable due to the large bandwidth needed to achieve useful amounts of spreading.

OFDM has emerged as a technology of choice for achieving high data rates. It is the core technology used by a variety of systems including Wi-Fi and WiMAX. The following advantages of OFDM led to its selection for LTE:

1. Elegant solution to multipath interference
2. Reduced computational complexity
3. Graceful degradation of performance under excess delay
4. Exploitation of frequency diversity
5. Enables efficient multi-access scheme
6. Robust against narrowband interference
7. Suitable for coherent demodulation
8. Facilitates use of MIMO
9. Efficient support of broadcast services

• Disadvantages of OFDM:
• Peak-to-Average Ratio (PAR): OFDM has high PAR, which causes non-linearity and clipping distortion when passed through an RF amplifier.
• High PAR increases the cost of the transmitter.

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2. SC-FDE and SC-FDMA

• To keep the cost down and the battery life up, LTE incorporated a power efficient transmission scheme for the uplink.
• Single Carrier Frequency Domain Equalization (SC-FDE) is conceptually similar to OFDM but instead of transmitting the Inverse Fast Fourier Transform (IFFT) of the actual data symbols, the data symbols are sent as a sequence of QAM symbols with a cyclic prefix added; the IFFT is added at the end of the receiver.
• SC-FDE retains all the advantages of OFDM such as multipath resistance and low complexity, while having a low peak-to-average ratio of 4-5dB.
• The uplink of LTE implements a multi-user version of SC-FDE, called SC-FDMA, which allows multiple users to use parts of the frequency spectrum.
• SC-FDMA closely resembles OFDMA and can in fact be thought of as “DFT precoded OFDMA.”
• SC-FDMA also preserves the PAR properties of SC-FDE but increases the complexity of the transmitter and the receiver.

3. Channel Dependent Multi-user Resource Scheduling

• The OFDMA scheme used in LTE provides enormous flexibility in how channel resources are allocated.
• OFDMA allows for allocation in both time and frequency and it is possible to design algorithms to allocate resources in a flexible manner to meet throughput, delay, and other requirements.
• The standard supports dynamic, channel-dependent scheduling to enhance overall system capacity.
• Frequency selective multiuser scheduling, calls for focusing transmission power in each user’s best channel portion, thereby increasing the overall capacity.

• Frequency selective scheduling requires good channel tracking and is generally only viable in slow varying channels.
• For fast varying channels, the overhead involved in doing this negates the potential capacity gains.
• In OFDMA, frequency selective scheduling can be combined with multi-user time domain scheduling, which calls for scheduling users during the crests of their individual fading channels.
• For high-mobility users, OFDMA can be used to achieve frequency diversity.
• By coding and interleaving across subcarriers in the frequency domain the signal can be made more robust against frequency selective fading or burst errors.
• Frequency diverse scheduling is best suited for control signalling and delay sensitive services.

4. Multi-antenna Techniques

The LTE standard provides extensive support for implementing advanced multi-antenna solutions to improve link robustness, system capacity and spectral efficiency.

Depending on the deployment scenario, one or more of the techniques can be used. Multi-antenna techniques supported in LTE include:

1. Transmit diversity
2. Beamforming
3. Spatial multiplexing
4. Multi-user MIMO

1. Transmit Diversity:

• This technique is used to combat multipath fading in the wireless channel.
• Copies of same signal is sent that are coded differently over multiple transmit antenna.
• LTE transmit diversity is based on space-frequency block coding (SFBC) techniques complemented with frequency shift time diversity(FSTD).
• Transmit diversity is used in common downlink channels that cannot make use of channel-dependent scheduling.
• It increases system capacity and cell range.

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2. Beamforming:

• Multiple antennas in LTE may also use beamforming technique to transmit the beam in the direction of the receiver and away from interference, thereby improving the received signal-to-interference ratio.
• It can provide significant improvements in coverage range, capacity, reliability and battery life.
• It can also be useful in providing angular information for user tracking.
• LTE supports beamforming in the downlink.

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3. Spatial multiplexing :

• In spatial multiplexing, multiple independent streams can be transmitted in parallel over multiple antennas and can be separated at the receiver using multiple receive chains through appropriate signal processing.
• Spatial multiplexing provides data rate and capacity gains proportional to the number of antennas used.
• It works well under good SNR and light load conditions. LTE standard supports spatial multiplexing with up to four transmits antennas and four receiver antennas.

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4. Multi-user MIMO:

• Since spatial multiplexing requires multiple transmit antennas, it is currently not supported in the uplink due to complexity and high cost.
• Multi-User MIMO (MU-MIMO) allows multiple users in the uplink, each with a single antenna, to transmit using the same frequency and time.
• The signals from the different MU-MIMO users are separated at the base station receiver using accurate channel state information of each user

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5. IP-Based Flat Network Architecture

• “Flat” here implies fewer nodes and a less hierarchical structure for the network.
• The lower cost and lower latency requirements drove the design toward a flat architecture since fewer nodes obviously implies a lower infrastructure cost.
• It also means fewer interfaces and protocol-related processing, and reduced interoperability testing, which lowers the development and deployment cost.

• Figure 1.3 shows how the 3GPP network architecture evolved over a few releases.
• 3GPP Release 6 architecture, which is conceptually very similar to its predecessors, has four network elements in the data path: the base station or Node-B, radio network controller (RNC), serving GPRS service node (SGSN), and gateway GRPS service node (GGSN).
• Release 7 introduced a direct tunnel option from the RNC to GGSN, which eliminated SGSN from the data path.
• LTE on the other hand, will have only two network elements in the data path: the enhanced Node-B or eNode-B, and a System Architecture Evolution Gateway (SAE-GW).
• Unlike all previous cellular systems, LTE merges the base station and radio network controller functionality into a single unit.
• The control path includes a functional entity called the Mobility Management Entity (MME), which provides control plane functions related to subscriber, mobility, and session management.
• The MME and SAE-GW could be collocated in a single entity called the access gateway (a-GW).

• A key aspect of the LTE flat architecture is that all services, including voice, are supported on the IP packet network using IP protocols.
• Unlike previous systems, which had a separate circuit-switched subnetwork for supporting voice with their own Mobile Switching Centers (MSC) and transport networks, LTE envisions only a single evolved packet-switched core, the EPC, over which all services are supported, which could provide huge operational and infrastructure cost savings.

LTE Network Architecture

• The core network design presented in 3GPP Release 8 to support LTE is called the Evolved Packet Core (EPC).
• EPC is designed to provide a high capacity, all IP, reduced latency, flat architecture that dramatically reduces cost and supports advanced real-time and media-rich services with enhanced quality of experience.
• It is designed not only to support new radio access networks such as LTE, but also provide interworking 2G GERAN and 3G UTRAN networks connected via SGSN.

LTE Network Architecture

Functions provided by the EPC include access control, packet routing and transfer, mobility management, security, radio resource management and network management.

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• A brief description of each of the four new elements is provided here:
• Serving Gateway (SGW)
• Packet Data Network Gateway (PGW)
• Mobility Management Entity (MME)
• Policy and Charging Rules Function (PCRF)

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Figure 1.4 shows the end-to-end architecture including how the EPC supports LTE as well as current and legacy radio access networks

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Serving Gateway (SGW)�

• The SGW acts as a demarcation point between the RAN and core network, and manages user plane mobility.
• It serves as the mobility anchor when terminals move across areas served by different eNode-B elements in E-UTRAN, as well as across other 3GPP radio networks such as GERAN and UTRAN.
• SGW does downlink packet buffering and initiation of network-triggered service request procedures.
• Other functions include lawful interception, packet routing and forwarding, transport level packet marking in the uplink and the downlink, accounting support for per user, and inter-operator charging.

Packet Data Network Gateway (PGW):

• The PGW acts as the termination point of the EPC toward other Packet Data Networks (PDN) such as the Internet, private IP network, or the IMS network providing end-user services.
• It provides functions such as user IP address allocation, policy enforcement, packet filtering, and charging support.
• Policy enforcement includes operator-defined rules for resource allocation to control data rate and usage.
• Packet filtering functions include deep packet inspection for application detection.

Mobility Management Entity (MME)�

• MME manages thousands of eNode-B elements, which is one of the key differences from 2G or 3G platforms using RNC and SGSN platforms.
• It is also responsible for selecting the appropriate serving and PDN gateways and selecting legacy gateways for handovers to other GERAN or UTRAN networks.
• MME controls all control plane functions related to subscriber and session management.
• The MME performs the signalling and control functions to manage the user terminal access to network connections, assignment of network resources, and mobility management function such as idle mode location tracking, paging, roaming, and handovers.
• The MME provides security functions such as providing temporary identities for user terminals, interacting with Home Subscriber Server (HSS) for authentication and negotiation of ciphering and integrity protection algorithms.

Policy and Charging Rules Function (PCRF)��

• The Policy and Charging Rules Function (PCRF) is a concatenation of Policy Decision Function (PDF) and Charging Rules Function (CRF).
• The PCRF interfaces with the PDN gateway and supports service data flow detection, policy enforcement and flow-based charging.
• The PCRF was actually defined in Release 7 of 3GPP ahead of LTE. Although not much deployed with pre-LTE systems, it is mandatory for LTE.
• Release 8 further enhanced PCRF functionality to include support for non-3GPP access (e.g., Wi-Fi or fixed line access) to the network.

Module-4 PART 2

Multicarrier Modulation

OFDMA and SC-FDMA

3.1 THE MULTICARRIER CONCEPT

• Multicarrier modulation is used to achieve high data rates and intersymbol interference (ISI) free channels.
• To have a channel without ISI, the symbol time T_s has to be larger than the channel delay spread τ.
• Digital communication systems simply cannot function if ISI is present—an error floor quickly develops and as T_s falls below τ, the bit error rate becomes intolerable.
• In wideband channels that provide the high data rates, the desired symbol time is usually much smaller than the delay spread, so inter symbol interference is severe.

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• In order to overcome this, multicarrier modulation divides the high-rate transmit bitstream into L lower-rate substreams,

Where, L is chosen such that each of the subcarriers has symbol time T_sL >> τ, and is hence effectively ISI-free.

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• These individual substreams are sent over L parallel subcarriers, maintaining the total desired data rate.

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• The subcarriers are orthogonal under ideal propagation conditions, in which case multicarrier modulation is often referred to as Orthogonal Frequency Division Multiplexing (OFDM).

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• The data rate on each of the subcarriers is much less than the total data rate, and that corresponds to subcarrier bandwidth is much less than the total system bandwidth.

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• Thus, the ISI on each subcarrier is small. In the digital implementation of OFDM, the ISI can be completely eliminated through the use of a cyclic prefix.

EXAMPLE 3.1

A certain wideband wireless channel has a delay spread of 1 μsec. In order to overcome ISI, assume a requirement that T_s ≥ 10τ.

1. What is the maximum bandwidth allowable in this system if the ISI constraint is to be met without using multicarrier modulation?
2. If multicarrier modulation is used, and we desire a 10MHz bandwidth, what is the required number of subcarriers?

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For part (1), if it is assumed that T_s = 10τ in order to satisfy the ISI-free condition, the maximum bandwidth would be 1/T_s = .1/τ = 100KHz, two orders of magnitude below the intended bandwidths for LTE systems.

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In part (2), if multicarrier modulation is employed, the symbol time goes to T = LT_s. The delay spread criterion mandates that the new symbol time is still bounded to 10% of the delay spread, that is, (LT_s)⁻¹ = 100KHz. But the 10MHz bandwidth requirement gives (T_s)⁻¹ = 10MHz.

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Hence, L ≥ 100, so a suitable³ choice of L might be 128 subcarriers to allow the full 10MHz bandwidth to be used with negligible ISI.

3.2 OFDM BASICS

• In order to overcome the requirement for L RF radios in both the transmitter and receiver, OFDM employs an efficient computational technique known as the Discrete Fourier Transform (DFT), which lends itself to a highly efficient implementation known as the Fast Fourier Transform (FFT).
• FFT (and its inverse, the IFFT) are able to create large number of orthogonal subcarriers using just a single radio.

3.2.1 Block Transmission with Guard Intervals

• Grouping ‘L’ data symbols into a block known as an OFDM symbol with duration of T seconds, where T = LTs.
• Guard time ‘Tg’ is introduced in between each OFDM symbol to keep independent of the others after going through a wireless channel, as shown below:

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• After receiving a series of OFDM symbols, as long as the guard time T_g is larger than the delay spread of the channel τ, each OFDM symbol will only interfere with itself.

• OFDM transmissions allow ISI within an OFDM symbol. But by including a large guard band, it is possible to guarantee that there is no interference between subsequent OFDM symbols.

3.2.2 Circular Convolution and the DFT

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• OFDM symbols is made orthogonal with a guard interval, the next task is to remove the ISI within each OFDM symbol.
• When an input data stream x[n] is sent through a linear time-invariant FIR channel h[n], the output is the linear convolution of the input and the channel, that is, 

y[n] = x[n] * h[n]

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• Let us consider that it is possible to compute y[n] in terms of a circular convolution, that is

Cyclic Prefix :

• The cyclic prefix acts as a buffer region or guard interval to protect the OFDM signals from ISI.
• The cyclic prefix is obtained by taking the last 𝑣 samples from the length N block of OFDM symbols, and it is appended at the start of the symbol block.
• As a result, the transmitted OFDM symbol block is of length N + 𝑣 as shown in the fig 3.4 .
• For each OFDM symbol to be independent and to avoid any ISI and ICI, the length 𝑣 of the CP should be at least equal to the channel order.

The cyclic prefix performs two main functions.

1. It provides a guard interval to eliminate ISI from the previous symbol.

2. It repeats the end of the symbol so the linear convolution of a frequency-selective multipath channel can be modeled as circular convolution.

• FFT/IFFT algorithms are used to realize OFDM with reduced computational complexity.
• The IFFT operation at the transmitter allows all the subcarriers to be created in the digital domain, and thus requires only a single radio to be used.

• In order for the IFFT/FFT to create an ISI-free channel, the channel must appear to provide a circular convolution.
• If a cyclic prefix is added to the transmitted signal, as shown in Figure 3.4, then this creates a signal that appears to be x[n]L, and so

y[n] = x[n]⊛ h[n].

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• Representing such an OFDM symbol in the time domain as a length L vector gives

X = [𝑥1, 𝑥2, 𝑥3,………..𝑥𝐿,]

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• After applying a cyclic prefix of length 𝑣, the actual transmitted signal is

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• The output of the channel is by definition

𝑌𝑐𝑝 = ℎ ∗ 𝑋𝑐𝑝

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Where, h is a length 𝑣 + 1 vector describing the impulse response of the channel during the OFDM symbols.

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• The output 𝑌𝑐𝑝 has samples = Length of OFDM symbol + Length of the channel response - 1

= (L + 𝑣) + (𝑣 + 1) - 1

= L + 2𝑣 samples.

• The first 𝑣 samples of 𝑌𝑐𝑝, contain interference from the preceding OFDM symbol, and so are discarded. The last 𝑣 samples disperse into the subsequent OFDM symbol, and so also are discarded. This leaves exactly L samples for the desired output ′𝑦 ′, which is precisely what is required to recover the L data symbols embedded in 𝑿 .

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• These L samples of 𝑦 will be equivalent to

𝑦 = h⊛ x.

• The circular convolution operation y[n] = x[n]⊛ h[n] as shown below figure 3.5.

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Figure 3.5: The OFDM cyclic prefix creates a circular convolution at the receiver (signal y) even though the actual channel causes a linear convolution.

• Due to the cyclic prefix 𝑦0 depends on 𝑥0 and the circularly wrapped values 𝑥 𝐿−𝑣……𝑥L−1, That is:

• The drawback of cyclic prefix need more bandwidth and power penalty.

• Since 𝑣 redundant symbols are sent, the required Bandwidth of OFDM in increase from 𝐵 𝑡𝑜 (𝐿+𝑣/𝐿) 𝐵 and power penalty of

10 𝑙𝑜𝑔10 (𝐿+𝑣/𝐿) dB

• In summary, the use of cyclic prefix entails data rate and power losses that are both

𝑅𝑎𝑡𝑒 𝐿𝑜𝑠𝑠 = 𝑃𝑜𝑤𝑒𝑟 𝐿𝑜𝑠𝑠 = 𝐿/𝐿 +𝑣

• The "wasted" power has increased importance in an interference-limited wireless system, since it causes interference to neighboring users.

3.2.3 Frequency Equalization:

• Equalization is the process of adjusting the balance between frequency components within a received OFDM signal.
• Frequency domain equalizers (FEQs) have been applied extensively in multicarrier systems to enhance transmission rate by reducing transmit redundancy in the form of guard interval.

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• After the FFT is performed, the data symbols are estimated using a one-tap frequency domain equalizer, or FEQ, as

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Where, 𝐻𝑙 is the complex response of the channel

3.2.5 An OFDM Block Diagram***

• The key steps in an OFDM communication system are briefly shown in Figure 3.6.

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Transmitter operations:

• Step 1: In OFDM, break a wideband signal of bandwidth 𝐵 into 𝐿 narrowband subcarriers each of bandwidth 𝐵/𝐿 and each subcarrier experiences flat fading, or ISI-free communication, as long as a cyclic prefix that exceeds the delay spread is used. The 𝐿 subcarriers for a given OFDM symbol are represented by a vector 𝑋, which contains the L current symbols.
• Step 2: 𝐿 independent narrow band subcarriers are created digitally using an IFFT operation.
• Step 3: IFFT/FFT decompose the ISI channel into orthogonal subcarriers, a cyclic prefix of length 𝑣 must be appended after the IFFT operation. The resulting 𝐿 + 𝑣 symbols are then sent in serial through the wideband channel.

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Receiver operations:

• At the receiver, the cyclic prefix is discarded, and the L received symbols are demodulated using an FFT operation, which results in L data symbols, each of the form 𝑌𝑙 = 𝐻𝑙 𝑋𝑙+ 𝑁𝑙 for subcarrier 𝑙.
• Each subcarrier can then be equalized via an FEQ by simply dividing by the complex channel gain H[i] for that subcarrier. This results in

𝑋̃𝑙 = 𝑋𝑙+𝑁𝑙 /𝐻𝑙

3.3 OFDM in LTE: ***

• LTE systems can be used as an example to brief time and frequency domain interpretations of OFDM.
• Figure 3.7 shows view of a pass band OFDM modulation engine. The inputs to this figure are L independent QAM symbols (the vector X), and these L symbols are treated as separate subcarriers.

• The L-point IFFT then creates a time domain L-vector x that is cyclic extended to length L(1 + G), where G is the fractional overhead. In LTE G ~ 0.07 for the normal cyclic prefix and G = 0.25 for the extended cyclic prefix.
• This longer vector is then parallel-to-serial (P/S) converted into a wideband digital signal that can be amplitude modulated with a single radio at a carrier frequency of 𝑓𝑐 = 𝜔𝑐/2𝜋.
• The key OFDM parameters are summarized in table below,

• For example, if 16QAM modulation was used (M = 16) with the normal cyclic prefix, the raw (neglecting coding) data rate of this LTE system would be:

3.4 Timing and Frequency Synchronization: ***

• In order to demodulate an OFDM signal, there are two important synchronization tasks that need to be performed by the receiver.
• Figure 3.8 shows a representation of an OFDM symbol in time (top) and frequency (bottom).

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• In Figure 3.8 only two of the carriers are shown: the actual transmitted signal is the superposition of all the individual carriers.

3.4.1 Timing Synchronization:

• The effect of timing errors in symbol synchronization is relaxed in OFDM due to the presence of a cyclic prefix.
• If the cyclic prefix length Ng is equivalent to the length of the channel impulse response 𝑣, successive OFDM symbols can be decoded ISI free.
• If the perfect synchronization is not maintained, it is possible to tolerate a timing offset of 𝜏 seconds without any degradation in performance as long as 0 ≪ 𝜏 ≪ ( 𝑇𝑔− 𝑇𝑚), where 𝑇𝑔 is the guard time (cyclic prefix duration) and 𝑇𝑚 is the maximum channel delay spread.

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• As long as 𝜏 remains constant, it includes a fixed phase offset and it can be corrected by the FEQ without loss in performance.
• This acceptable range of 𝜏 is referred to as the timing synchronization margin, and is shown in Figure 3.9.

• If the timing offset 𝜏 is not within this window 0 ≪ 𝜏 ≪ ( 𝑇𝑔− 𝑇m), ISI occurs. The desired energy is lost while interference from the preceding symbol is included in the receive window.
• For both of these scenarios, the SNR loss can be approximated by,

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3.4.2 Frequency Synchronization:

• OFDM achieves a high degree of bandwidth efficiency compared to other wideband systems.
• In OFDM, the subcarrier packing is extremely tight compared to conventional modulation techniques, which require a guard band on the order of 50% or more.
• Frequency offsets is very sensitive in OFDM due to the fact that the subcarriers overlap, rather than having each subcarrier spectrally isolated.
• frequency offset 𝛿= 0, there is no interference between the subcarriers.

• In practice, the frequency offset is not always zero. The major causes for this are,
• Mismatched oscillators at the transmitter and receiver
• Doppler frequency shifts due to mobility.
• Crystal oscillators are expensive, tolerating some degree of frequency offset is essential in a consumer OFDM system like LTE.
• Hence the received samples of the FFT will contain interference from the adjacent subcarriers, called inter-carrier interference (ICI).

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Where, Co is a constant that depends on various assumptions and is the average symbol energy.

• The SNR loss induced by frequency offset is given by,

3.5 The Peak-to-Average Power Ratio (PAPR) ***

• Definition: The PAPR is the ratio the maximum power of a sample in a given OFDM transmit symbol to the average power of that OFDM symbol. In simple terms, PAPR is the ratio of peak power to the average power of a signal. It is expressed in the units of dB.
• PAPR occurs when in a multicarrier system the different sub-carriers are out of phase with each other.
• OFDM signals have a higher peak-to-average ratio (PAPR). This high PAR is one of the most important implementation challenges that face OFDM because it reduces the efficiency and hence increases the cost of the RF power amplifier, which is one of the most expensive components in the LTE transmitter.

• Alternatively, the same power amplifier (PA) can be used but the input power to the PA must be reduced: this is known as input backoff (IBO) and results in a lower average SNR at the receiver, and hence a reduced transmit range.

3.5.1 The PAR Problem:

• When a high-peak signal is transmitted through a nonlinear device such as a high-power amplifier (HPA) or digital-to-analog converter (DAC), it generates out-of-band energy and in-band distortion. These degradations may affect the system performance severely.
• The nonlinear behavior of HPA can be characterized by amplitude modulation/amplitude modulation (AM/AM) and amplitude modulation/phase modulation (AM/PM) responses.

• To avoid the undesirable nonlinear effects, a waveform with high-peak power must be transmitted in the linear region of the HPA by decreasing the average power of the input signal. This is called input backoff (IBO) and results in a proportional output backoff (OBO).
• High backoff reduces the power efficiency of the HPA, and may limit the battery life for mobile applications.
• The input backoff is defined as

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3.5.2 Quantifying the PAR:

• The OFDM carries L narrowband signals. Each of the L output samples from an L-point IFFT operation involves the sum of L complex numbers, the resulting output values {x1, x2,…… ,xL} can be accurately modelled and the amplitude of the output signal is

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which is exponentially distributed with mean 2𝜎2.

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• The PAR of the transmitted analog signal can be defined as

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• The discrete-time PAR can be defined for the IFFT output as

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• The maximum possible value of the PAR is L or 10 log10 L dB, which would occur if all the subcarriers add up constructively at a single point.

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Clipping and Other PAR Reduction Techniques:

• Clipping Techniques:
• In this technique "clip" off the highest peaks, at the cost of some minimal distortion of the signal.
• Clipping, called as "soft limiting," truncates the amplitude of signals that exceed the clipping level as

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Where, x (n) is the original signal and 𝑥̃(𝑛) is the output after clipping, and A is the clipping level, that is, the maximum output envelope value.

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The clipping ratio can be used as a metric and is defined as

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Conclusion:

o Clipping reduces the PAR at the expense of distorting the desired signal.

o The two primary drawbacks from clipping are

1.Spectral regrowth (frequency domain leakage), which causes unacceptable interference to users in neighboring RF channels,

2. Distortion of the desired signal.

i) Spectral Regrowth:

o It is the frequency domain leakage noise due to clipping. The clipping noise can be expressed in the frequency domain through the use of the DFT.

o The resulting clipped frequency domain signal,

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Where Ck represents the clipped off signal in the frequency domain.

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ii) In-band Distortion

• In-band distortion due to clipping process as the combination of uncorrelated additive noise and attenuation of desired signal as,

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• The attenuation factor α is obtained by,

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• The attenuation factor α vs clipping ratioγis plotted as shown in figure 3.15.

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• Attenuation factor α is negligible when compared to clipping ratioγis greater than 8dB (for high clipping ratio).

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• The correlated time-domain clipped-off signal c[n] can be approximated by uncorrelated noise d[n].

c[n]~d[n] as γincreases

• The variance of uncorrelated clipping noise can be expressed assuming a stationary Gaussian noise input x[n] as

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• The Signal-to-noise-plus-distortion ratio (SNDR) of one OFDM symbol in order to estimate the impact of clipped OFDM signals over an AWGN channel under the assumption that the distortion d[n] is Gaussian and uncorrelated with the input and channel noise(that has variance No/2).

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• The Bit Error Probability (BER) for M-QAM and average power Ex is given by,

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• Figure shows Bit error rate probability for a clipped OFDM signal in AWGN with different clipping ratios.

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Figure 3.16: Bit error rate probability for a clipped OFDM signal in AWGN with different clipping ratios.

3.5.4 LTE's Approach to PAR in the Uplink:

• In the downlink PAR is less important because the base stations are fewer in number and generally higher in cost, and so are not much sensitive to the exact PAR.
• If the PAR is still considered to be too high, a number of techniques can be utilized to bring it down, all with some complexity and performance tradeoffs.
• For uplink, mobiles are many in number and are sensitive to cost, so SCFDMA/SC-FDE is used.

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Single carrier frequency domain equalization (SC-FDE)

An alternative approach to OFDM is SC-FDE approach to ISI suppression, SC-FDE maintains OFDM’s three most important benefits:

1. Low complexity even for severe multipath channels
2. Excellent BER performance, close to theoretical bounds
3. A decoupling of ISI from other types of interference.

SC-FDE System Description

• Frequency domain equalization is used in both OFDM and SC-FDE systems to reduce the complexity inherent to time-domain equalization.

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• IFFT is moved to the end of the receive chain rather than operating at the transmitter, to create a multicarrier waveform as in OFDM.
• An SC-FDE still utilizes a cyclic prefix at least as long as the channel delay spread, but now the transmitted signal is simply a sequence of QAM symbols, which have low PAR, on the order of 4-5 dB depending on the constellation size.
• Because of the application of the cyclic prefix, the received signal appears to be circularly convolved, that is,

y[n]= x[n] * h [n] + w[n],

where w[n] is noise.

FFT {y[n]} = Y[m]= H[m] X[m] + W[m]

Design Considerations for SC-FDE and OFDM

• Since the performance difference between SC-FDE and OFDM is not that significant, other considerations are more important in determining which is the appropriate method to use for a given application.
• An obvious difference is that SC-FDE has a lower-complexity transmitter but a higher-complexity receiver, compared to OFDM. Since the receiver was already considerably more complex than the transmitter in a typical OFDM system due to channel estimation, synchronization, and the error correction decoder, this further skews the asymmetry.
• In a cellular system like LTE, this asymmetry can in fact be a favourable feature, since the uplink could utilize SC-FDE and the downlink could utilize OFDM.

• In such a situation, the base station would therefore perform 3 IFFT/FFT operations and the mobile, which is more power- and cost-sensitive, would perform only a single FFT operation (to receive its OFDM waveform from the base station).
• Adding in SC-FDE’s benefits of reduced PAR and the commensurate cost and power savings, it appears that the case for using SC-FDE in the uplink of a wideband data system is favourable indeed.
• Channel estimation and synchronization are a bit different in practice for an SC-FDE system vs. an OFDM system.
• In a typical wireless OFDM system—including LTE, WiMAX, and 802.11a/g/n—channel estimation and synchronization are accomplished via a preamble of known data symbols, and then pilot tones, which are inserted at known positions in all subsequent OFDM symbols.

• Although SC-FDE systems would typically also include a preamble, this preamble is in the time domain so it is not as straightforward to estimate the frequency domain values Hl. Similarly, it is not possible to insert pilot tones on a per-frame basis. SC-FDMA overcomes these potential problems for LTE by using both a DFT and an IFFT at the transmitter.
• Another commonly cited disadvantage of SC-FDE is that it has a nominally more dispersive spectrum compared to OFDM. OFDM’s sharper spectrum results in less co-channel interference and/or less restrictive RF roll-off requirements. On the other hand, because OFDM has a higher PAR, it is more subject to clipping that can cause spectral dispersion.
• Finally, the combination of SC-FDE with MIMO is not as natural because detection cannot be done in the frequency domain. Hence, it is not possible to use maximum likelihood detection for MIMO with SC-FDE; suboptimal linear detectors (such as MMSE) or interference cancellation approaches must instead be adopted.

• On the whole, OFDM continues to be much more popular than SC-FDE, but the fundamental technical arguments for this imbalance are not very clear. Instead, it is reasonable to posit that the longevity and familiarity with OFDM are bigger factors.

THE COMPUTATIONAL COMPLEXITY ADVANTAGE OF OFDM AND SC-FDE

• One of the principal advantages of frequency domain equalization relative to time domain equalization is that FDE—whether in OFDM or
• SC-FDE systems—requires much lower computational complexity, especially for high data rates. In this section, we compare the computational complexity of an equalizer with that of a standard IFFT/FFT implementation of OFDM.
• A time-domain equalizer consists of a series of multiplications with several delayed versions of the signal. The number of delay taps in an equalizer depends on the symbol rate of the system and the delay spread in the channel.

• To be more precise, the number of equalizer taps is proportional to the bandwidth-delay spread product Tm/Ts ≈ BTm. We have been calling this quantity ν, or the number of ISI channel taps. An equalizer with ν taps performs ν complex multiply and accumulate (CMAC) operations per received symbol. Therefore, the complexity of an equalizer is of the order

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• In an OFDM or SC-FDE system, the IFFT and FFT are the principal computational operations. It is well known that the IFFT and FFT each have a complexity of O(L log2 L), where L is the FFT block size. In the case of OFDM, L is the number of subcarriers. As this chapter has shown, for a fixed cyclic prefix overhead, the number of subcarriers L must grow linearly with the bandwidth-delay spread product ν = BTm.

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• The computational complexity for each OFDM symbol (or SC-FDE block) is of the order O(BTm log2 BTm). There are B/L OFDM symbols sent each second. Since L ∝ BTm, this means there are order O(1/Tm) OFDM symbols per second, so the computational complexity in terms of CMACs for OFDM is

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• The complexity of a time-domain equalizer grows as the square of the data rate since both the symbol rate and the number of taps increases linearly with the data rate.
• For an OFDM or SC-FDE system, the increase in complexity grows with the data rate only slightly faster than linearly. This difference is dramatic for very large data rates, as shown in Figure. It should be noted, however, that LTE uses SC-FDMA, which is not precisely the same as SC-FDE.
• The complexity of SC-FDMA still scales as O(Blog2 BTm), but there are twice as many FFT/IFFT operations as there are in SC-FDE.

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Figure : OFDM and SC-FDE have an enormous complexity advantage over equalization for broadband data rates. The delay spread is Tm = 2μsec, the OFDM symbol period is T = 20μsec, 16 QAM (4 bps/Hz) is used, and the considered time-domain equalizer is a DFE.

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