lecture3 cellular’systems -...
TRANSCRIPT
• So far: focus on point-to-point communication• In a cellular system (network), additional issues arise:
Cellular Systems: Additional Challenges
2
Multiple access
Inter-cell interference management
Issues Less Emphaized in the Lecture• Handoff (focus of the network layer)
• Duplexing between uplink and downlink:- Frequency Division Duplex (FDD)- Time Division Duplex (TDD)
• Sectorization
• Focus mainly on licensed cellular systems- WiFi, various wireless personal communication systems, are not
discussed here
3
Some History• Cellular concept (Bell Labs, early 70’s)
• AMPS (analog, early 80’s)
• GSM (digital, narrowband, late 80’s)
• IS-95 (digital, wideband, early 90’s)
• 3G/4G systems
4
Plot• Three cellular system designs as case studies to
illustrate approaches to multiple access and (inter-cell) interference management
• Both uplink and downlink will be mentioned
5
Downlink Uplink
Outline• Narrowband (GSM)
• Wideband system: CDMA (IS-95, CDMA 2000, WCDMA)
• Wideband system: OFDMA (Flash OFDM, LTE)
6
Narrowband Systems
Basic Ideas• Total bandwidth divided into narrowband sub-channels- GSM: 25 MHz → 200 kHz × 125 sub-channels - Uplink (890 – 915 MHz) and Downlink (935 – 960 MHz): the same
• Time Division Multiple Access (TDMA)- Users share time slots in a sub-channel; each user per time slot- Multiple access is orthogonal: intra-cell users never interfere with
each other
• Partial Frequency Reuse- Neighboring cells uses disjoint sets of sub-channels- Careful frequency planning → essential no inter-cell interference
8
Time Division Multiple Access
9
70 Point-to-point communication
125 sub-channels
25 MHz200 kHz
TS0 TS2 TS3 TS5 TS6 TS7TS4TS1
8 users per sub-channel
Figure 3.9 The 25-MHz band of a GSM system is divided into 200-kHz sub-channels, which arefurther divided into time slots for eight different users.
Since one time slot occurs every 4.615ms for each user, this translatesinto a delay of roughly 40ms, a delay judged tolerable for voice. The eighttime slots are shared between two 20-ms speech frames. The interleavingstructure is summarized in Figure 3.10.
The maximum possible time diversity gain is 8, but the actual gain thatcan be obtained depends on how fast the channel varies, and that dependsprimarily on the mobile speed. If the mobile speed is v, then the largestpossible Doppler spread (assuming full scattering in the environment) isDs = 2fcv/c, where fc is the carrier frequency and c is the speed of light.(Recall the example in Section 2.1.4.) The coherence time is roughlyTc = 1/!4Ds"= c/!8fcv" (cf. (2.44)). For the channel to fade more or lessindependently across the different time slots for a user, the coherence timeshould be less than 5ms. For fc = 900MHz, this translates into a mobilespeed of at least 30 km/h.
User 1’s time slots
User 1’s coded bitstream
Figure 3.10 How interleaving is done in GSM.
577 μs
GSM: 8 users share a 200 kHz sub-channel, time slot: 577 μs
Partial Frequency Reuse
10
124 Cellular systems
Figure 4.2 A hexagonalarrangements of cells and apossible reuse pattern ofchannels 1 through 7 with thecondition that a channelcannot be used in oneconcentric ring of cells aroundthe cell using it. The frequencyreuse factor is 1/7.
5
5
5
4
4
4
3
3
3
3
2
2
2
1
1
1
1
5
4
7
7
7
7
7
6
6
6
6
6
6
5
5
4
32
1
1
1
cells, a channel is allocated to a cell only if it is not used by a few con-centric rings of neighboring cells. Assuming a regular hexagonal cellulararrangement, Figure 4.2 depicts cells that can use the same channel simulta-neously (such cells are denoted by the same number) if we want to avoid anyneighboring cell from using the same channel.
The maximum number n of channels that a cell can be allocated dependson the geometry of the cellular arrangement and on the interference avoid-ance pattern that dictates which cells can share the same channel. The ration/N denotes how often a channel can be reused and is termed the frequencyreuse factor. In the regular hexagonal model of Figure 4.2, for example, thefrequency reuse factor is at least 1/7. In other words, W/7 is the effectivebandwidth used by any base-station. This reduced spectral efficiency is theprice paid up front towards satisfying the design goal of reducing all interfer-ence from neighboring base-stations. The specific reuse pattern in Figure 4.2is ad hoc. A more careful analysis of the channel allocation to suit trafficconditions and the effect of reuse patterns among the cells is carried out inExercises 4.1, 4.2, and 4.3.
Within a cell, different users are allocated transmissions that are non-overlapping, in both time and channels. The nature of this allocation affectsvarious aspects of system design. To get a concrete feel for the issues involved,we treat one specific way of allocation that is used in the GSM system.
4.2.1 Narrowband allocations: GSM system
The GSM system has already been introduced in Example 3.1. Each narrow-band channel has bandwidth 200 kHz (i.e. W/N = 200kHz). Time is dividedinto slots of length T = 577!s. The time slots in the different channels are thefinest divisible resources allocated to the users. Over each slot, n simultaneous
• Neighboring cells uses disjoint sets of sub-channels
• Each cell gets only 1/7 of the total bandwidth
• Frequency reuse factor = 1/7
• High SINR, but price to pay: - Reducing the available
degrees of freedom- Higher complexity in
network planning in real world
Time-‐Frequency Resource Allocation
11
Time
Frequency
cell 4
cell 3
cell 2
cell 1
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
user index within a cell
Time and Frequency Diversity• Time diversity: Coding + Interleaving
• Frequency diversity- Within a narrowband sub-channel: flat fading ⟹ no diversity- Obtained via frequency hopping
12
Frequency
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
Time
9 10 11 12 13 14 15 16
1 2 3 4 5 6 7 8
Why Full Frequency Reuse won’t Work• Signal-to-Interference-plus-Noise Ratio
• Limiting factor: interference power I- I is due to the single interferer from the neighbor cell- I is random since the location of the single interferer is uncertain- Variance of I is quite large and I can be comparable with |h|2P- Like deep fade, but can’t be handled by current diversity schemes
• Interference averaging is desired:- If interference come from multiple interferers with smaller power,
then a similar effect in diversity schemes will emerge due to LLN!
13
SINR =|h|2PN0 + I
Ibecomes�����!
NX
k=1
Ik, E [I] =NX
k=1
E [Ik]
Summary• Orthogonal narrowband channels are assigned to users
within a cell
• Users in adjacent cells can’t be assigned the same channel due to lack of interference averaging across users ⟹ reduces the frequency reuse factor and leads to inefficient use of the total bandwidth
• The network is decomposed into a set of high SINR point-to-point links, simplifying the physical-layer design
• Frequency planning is complex, particularly when new cells have to be added
14
Wideband System: CDMA
Features of CDMA• Universal frequency reuse: - All users in all cells share the same bandwidth
• Main advantages:- Maximizes the degrees of freedom usage- Allows interference averaging across many users- Soft capacity limit (i.e., no hard limit on the # of users supported)- Allows soft handoff- Simplify frequency planning
• Challenges- Very tight power control to solve the near-far problem- More sophisticated coding/signal processing to extract the
information of each user in a very low SINR environment
16
Design Goals• Make the interference look as much like a white
Gaussian noise as possible:- Spread each user’s signal using a pseudonoise sequence- Tight power control for managing interference within the cell- Averaging interference from outside the cell as well as fluctuating
voice activities of users
• Apply point-to-point design for each link- Extract all possible diversity in the channel
17
Point-‐to-‐Point Link Design• Extracting maximal diversity is the name of the game- Because each user has an equivalent point-to-point link!
• Time diversity is obtained by interleaving across different coherence time periods and (convolutional/turbo) coding
• Frequency diversity is obtained by the Rake receiver – combining of the multipaths
• Transmit diversity is supported in 3G CDMA systems
18
CDMA Uplink
19
132 Cellular systems
Figure 4.3 Schematic of theCDMA uplink.
+
h (1)
h(K )
{a1[m]}I
I{s1[m]}
{a1[m]}Q
{s1[m]}Q
I{aK[m]}
I{sK[m]}Q{aK[m]}Q
{sK[m]}
{w[m]}+
Σ
×
×
×
×
The receiver for user k multiplies the I and Q components of the outputsequence !y"m#$ by the pseudonoise sequences !sIk"m#$ and !sQk "m#$ respec-tively to extract the coded streams of user k, which are then fed into ademodulator to recover the information bits. Note that in practice, the users’signals arrive asynchronously at the transmitter but we are making the ide-alistic assumption that users are chip-synchronous, so that the discrete-timemodel in Chapter 2 can be extended to the multiuser scenario here. Also, weare making the assumption that the receiver is already synchronized with eachof the transmitters. In practice, there is a timing acquisition process by whichsuch synchronization is achieved and maintained. Basically, it is a hypothesistesting problem, in which each hypothesis corresponds to a possible relativedelay between the transmitter and the receiver. The challenge here is thatbecause timing has to be accurate to the level of a chip, there are manyhypotheses to consider and efficient search procedures are needed. Some ofthese procedures are detailed in Chapter 3 of [140].
Generation of pseudonoise sequencesThe pseudonoise sequences are typically generated by maximum length shiftregisters. For a shift register of memory length r , the value of the sequenceat time m is a linear function (in the binary field of !0%1$) of the values attime m− 1%m− 2% & & & %m− r (its state). Thus, these binary 0−1 sequencesare periodic, and the maximum period length is p = 2r − 1, the number ofnon-zero states of the register.6 This occurs when, starting from any non-zero state, the shift register goes through all possible 2r −1 distinct non-zerostates before returning to that state. Maximum length shift register (MLSR)sequences have this maximum periodic length, and they exist even for r very
6 Starting from the zero state, the register will remain at the zero state, so the zero state cannotbe part of such a period.
user 1 Tx
user K Tx
user 1 Ch.
user K Ch.
BS Rx
131 4.3 Wideband systems: CDMA
A comprehensive capacity comparison between CDMA and narrowbandsystems depends on the specific coding schemes and power control strategies,the channel propagation models, the traffic characteristics and arrival patternsof the users, etc. and is beyond the scope of this book. Moreover, many ofthe advantages of CDMA outlined above are qualitative and can probably beachieved in the narrowband system, albeit with a more complex engineeringdesign. We focus here on a qualitative discussion on the key features of aCDMA system, backed up by some simple analysis to gain some insights intothese features. In Chapter 5, we look at a simplified cellular setting and applysome basic information theory to analyze the tradeoff between the increasein degrees of freedom and the increase in the level of interference due touniversal frequency reuse.
In a CDMA system, users interact through the interference they cause eachother. We discuss ways to manage that interference and analyze its effect onperformance. For concreteness, we first focus on the uplink and then moveon to the downlink. Even though there are many similarities in their design,there are several differences worth pointing out.
4.3.1 CDMA uplink
The general schematic of the uplink of a CDMA system with K users in thesystem is shown in Figure 4.3. A fraction of the K users are in the cell and therest are outside the cell. The data of the kth user are encoded into two BPSKsequences4 !aI
k"m#$ and !aQk "m#$, which we assume to have equal amplitude
for all m. Each sequence is modulated by a pseudonoise sequence, so that thetransmitted complex sequence is
xk"m#= aIk"m#sIk"m#+ jaQ
k "m#sQk "m#% m= 1%2% & & & % (4.1)
where !sIk"m#$ and !sQk "m#$ are pseudonoise sequences taking values ±1.Recall that m is called a chip time. Typically, the chip rate is much larger thanthe data rate.5 Consequently, information bits are heavily coded and the codedsequences !aI
k"m#$ and !aQk "M#$ have a lot of redundancy. The transmitted
sequence of user k goes through a discrete-time baseband equivalent multipathchannel h'k( and is superimposed at the receiver:
y"m#=K!
k=1
"!
ℓ
h'k(ℓ "m#xk"m−ℓ#
#
+w"m#* (4.2)
The fading channels !h'k($ are assumed to be independent across users, inaddition to the assumption of independence across taps made in Section 3.4.3.
4 Since CDMA systems operate at very low SINR per degree of freedom, a binary modulationalphabet is always used.
5 In IS-95, the chip rate is 1.2288MHz and the data rate is 9.6 kbits/s or less.
131 4.3 Wideband systems: CDMA
A comprehensive capacity comparison between CDMA and narrowbandsystems depends on the specific coding schemes and power control strategies,the channel propagation models, the traffic characteristics and arrival patternsof the users, etc. and is beyond the scope of this book. Moreover, many ofthe advantages of CDMA outlined above are qualitative and can probably beachieved in the narrowband system, albeit with a more complex engineeringdesign. We focus here on a qualitative discussion on the key features of aCDMA system, backed up by some simple analysis to gain some insights intothese features. In Chapter 5, we look at a simplified cellular setting and applysome basic information theory to analyze the tradeoff between the increasein degrees of freedom and the increase in the level of interference due touniversal frequency reuse.
In a CDMA system, users interact through the interference they cause eachother. We discuss ways to manage that interference and analyze its effect onperformance. For concreteness, we first focus on the uplink and then moveon to the downlink. Even though there are many similarities in their design,there are several differences worth pointing out.
4.3.1 CDMA uplink
The general schematic of the uplink of a CDMA system with K users in thesystem is shown in Figure 4.3. A fraction of the K users are in the cell and therest are outside the cell. The data of the kth user are encoded into two BPSKsequences4 !aI
k"m#$ and !aQk "m#$, which we assume to have equal amplitude
for all m. Each sequence is modulated by a pseudonoise sequence, so that thetransmitted complex sequence is
xk"m#= aIk"m#sIk"m#+ jaQ
k "m#sQk "m#% m= 1%2% & & & % (4.1)
where !sIk"m#$ and !sQk "m#$ are pseudonoise sequences taking values ±1.Recall that m is called a chip time. Typically, the chip rate is much larger thanthe data rate.5 Consequently, information bits are heavily coded and the codedsequences !aI
k"m#$ and !aQk "M#$ have a lot of redundancy. The transmitted
sequence of user k goes through a discrete-time baseband equivalent multipathchannel h'k( and is superimposed at the receiver:
y"m#=K!
k=1
"!
ℓ
h'k(ℓ "m#xk"m−ℓ#
#
+w"m#* (4.2)
The fading channels !h'k($ are assumed to be independent across users, inaddition to the assumption of independence across taps made in Section 3.4.3.
4 Since CDMA systems operate at very low SINR per degree of freedom, a binary modulationalphabet is always used.
5 In IS-95, the chip rate is 1.2288MHz and the data rate is 9.6 kbits/s or less.
Statistics of Interference (1/2)• Pseudorandom sequence properties:- Different users use different random shift of a sequence
generated by maximum length shift register (MLSR):
- I and Q channels of the same user can use the same sequence
- Near-orthogonal property:
• Effective interference for user 1:- Circular symmetric because each hl(k) is
• Second-order statistics: approximately white
20
I[m] :=X
k>1
X
l
h
(k)l xk[m� l]
⇥s[0] s[1] · · · s[G� 1]
⇤T
G�1X
m=0
s[m]s[m+ l] =
(G, l = 0
�1, l 6= 0
E [I[m]I[m+ 1]⇤]
(=
Pk>1 Ec
k, l = 0
⇡ 0, l 6= 0Eck := E
⇥|xk[m]|2
⇤X
l
Eh|h(k)
l [m]|2i
Statistics of Interference (2/2)• Due to central limit theorem (CLT), further approximate
the interference as a Gaussian random process
• Hence, the effective noise + interference for each user can be viewed as an additive white Gaussian noise!
• Remark: the assumption that each interferer contributes a roughly equal small fraction to the total interference is valid due to tight power control in CDMA
21
Processing Gain• Received energy per chip:
• SINR per chip: small
• SINR per bit:
• G: Processing Gain
22
Eck := E
⇥|xk[m]|2
⇤X
l
Eh|h(k)
l [m]|2i
SINR1,c :=Ec1P
k 6=1 Eck + �2
SINR1,b :=||u||2Ec
1Pk 6=1 Ec
k + �2=
GEc1P
k 6=1 Eck + �2
u =⇥sI1[0] sI1[1] · · · sI1[G� 1]
⇤T
Eb1
IS-‐95 Uplink Architecture
23
136 Cellular systems
Forward Link Data
9.6 kbpsRepetition
×44.8 kbps2.4 kbps1.2 kbps
BlockInterleaver
PN CodeGenerator
for I channel
PN CodeGenerator
for Q channel
28.8ksym / s
64-aryOrthogonalModulator
1.2288 Mchips/s
BasebandShaping
Filter
–90˚Carrier
Generator
BasebandShaping
Filter
1.2288 Mchips/s
1.2288 Mchips/s
OutputCDMASignal
Rate = 1/3, K = 9Convolutional
Encoder
processing gain G increase proportionally as well. This means that CDMA isFigure 4.4 The IS-95 uplink.
an inherently scalable multiple access scheme.9
IS-95 link designThe above scheme is based on repetition coding. By using more sophisti-cated low-rate codes, even better performance can be achieved. Moreover,in practice the actual channel is a multipath fading channel, and so tech-niques such as time-interleaving and the Rake receiver are important toobtain time and frequency diversity respectively. IS-95, for example, uses acombination of convolutional coding, interleaving and non-coherent demod-ulation of M-ary orthogonal symbols via a Rake receiver. (See Figure 4.4.)Compressed voice at rate 9.6 kbits/s is encoded using a rate 1/3, constraintlength 9, convolutional code. The coded bits are time-interleaved at the levelof 6-bit blocks, and each of these blocks is mapped into one of 26 = 64orthogonal Hadamard sequences,10 each of length 64. Finally, each symbolof the Hadamard sequence is repeated four times to form the coded sequence!aI"m#$. The processing gain is seen to be 3 ·64/6 ·4= 128, with a resultingchip rate of 128 ·9%6= 1%2288Mchips/s.Each of the 6-bit blocks is demodulated non-coherently using a Rake
receiver. In the binary orthogonal modulation example in Section 3.5.1, foreach orthogonal sequence the non-coherent detector computes the correlation
9 But note that as the bandwidth gets wider and wider, channel uncertainty may eventuallybecome the bottleneck, as we have seen in Section 3.5.
10 The Hadamard sequences of length M = 2J are the orthogonal columns of the M byM matrix HM , defined recursively as H1 = "1# and for M ≥ 2:
HM =!HM/2 HM/2HM/2 −HM/2
"%
Processing gain= 1238.8/9.6 = 128
Power Control• Maintain equal received power for all users in the cell• Tough problem since the dynamic range is very wide.
Users’ attenuation can differ by many 10’s of dB
• Consists of both open-loop and closed loop- Open loop sets a reference point- Closed loop is needed since IS-95 is FDD
• Consists of 1-bit up-down feedback at 800 Hz
• Consumes about 10% of capacity in IS-95• Latency in access due to slow powering up of mobiles
24
Power Control Architecture
25
139 4.3 Wideband systems: CDMA
Channel
±1dB
Transmittedpower
Measurederror probability
> or < target rate
MeasuredSINR < or > β
MeasuredSINR
Inner loop
Closed loop
Out
er lo
op
Open loop
Updateβ
Receivedsignal
Framedecoder
Estimateuplink power
required
Initial downlinkpower
measurement
adjusts the SINR threshold as a function of frame error rates (Figure 4.5).Figure 4.5 Inner and outerloops of power control. An important point, however, is that even though feedback occurs at a high
rate (800Hz), because of the limited resolution of 1 bit per feedback, powercontrol does not track the fast multipath fading of the users when they are atvehicular speeds. It only tracks the slower shadow fading and varying pathloss. The multipath fading is dealt with primarily by the diversity techniquesdiscussed earlier.
Soft handoffHandoff from one cell to the other is an important mechanism in cellularsystems. Traditionally, handoffs are hard: users are either assigned to onecell or the other but not both. In CDMA systems, since all the cells sharethe same spectrum, soft handoffs are possible: multiple base-stations cansimultaneously decode the mobile’s data, with the switching center choosing
Figure 4.6 Soft handoff.
Switchingcenter
Base-station 1 Base-station 2
Mobile
Power control bits± 1 dB ± 1 dB
Interferene Averaging• The received SINR for a user:
• In a large system, each interferer contributes a small fraction of the total out-of-cell interference- Made possible due to power control
• This can be viewed as providing interference diversity
• Same interference-averaging principle applies to voice bursty activity and imperfect power control
26
SINR =P
N0 + (K � 1)P +P
i/2cell Ii
Soft Handoff• Provides another form of diversity: macrodiversity- Two base stations can simultaneously decode the data
27
139 4.3 Wideband systems: CDMA
Channel
±1dB
Transmittedpower
Measurederror probability
> or < target rate
MeasuredSINR < or > β
MeasuredSINR
Inner loop
Closed loop
Out
er lo
op
Open loop
Updateβ
Receivedsignal
Framedecoder
Estimateuplink power
required
Initial downlinkpower
measurement
adjusts the SINR threshold as a function of frame error rates (Figure 4.5).Figure 4.5 Inner and outerloops of power control. An important point, however, is that even though feedback occurs at a high
rate (800Hz), because of the limited resolution of 1 bit per feedback, powercontrol does not track the fast multipath fading of the users when they are atvehicular speeds. It only tracks the slower shadow fading and varying pathloss. The multipath fading is dealt with primarily by the diversity techniquesdiscussed earlier.
Soft handoffHandoff from one cell to the other is an important mechanism in cellularsystems. Traditionally, handoffs are hard: users are either assigned to onecell or the other but not both. In CDMA systems, since all the cells sharethe same spectrum, soft handoffs are possible: multiple base-stations cansimultaneously decode the mobile’s data, with the switching center choosing
Figure 4.6 Soft handoff.
Switchingcenter
Base-station 1 Base-station 2
Mobile
Power control bits± 1 dB ± 1 dB
Uplink vs. Downlink• Near-far problem does not exist in DL ⟹ power control
is less crucial• Tx can make DL signals for different users orthogonal- Still, due to multipaths, not completely orthogonal at the receiver
• Rake is highly sub-optimal in the downlink- Equalization is beneficial as all users’ data go through the same
channel and the aggregate rate is high
• Less interference averaging in the downlink- Interference comes from a few high-power base stations as
opposed to many low-power mobiles
28
Issues with CDMA• In-cell interference reduces capacity
• Power control is expensive, particularly for data applications where users have low duty cycle but require quick access to resource
• In-cell interference is not an inherent property of systems with universal frequency reuse⟹ We can keep users in the cell orthogonal, and still have universal frequency reuse
29
Wideband System: OFDMA
Basic Ideas• Lecture 2: OFDM as a point-to-point modulation scheme,
converting an ISI channel into parallel channels
• It can also be used as a multiple access technique!- By assigning different time/frequency slots to users, they can be
kept orthogonal within a cell- Equalization is no longer needed
• How to deal with inter-cell interference?• ⟹ Interference averaging• Achieved by careful design of hopping matrices (a way of
subcarrier allocation)
31
Hopping Sequences as Virtual Channels• Basic unit of resource: a virtual channel• – Hopping sequence over time-frequency plane
• Coding across the symbols in a hopping sequence- If there were no coding and coding across subcarriers, the OFDM
system would behave like narrowband systems due to lack of interference averaging!
• Hopping sequences are orthogonal within a cell• Each user is assigned a number of virtual channels
depending on their data rate requirement
32
Design Principles• Spread out the subcarriers for one user to gain
frequency diversity• Hop the subcarrier allocation every OFDM block
33
Frequency
Time
Nc = 5, and 5 users
0
2
4
1
3
1
3
0
2
4
2
4
1
3
0
3
0
2
4
1
4
1
3
0
2
!
2
66664
0 1 2 3 42 3 4 0 14 0 1 2 31 2 3 4 03 4 0 1 2
3
77775
Hopping Matrix(Latin square)
Each row/column is a permutation of [0:Nc–1]
Hopping Sequences
34
151 4.4 Wideband systems: OFDM
Figure 4.9 Virtual channelhopping patterns for Nc = 5.
Virtual Channel 4
Virtual Channel 0 Virtual Channel 1 Virtual Channel 2
Virtual Channel 3
For example, we see that the virtual channel 0 is assigned the OFDM symboltime and sub-carrier pairs (0, 0), (1, 2), (2, 4), (3, 1), (4, 3). Now users couldbe allocated n virtual channels, accommodating !Nc/n" users.
Each base-station has its own hopping matrix (Latin square) that determinesthe physical structure of the virtual channels. Our design rule to maximizeinterferer diversity requires us to have minimal overlap between virtual chan-nels of neighboring base-stations. In particular, we would like to have exactlyone time/sub-carrier collision for every pair of virtual channels of two base-stations that employ these hopping patterns. Two Latin squares that have thisproperty are said to be orthogonal.When Nc is prime, there is a simple construction for a family of Nc − 1
mutually orthogonal Latin squares. For a= 1! " " " !Nc−1 we define anNc×Nc
matrix Ra with #i! j$th entry
Raij = ai+ j modulo Nc% (4.23)
Here we index rows and columns from 0 through Nc− 1. In Exercise 4.14,you are asked to verify that Ra is a Latin square and further that for everya ̸= b the Latin squares Ra and Rb are orthogonal. Observe that Figure 4.9depicts a Latin square hopping pattern of this type with a= 2 and Nc = 5.
With these Latin squares as the hopping patterns, we can assess theperformance of data transmission over a single virtual channel. First, dueto the hopping over the entire band, the frequency diversity in the chan-nel is harnessed. Second, the interference seen due to inter-cell transmis-sions comes from different virtual channels (and repeats after Nc symboltimes). Coding over several OFDM symbols allows the full interferer diver-sity to be harnessed: coding ensures that no one single strong interferencefrom a virtual channel can cause degradation in performance. If sufficient
Hopping Matrix Design• Each base station has its own hopping matrix• Design rule: maximize the number of interferers that one
user encountered ⟹ min. overlap of hopping matrices- Latin squares with this property are called orthogonal
35
2
66664
0 1 2 3 42 3 4 0 14 0 1 2 31 2 3 4 03 4 0 1 2
3
77775
Cell A2
66664
0 1 2 3 42 3 4 0 14 0 1 2 31 2 3 4 03 4 0 1 2
3
77775
Cell B
Bad Choice Good Choice
2
66664
0 1 2 3 42 3 4 0 14 0 1 2 31 2 3 4 03 4 0 1 2
3
77775
Cell A Cell B2
66664
0 1 2 3 41 2 3 4 02 3 4 0 13 4 0 1 24 0 1 2 3
3
77775
user 0 in cell A always interferes with user 0 in cell B!
user 0 in cell A interferes with user 0, 3, 1, 4, 2 in cell B respectively
Mutually Orthogonal Latin Squares• For a prime Nc, a simple construction of a family of Nc–1
mutually orthogonal Latin squares are as follows:
• It can be shown that a≠b ⟹ Ra and Rb are orthogonal
36
For a 2 {1, 2, . . . , Nc � 1}, define an Nc ⇥Nc matrix Ra
with (i, j)-th enrty Raij = ai+ j mod Nc,
where i, j 2 {0, 1, . . . Nc � 1}
Out-‐of-‐Cell Interference Averaging• The hopping patterns of virtual channels in adjacent cells
are designed such that any pair has minimal overlap
• This ensures that a virtual channel sees interference from many users instead of a single strong user
• This is a form of interference diversity
37
Example: Flash OFDM• Bandwidth = 1.25 Mz• # of data sub-carriers = 113• OFDM symbol = 128 samples = 100 μ s # #• Cyclic prefix = 16 samples = 11 μ s delay spread
• OFDM symbol time determines accuracy requirement of user synchronization (not chip time, better than CDMA)
• Ratio of cyclic prefix to OFDM symbol time determines overhead (fixed, unlike power control in CDMA)
38
States of Users• Users are divided into 3 states:- Active: users that are currently assigned virtual channels (<30)- Hold: users that are not sending data but maintain
synchronization (<130)- Inactive (<1000)
• Users in hold state can be moved into active state very quickly
• Because of the orthogonality property, tight power control is not crucial and this enables quick access for users- Important for certain applications (requests for http transfers,
acknowledgements, etc.)
39
OFDMA in LTE• In LTE, OFDMA is used in downlink- Basic unit of resource is a 12 sub-carrier × 7 OFDM symbol time block
40
8 Overview of the 3GPP Long Term Evolution Physical Layer Freescale Semiconductor
x Setting AGC
x Frequency offset estimation
x Timing synchronization
x Channel estimation
The address of the intended recipient is not in the PHY preamble. It is actually in the packet data and is interpreted at the MAC layer. From a networking perspective, the packet-oriented approach of 802.11a has the advantage of simplicity. Each packet is addressed to a single recipient (broadcast mode not withstanding). However, the randomized backoff period of the CSMA multiplexing scheme is idle time and therefore represents an inefficiency. The PHY preamble is also network overhead and further reduces efficiency, particularly for shorter packets.
The typical real-world efficiency of an 802.11a system is approximately 50 percent. In other words, for a network with a nominal data rate of 54 Mbps, the typical throughput is about 25 – 30 Mbps. Some of the inefficiencies can be mitigated by abandoning the CSMA multiplexing scheme and adopting a scheduled approach to packet transmission. Indeed, subsequent versions of the 802.11 protocol include this feature. Inefficiencies due to dedicated ACK packets can also be reduced by acknowledging packets in groups rather than individually.
In spite of potential improvements, it remains difficult to drive packet-oriented network efficiency much beyond 65 to 70 percent. Further, because each packet completely consumes all network resources during transmission and acknowledgement, the AP can provide addressed (non-broadcast) traffic to user terminals only on a sequential basis. When many users are active within the cell, latency can become a significant problem. Clearly, the objective of cellular carriers is to create as much network demand as possible for a wide variety of traffic that includes voice, multimedia, and data. Efficiency and low latency are therefore paramount. As we will see in the following section, OFDMA is superior to packet-oriented schemes in both of these critical dimensions.
2.3.2 OFDMA and the LTE Generic Frame Structure OFDMA is an excellent choice of multiplexing scheme for the 3GPP LTE downlink. Although it involves added complexity in terms of resource scheduling, it is vastly superior to packet-oriented approaches in terms of efficiency and latency. In OFDMA, users are allocated a specific number of subcarriers for a predetermined amount of time. These are referred to as physical resource blocks (PRBs) in the LTE specifications. PRBs thus have both a time and frequency dimension. Allocation of PRBs is handled by a scheduling function at the 3GPP base station (eNodeB).
Figure 2.3.2-1 LTE Generic Frame Structure
0 1 2 3 10 11 19
1 Sub-Frame (1.0 msec)
1 Frame (10 msec)
50 1 2 3 4 6 50 1 2 3 4 6
7 OFDM Symbols(short cyclic prefix)
cyclic prefixes
1 Slot (0.5 msec)
In order to adequately explain OFDMA within the context of the LTE, we must study the PHY layer generic frame structure. The generic frame structure is used with FDD. Alternative frame structures are defined for use with TDD. However, TDD is beyond the scope of this paper. Alternative frame structures are therefore not considered.
As shown in figure 2.3.2-1, LTE frames are 10 msec in duration. They are divided into 10 subframes, each subframe being 1.0 msec long. Each subframe is further divided into two slots, each of 0.5 msec duration. Slots consist of either 6 or 7 ODFM symbols, depending on whether the normal or extended cyclic prefix is employed.
Freescale Semiconductor, Inc. Overview of the 3GPP Long Term Evolution Physical Layer 9
Table 2.3.2-1 Available Downlink Bandwidth is Divided into Physical Resource Blocks
Bandwidth (MHz) 1.25 2.5 5.0 10.0 15.0 20.0
Subcarrier bandwidth (kHz) 15
Physical resource block (PRB) bandwidth (kHz)
180
Number of available PRBs 6 12 25 50 75 100
The total number of available subcarriers depends on the overall transmission bandwidth of the system. The LTE specifications define parameters for system bandwidths from 1.25 MHz to 20 MHz as shown in Table 2.3.2-1. A PRB is defined as consisting of 12 consecutive subcarriers for one slot (0.5 msec) in duration. A PRB is the smallest element of resource allocation assigned by the base station scheduler.
Figure 2.3.2-2 Downlink Resource Grid
downlink slotTslot
NBW
subc
arrie
rs
Resource Block:
7 symbols X 12 subcarriers (short CP), or;
6 symbols X 12 subcarriers (long CP)
Resource Element
12 s
ubca
rrier
s
- Interference averaging is achieved by hopping over different blocks over time
- Less averaging than symbol-by-symbol hopping but facilitate channel estimation
Channel Estimation• Channel estimation is achieved by interpolating between
the pilots
41
10 Overview of the 3GPP Long Term Evolution Physical Layer Freescale Semiconductor
The transmitted downlink signal consists of NBW subcarriers for a duration of Nsymb OFDM symbols. It can be
represented by a resource grid as depicted in Figure 2.3.2-2. Each box within the grid represents a single subcarrier for
one symbol period and is referred to as a resource element. Note that in MIMO applications, there is a resource grid for
each transmitting antenna.
In contrast to packet-oriented networks, LTE does not employ a PHY preamble to facilitate carrier offset estimate,
channel estimation, timing synchronization etc. Instead, special reference signals are embedded in the PRBs as shown
in Figure 2.3.2-3. Reference signals are transmitted during the first and fifth OFDM symbols of each slot when the short
CP is used and during the first and fourth OFDM symbols when the long CP is used.
Figure 2.3.2-3 LTE Reference Signals are Interspersed Among Resource Elements
R
R
R
R
R
R
R
R
12 S
ubcarr
iers
Subframe
Slot Slot
Note that reference symbols are transmitted every sixth subcarrier. Further, reference symbols are staggered in both
time and frequency. The channel response on subcarriers bearing the reference symbols can be computed directly.
Interpolation is used to estimate the channel response on the remaining subcarriers.
2.4 MIMO and MRC The LTE PHY can optionally exploit multiple transceivers at both the basestation and UE in order to enhance link
robustness and increase data rates for the LTE downlink. In particular, maximal ratio combining (MRC) is used to
enhance link reliability in challenging propagating conditions when signal strength is low and multipath conditions are
challenging. MIMO is a related technique that is used to increase system data rates.
Figure 2.4-1a Figure 2.4-1b MRC/MIMO Operation Requires Multiple Transceivers
XCVRBaseband
XCVR-A
Baseband
XCVR-B
Conventional Single Channel
Receiver w/Antenna Diversity
MRC/MIMO Receiver
Configuration (2-ch)
Peak-‐to-‐Average Power Ratio• OFDM transmitted signal has a high PAPR due to
superposition of many independent sub-carrier symbols
• This leads to significant backoff in the power amplifier setting and low efficiency
• Particularly significant issue in the uplink
• Several engineering solutions to this problem• Current version of LTE uplink uses OFDM for multiple
access but single carrier transmission per user.
42
LTE Uplink: SC-‐FDMA
43
Freescale Semiconductor, Inc. Overview of the 3GPP Long Term Evolution Physical Layer 13
impulse responses are known, data can be transmitted from both antennas simultaneously. The linear combination of the two data streams at the two receiver antennas results in a set of two equations and two unknowns, which is resolvable into the two original data streams.
2.5 SC-FDMA LTE uplink requirements differ from downlink requirements in several ways. Not surprisingly, power consumption is a key consideration for UE terminals. The high PAPR and related loss of efficiency associated with OFDM signaling are major concerns. As a result, an alternative to OFDM was sought for use in the LTE uplink.
Single Carrier – Frequency Domain Multiple Access (SC-FDMA) is well suited to the LTE uplink requirements. The basic transmitter and receiver architecture is very similar (nearly identical) to OFDMA, and it offers the same degree of multipath protection. Importantly, because the underlying waveform is essentially single-carrier, the PAPR is lower.
Fig. 2.5-1 SC-FDMA and OFDMA Signal Chains Have a High Degree of Functional Commonality
BitStream
SingleCarrier
ConstellationMapping
S/PConvert
M-PointDFT
SubcarrierMapping
N-PointIDFT
CyclicPrefix
&Pulse
Shaping
RFE
Channel
RFEN-Point
DFTCyclicPrefix
Removal
FreqDomain
Equalizer
SCDetector
BitStream
Functions Common to OFDMA and SC-FDMA
SC-FDMA Only
Symbol
Block
P/SConvert
M-PointIDFT
Symbol
Block
Const.De-map
The block diagram of Figure 2.5-1 shows a basic SC-FDMA transmitter / receiver arrangement. Note that many of the functional blocks are common to both SC-FDMA and OFDMA, thus there is a significant degree of functional commonality between the uplink and downlink signal chains. The functional blocks in the transmit chain are:
1. Constellation mapper: Converts incoming bit stream to single carrier symbols (BPSK, QPSK, or 16QAM depending on channel conditions)
2. Serial/parallel converter: Formats time domain SC symbols into blocks for input to FFT engine
3. M-point DFT: Converts time domain SC symbol block into M discrete tones
4. Subcarrier mapping: Maps DFT output tones to specified subcarriers for transmission. SC-FDMA systems either use contiguous tones (localized) or uniformly spaced tones (distributed) as shown in Figure 2.5-2. The current working assumption in LTE is that localized subcarrier mapping will be used. The trades between localized and distributed subcarrier mapping are discussed further below.
5. N-point IDFT: Converts mapped subcarriers back into time domain for transmission
6. Cyclic prefix and pulse shaping: Cyclic prefix is pre-pended to the composite SC-FDMA symbol to provide multipath immunity in the same manner as described for OFDM. As in the case of OFDM, pulse shaping is employed to prevent spectral regrowth.
7. RFE: Converts digital signal to analog and upconvert to RF for transmission
In the receive side chain, the process is essentially reversed. As in the case of OFDM, SC-FDMA transmissions can be thought of as linear summations of discrete subcarriers. Multipath distortion is handled in the same manner as in OFDM
Summary
44
Narrowband system Wideband CDMA Wideband OFDMA
Signal Narrowband Wideband Wideband
Intra-cell bandwidth allocation Orthogonal Pseudorandom Orthogonal
Intra-cell interference None Significant None
Inter-cell bandwidth allocation Partial reuse Universal reuse Universal reuse
Inter-cell uplink interference Bursty Averaged Averaged
Accuracy of power control Low High Low
Operating SINR High Low Range: low to high
PAPR of uplink signal Low Medium High