Chapter 9
OFDM

This chapter provides an introduction to OFDM concepts. It first introduces simple signal transmission concepts and orthogonal subcarrier properties. It then illustrates how standards like Wi-Fi, WiMAX, and LTE make use of OFDM properties. We present a cursory overview that allows the reader to understand the fundamentals of OFDM and OFDMA. For a more details, refer for instance to [10], [104], [119].

9.1 Overview of OFDM

We’ve seen important and popular standards that use direct spreading sequences on user data, thus implementing a CDMA scheme. We now review another technique called Orthogonal Frequency Division Multiplex (OFDM), which is increasingly popular and adopted by standards like Wi-Fi, WiMAX, and LTE.

9.1.1 OFDM Basics

OFDM techniques consist in splitting a user data stream into several sub-streams, which are sent in parallel on several subcarriers. These sub-streams and subcarriers benefit from a number of properties that we now review in details.

Recall the classic example of continuous wave to encode information: the carrier frequency in itself in not capable of encoding information. The quantity of information s(t) is encoded by changes or modulation of the wave, and affects the amount of spectrum required Δfc as shown on figure 9.1.


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Figure 9.1: Duality time-frequency.

One can of course use several carriers fi,i ∈{1,2,,Nc}, and filter them separately. That is a common approach and is used extensively in FDMA systems: in particular multiple network operators who own licenses over a same area must take care not to exceed allowed levels of adjacent channel interference into one-another’s bands.

OFDM improves on the idea by using orthogonal properties of functions to increase spectral efficiency by choosing a specific interval Δf = fi+1 -fi between subcarriers. Multiple parallel signal streams are used: si(t) = exp(it) (where ωi = 2πfi), and in frequency domain: Si(f) = δ(f - fi).

In fact time signals are limited in a time window, and a user information symbol has a time interval for transmission: [0, Ts], so

si(t) = ui ⋅1[0,Ts] ⋅exp(jωit)
(9.1)

(where ui is a user information symbol) and the frequency domain representation of the signal is modified from a perfect Dirac function δ(f - fi) to a sinc function1:

Si(f) = ui ⋅exp(πjfTs) ⋅Ts ⋅sinc(πfTs )
(9.2)

This last expression is derived from Fourier transform, using definitions from the next section.


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Figure 9.2: Orthogonal carrier spacing.

9.1.2 Fourier Transform

Now recall the duality between time domain and frequency domain, with Fourier transform (and inverse Fourier transform) to switch from one domain to the other. Several definitions exist; let us the following definition of Fourier transform

        ∫ ∞
U (f) =     u(t)⋅ej2πftdt
         -∞
(9.3)

and inverse Fourier transform

       ∫ ∞        - j2πft
u (t) =     U (f)⋅e      df
        -∞
(9.4)

(Other definitions exist, with different signs under the exponent and different 2π factors, so it is important to always specify what definitions are used.) With this definition, the reader can readily derive formula (9.2):

           ∫ Ts                             sin(πfT  )
Si(f ) = ui ⋅   ej2πftdt = ui ⋅exp(jπfTs) ⋅Ts ⋅------s-
            0                                 πfTs
(9.5)

9.1.3 Orthogonality

OFDM is a multicarrier modulation in which a user bit stream (of rate Ru) is transmitted over Nc subcarriers, each having a symbol rate Rs = Ru-
Nc, or a symbol duration Ts = -1
Rs = Nc-
Ru. The advantage of that parallel transmission is that the symbol time may be increased, which mitigates inter-symbol interference.

Each symbol stream is multiplied by a function φk from a family of orthogonal functions {φk},k ∈{0,,Nc - 1}. In CDMA, these functions were Walsh codes, in OFDM, they are windowed complex exponentials (or possibly cosine functions):

        {
          ejωkt if t ∈ [0,Ts]
φk (t) =   0     elsewhere
(9.6)

So in a similar manner to the CDMA forward link presented in section 8.1, multiple channels are multiplexed and combined, using exponential functions instead of Walsh code sequences:

         Nc-1
S   (t) = ∑   s g φ (t)
  tot          k k k
         k=0
(9.7)

(where ui = sigi; si represents the information symbol (+1 or -1), gi is the individual channel gain) or for many successive bits m = 0,1,2,..., etc.

         ∞  N -1
 ′       ∑   c∑
Stot(t) =         sk,m ⋅gk,m ⋅φk (t - mTs )
        m=0  k=0
(9.8)

That sequence is manipulated further and sent over the air; on the receiver side, that sequence may decoded by using orthogonal properties of {φk}.

 1 ∫ Ts        *
T--    φk(t)⋅φ l(t)dt = δk- l
  s 0
(9.9)

where δk-l is the Kronecker symbol (i.e. 0 if k = l, 1 otherwise), and the asterisk (*) denotes the complex conjugate of the expression. Equations (9.6) and (9.9) gives us the orthogonal condition for subcarriers’ spacing: the right hand side equals zero if and only if (ωk -ωl)Ts = 2πn, for n non-zero integer. This leads to the condition Δf = n∕Ts, and 1∕Ts is the smallest separation between two subcarriers.

On the receiving side, the sequence may be decoded by simply integrating for each channel; for channel k, the information bit is retrieved from the sign of the integral:

∫                  N -1    ∫
  Ts               ∑c        Ts
 0  Stot(t)φk(t)dt =     sigi 0  φi(t)φk (t)dt = skgkTs
                    i=0
(9.10)

Although in this case an additional trick is used, and direct and inverse Fourier transforms are used for decoding.

9.1.4 Discrete Fourier Transform

If we then examine the Fourier transform of our functions given in equation (9.6), we obtain a sinc function of pseudo-period Ts, which means that in the frequency domain subcarriers are spaced exactly such that the peak of the next one corresponds to the previous one’s first zero – see figure 9.3.


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Figure 9.3: OFDM subcarrier spacing.

The overall envelope looks a bit like a spread spectrum signal, and may be tapered further to reduce out of band spectral power density.

The above choice of orthogonal basis functions has another useful property, relating to Fourier transform. Indeed sampling Stot turns the above expressions into the usual discrete Fourier Transform (DFT), and therefore, instead of multiplying, summing, and then integrating for decoding, OFDM allows to simply carry out a DFT and its inverse (IFT), which are very efficient operations.

Looking back at the Fourier transform (9.3), and sampling the time function and its Fourier transform (with N samples), one may define the following notations: uk = u(tk),tk = kτ,k  ∈  {0,1,,N - 1}, and Un = U(fn),fn = n--
Nτ,n  ∈  {-N∕2,,N∕2}. And one obtains the discrete Fourier transform

               N∑-1               N∑-1
Un = U (fn ) = τ   uk ⋅ej2πfntk = τ    uk ⋅ej2π knN-
               k=0                k=0
(9.11)

and the inverse discrete Fourier transform

                  N∕2
u  = u(t ) = -1-- ∑    U  ⋅e-j2πkNn
 k      k    τN          n
                n= -N∕2
(9.12)

Now comparing these discrete transforms to above Stot with the particular OFDM orthogonal functions, one sees that the sk,m gk,m coefficients are Fourier transforms 2 of the complex amplitude of the subcarriers.

Consequently, encoding-decoding of an OFDM signal is practically not done with integration like (9.10), but by simple FFT. The transmitter builds: {S(ωn)} = DFT{sk,m gk,m}. And the receiver decodes the received spectral signal: Stot = IDFT{S(ωn)}.

If sampling is made as a power of 2 (N = 2p), DFT (and IFT) algorithms are in O(Nlog2N), referred to as fast Fourier transform (FFT) and very efficient to implement. OFDM schemes are therefore based on the nearest power of two, and when fewer subcarriers are users, the same order N = 2p is used for the FFT algorithms, but with zero entries for a subset Nz = N - Nc.

9.1.5 Number of Subcarriers

Note that increasing the number of subcarriers in a given band of spectrum does not increase capacity but provides a useful parameter to optimize: there is an interesting tradeoff between number of subcarriers Nc and subcarriers symbol time Tc. The more subcarriers are used, the longer their symbol rate is, which means that the overall rate of information remains the same, but a longer symbol rate is useful for multipath mitigation (recall conditions when equalizers are required). Consequently subcarrier spacing is a fundamental parameter to chose for an OFDM standard like Wi-Fi or WiMAX.3

9.1.6 Other Usual Techniques

A few more standard techniques are used in combination with the above OFDM definition in practical radio systems. [104]

OFDM systems are therefore well suited to resolve rich multipath situations and slow time varying channels, which explains their popularity for standards like Wi-Fi. They are however not ideal for Doppler shift and phase noise.

9.2 Overview of Wi-Fi

Wi-Fi is a standard for interoperable equipment, certified by the Wi-Fi alliance, and based on various iterations of IEEE 802.11, which uses OFDM for its highest throughput profiles. Wi-Fi has been the most successful local area network standard, and it is worth spending some time examining some of its OFDM parameters.

Details of the 802.11 air interface can be found in a number of references, and recent books have good overview of the latest efforts [105], including good overview of 802.11n [106]. We only examine here some aspects of 802.11 as they relate to OFDM in order to provide some insight on performance goals and limitations.

9.2.1 802.11a/g

General Parameters: 802.11a/g uses an N = 64 point FFT in a 20MHz channel, δf = 1∕Ts = 312.5kHz, Ts = 3.2μs, 4 μs time block is used, with cyclic, 52 of the 64 subcarriers are populated, 4 are pilots (for phase and frequency training and tracking), 48 actually carry data.

The 802.11g packet structure includes the following:

Short training field (STF):
8 μs; 10x repetition of 0.8 μs symbol. Uses 12 subcarriers; good autocorrelation property and low peak to average ratio; also used for automatic gain control (AGC)
Long training field (LTF):
8 μs, composed of two 3.2μs training symbols and prepended by a 1.6μs cyclic prefix. Used for time acquisition and channel estimation.
Signal field (SiG):
4 μs (3.2 + 0.8 cyclic prefix), contains 24 bits BPSK describing transmit rate, modulation, coding, length. Forms together with the training field the preamble (totaling 20 μs).
Data Field:
includes service field (16 bits: 7 used to synchronize descrambler, 9 reserved for future use), data bits, and tail bits, and optionally padding bits. The Data field consists of a stream of symbols, each 4 μs (3.2 + 0.8 cyclic prefix), transmitted over 48 subcarriers, and 4 pilots.

9.2.2 802.11n

802.11n is a high throughput amendment to 802.11 containing improvements over 802.11a/g. So what exactly does improve in this high throughput amendment? We review its major improvements in the physical and MAC layers.

Physical layer

A number of improvements in the physical (PHY) layer were designed to increase throughput in some situations, although these improvements may come at a cost, which will be pointed out.









Modul.

bits/ Hz

bits/ subcx

48cx

11g rates

40MHz 11n rates

40MHz 4x4MIMO








BPSK1/2

1

1/2

24

6

13.5

54

BPSK3/4

1

3/4

36

9

QPSK1/2

2

1

48

12

27

108

QPSK3/4

2

1.5

72

18

40.5

162

16QAM1/2

4

2

96

24

54

216

16QAM3/4

4

3

144

36

81

324

64QAM2/3

6

4

192

48

108

432

64QAM3/4

6

4.5

216

54

121.5

486

64QAM5/6

6

5

135

540









Table 9.1: Throughput rates for 802.11a/g/n calculated for different modulations, given the number of data subcarriers used (48 for 11g, and 52 for 11n, 108 in 40MHz) and the symbol time of 3.2μs hence a data rate per subcarrier of 312.5kbps ×3.24 = 250kbps, because only 3.2 of 4 μs carry actual data.

OFDM carriers:
48 data subcarriers (+4 pilots) for 11g, 52 (+4 pilots) for 11n, and 108 (+6 pilots) for 40MHz operations. That increase in data subcarriers brings the maximum throughput up from 54Mbps to 58.5Mbps. Tradeoff: higher cost of mitigating interference in adjacent channel.
FEC:
Maximum FEC rate is increased from 3/4 to 56, hence reaching maximum data rate of 65Mbps, or 135Mbps in 40MHz channels. Tradeoff: more errors may occur, in which case the system can revert to lower modulation.
Guard interval:
The guard interval, or cyclic prefix may be shortened from 0.8μs to 0.4μs, thus increasing actual data rate to 72.25Mbps, or 150Mbps in 40MHz. Tradeoff: more ISI.
Multiple spatial streams:
MIMO offers 2, 3, or even 4 times the above rates, reaching 270/300, 540/600Mbps rates. Tradeoff: system complexity and cost.
Greenfield Preamble:
The 802.11n preamble is modified for higher throughput, adding a high throughput training field (series of 4 μs fields). A legacy mode appends this new preamble to the 11g preamble for backward compatibility, whereas the shorter “greenfield” 802.11n only preamble increase throughput by 10 to 15 percent, at the cost of backward compatibility.
Low density parity check (LDPC):
increases FEC efficiency and throughput in some cases.
MAC layer

The media access control (MAC) layer deals with multiple element addressing, channel access prioritization, and control. It transmits among other things beacons with regulatory and management information (such as country code, allowed channels, max power), and scans channels for beacons. Scanning is usually done passively but when regulations allow it, active probe requests can be sent for specific SSIDs or BSSIDs. MAC improvements for 802.11n include:

Fragmentation:
large frame may see considerable channel variations over time (especially in poor condition, thus low bitrates). Consequently frames can be fragmented, and only an erred fragment needs to be resent. MAC service data units (MSDU) above a certain settable threshold are broken into several fragments sent over different MAC protocol data units (MPDU).
Aggregation:
Aggregated MSDU or MPDU: A-MSDU is an efficient MAC frame format that aggregates multiple MSDUs in a single MPDU which maximum size is extended to 4 KBytes and optionally 8 KBytes. A-MPDU is another form of aggregation that aggregates multiple MPDUs in a single MPDU, which maximum size is extended to 64 KBytes.
Enhanced Block Ack:
a new scheme in which the sender requests to enter block acknowledgement (BA) request session, in which BA are requested periodically instead of having ongoing BA.
Optional features:
Other optional features are standardized as part of the 802.11n MAC:

9.2.3 802.11ac, ad, af

A number of further development are in the work for 802.11. They produce new amendments to the specification with the following goals:

802.11ac:
is another high throughput amendment to 802.11 containing improvements over 802.11a/g/n. It aims at providing very high throughput at 5-6GHz, it makes use of higher modulation schemes, bonding multiple channels, and multiple spatial streams (up to 8x8 MIMO) to reach several Gbps throughput.
802.11ad:
is also a high throughput amendment to 802.11, at 60GHz rather that the typical 2.4GHz and 5GHz of 802.11a/g/n. 802.11ad uses higher modulation schemes, wider channels and multi user MIMO techniques. The standard aims at reaching multi Gbps throughput.
802.11af:
This is the Wi-Fi version (based on 802.11ac physical layer) for use in several contiguous channels of TV White Space spectrum (TVWS), 5,10,20,40MHz channels, 8-16μs symbol time for LAN application, unlike the larger symbol times of 802.22 for wider areas. Planned March 2013.

9.2.4 802.22

In addition, a similar standard was recently produced to deal with longer links in TV white space. 802.22 addresses Wireless Regional Area Networks (WRAN), PHY MAC, policies and procedures for operations in TV white spaces (TVWS); the standard was published 7/2011, and was widely reported on in the press, nicknamed super Wi-Fi. Given the TVWS spectrum landscape, 802.22 defines 6, 7, or8 MHz channels, it uses 2048FFT, up to 64QAM, 200-300μs symbol time, which adapts well to wider area delay spreads.

9.3 Overview of WiMAX

IEEE 802.16 is a standard for wide area wireless networks [107]. The group focuses from the beginning on important service providers’ requirements for service reliability. Consequently 802.16 standardizes important features such as quality of service (QoS), security, flexible and scalable operations in many RF bands. WiMAX goes one step further and narrows down some implementation choices of 802.16 in order to achieve interoperation between equipment manufacturers. WiMAX still standardizes several air interfaces and several profiles in different frequency bands. Of course, performance varies with frequency, channel bandwidth, and other profile characteristics; and conformance between products and suppliers exist only in a given profile. [108]

9.3.1 Fixed and Mobile

Two very different families of WiMAX systems exist: fixed and mobile WiMAX. In addition, a regional initiative, WiBro, which resembles mobile WiMAX, has been standardized in Korea.

Fixed WiMAX
(802.16-2004 [109]) is a standard for fixed broadband access. Several profiles exist for fixed WiMAX, including different bandwidths, carrier frequencies, and duplexing schemes. Its air interface is based on Orthogonal Frequency Division Multiplexing (OFDM), and access between multiple users within a sector is managed by time-division multiple access (TDMA). While equipment has been available since 2004, true conformance testing [110] led to the first WiMAX equipments to be certified in January 2006. We will examine in this chapter profiles at 3.5 MHz (TDD and FDD) at 3.5 GHz, and 10 MHz TDD channels at 5.8 GHz.
Mobile WiMAX
(802.16e-2005 [111]) defines a different standard with considerations such as location register, paging, handoff, battery saving modes, and other network functions to manage mobility. Its air interface is based on Orthogonal Frequency Division Multiple Access (OFDMA), with 5, 7, 8.75, and 10 MHz channel widths for operations in the 2.3 GHz, 2.5 GHz, 3.3 GHz, and 3.5 GHz frequency bands.
WiBro
is a Korean initiative for Wireless Broadband. Similar in many ways to mobile WiMAX, WiBro includes mobility and handoff, and is commercially available in Korea since mid 2006. WiBro operates in 10 MHz TDD channels at 2.3 GHz, and uses OFDMA. It targets mobile usage up to 60 mph.

9.3.2 OFDM Fixed WiMAX

Although the standard community is focusing on mobile WiMAX, fixed WiMAX applications still have a small role to play, especially in less dense areas. Small and large service providers worldwide have conducted over 200 fixed WiMAX trials, and analysts once estimated some growth potential for fixed wireless market. 4 All in all, fixed wireless access remains usually a fairly small scale offering, led by small carriers, and do not achieve the order of magnitude of mobile wireless carriers. (Recall figure 1.4 from chapter 1.)

Fixed WiMAX is based on the 802.16d standard and has the following properties:

9.3.3 OFDMA Mobile WiMAX

OFDM is primarily used for fixed access. For mobility WiMAX uses a method for providing multiple user access in different simultaneous OFDM subchannels. This Orthogonal Frequency Division Multiple Access (OFDMA) is the true focus of 802.16 and WiMAX standards. Figure 9.4 shows how groups of subcarriers form subchannels, which are allocated to different users (as well as pilot and control channels). [113] [114]

Mobile WiMAX is based on the 802.16e standard and has the following properties:


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Figure 9.4: OFDMA subcarriers, as used by WiMAX: at a given time certain subgroups of subcarriers are dedicated to specific subscribers.


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Figure 9.5: WiMAX subframes are flexible in allocating subcarriers to different subscribers according to demand. (Source: www.wimaxforum.org white paper)

WiMAX frame structures are flexible in terms of use of subcarriers, which can be allocated to different subscriber units according to their needs (figure 9.5). The number of subcarriers is used as a mean to establish frequency reuse schemes. Recall from 2.1.1 that the reuse factor has a strong impact on spectrum efficiency, and that one of the strength of CDMA is to allow a reuse factor of one whereas TDMA schemes needed higher reuse factors. Mobile WiMAX and OFDMA use fractional reuse to optimize spectrum in different areas: the concept is simple, use all subcarriers near the center of the cell (full use of subcarriers, or FUSC), but only make partial use of subcarriers (PUSC) in areas where they would interfere.


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Figure 9.6: Fractional reuse of subcarriers, some areas only use subgroups of subcarriers (F1, F2, or F3), to avoid interference where they overlap. Areas near the center can make full use of all subcarriers.

Further work in 802.16m will provide the 4G evolution in a backward compatible way (including MIMO and OFDMA); 4G improvements are inserted in reserved fields that can be ignored from legacy 802.16e gear, but utilized by future 802.16m equipment.

9.4 Overview of LTE

The goal of LTE is to provide 3GPP with further evolutions, improving its architecture, throughput, and spectrum efficiency. LTE can:

LTE’s air interface, like other 4G standards, revolves around OFDMA. MIMO is used to either enhance data rates or increase data integrity (diversity and MRC). And the other usual tools are used as well: convolutional and turbo codes, and adaptive modulation (QPSK, 16QAM, 64QAM). LTE offers a flexible range of channel bandwidth (1.4, 3, 5, 10, or 20 MHz), which is well adapted to the current cellular and PCS bands.


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Figure 9.7: 4G throughput goals as they apply to LTE were represented in the standard community by this picture nicknamed ‘the van’ for its shape: it shows throughout evolution goals as a function of mobility speed.

Subsequent releases of 3GPP LTE have been published:

9.4.1 Physical Layer

LTE uses OFDMA for the downlink, with a fairly simple frame structure, and SC-FDMA for the uplink.

Downlink

LTE FDD uses 10ms frames, divided into 20 sub-frames or slots (of 0.5ms each). Each sub-frame uses 7 OFDM symbols, each with a cyclic prefix. Subchannels separation is Δf = 1∕T =15kHz, where T is the OFDM symbol period. (For multimedia broadcast multicast service MBMS dedicated cell, reduced carrier spacing can be used in the downlink Δf=7.5kHz). A cyclic prefix (CP) is used to duplicate part of the symbol: total symbol duration Ts = Tu + Tcp. For normal 15kHz subcarrier spacing, the normal CP is 7 OFDM symbols per slot, which works well in typical urban multipath (Tu = 66.7μs, and Tcp = 5.21μs for first symbol, 4.7μs for the following symbols). An extended CP for larger cells or heavy multipath is available: Tcp = 16.67μs.

This splits radio resources into time and frequency elements, called resource blocks. On the frequency scale a resource block is 12 subcarriers wide (180kHz), on the time scale it is one slot (0.5ms).







CP

OFDMA symbols

Subcx

CP symbols

CP (μs)






Δf=15kHz, normal

7

12

160 first

5.2 first

144 after

4.7 after

Δf=15kHz, extended

6

12

512

16.7







Table 9.2: LTE cyclic prefix lengths in number of symbols, subcarriers, and time.

There are three downlink channels in the physical layer, shared, control, and common control. And there are two uplink channels, the shared and the control channel. Modulation techniques used for uplink and downlink are QPSK, 16 QAM, 64 QAM while the broadcast channel uses only QPSK.


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Figure 9.8: LTE physical layer uses multiple OFDMA subcarriers and symbols separated by guard intervals.


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Figure 9.9: LTE OFDMA Physical layer structure.


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Figure 9.10: LTE resource blocks and resource elements (from the 3GPP standard).

Uplink

The uplink standard is departing from the usual OFDMA approach: it uses single carrier FDMA (SC-FDMA). SC-FDMA is a type of frequency domain equalization (FDE). In SC-FDMA, a bit stream is converted into single carrier symbols, then a Discrete Fourier transform (DFT) is applied to it, subcarriers are mapped to these DFT tones and an inverse DFT (IDFT) is performed to convert back for transmission. Much like in OFDMA, the signal has a cyclic prefix to limit ICI, and pulse shaping is used to limit ISI.

Similar parameters are used as for downlink: subcarrier spacing 15kHz, CP normal or extended (Note that CP is the same for all UE in cell, and the same as downlink). The uplink uses the same symbol period and resource elements as in the downlink. Resource blocks are defined in the same manner, with NSCRB = 12 subcarriers and NRB depends on bandwidth: 6, 15, 25, 50, 75, or 100.

The reasons for preferring SC-FDMA over OFDMA are mainly that transmitting mobile units have strict limitations on the transmit power, and that peak-to-average power ratios (PAPR) are high for OFDMA. [118]


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Figure 9.11: CDF PAPR comparison for OFDMA used in the LTE downlink, and SC-FDMA localized mode (LFDMA) used in the LTE uplink – 256 total subcarriers, 64 subcarrier per user, 0.5 roll-off factor, (a) QPSK, (b) 16QAM.

9.4.2 LTE Throughput

LTE physical layer throughput calculations are easily derived from the 3GPP specifications: 1 Radio Frame has 10 sub-frames, each sub-frame has 2 time-slots, each time-slot is 0.5 ms long, 1 time-slot has 7 modulation symbols or OFDMA symbols (when normal CP length is used). Each modulation symbol = 6 bits at 64 QAM (note that these are physical layer bits, not actual user information).

A Resource Block (RB) uses 12 Sub-carriers. Assume 20 MHz channel bandwidth (100 RBs), normal CP. The number of bits in a 1ms sub-frame is 100RBs x 12 sub-carriers x 2 slots x 7 modulation symbols x 6bits=100800 bits. So the data rate is 100.8 Mbps. For 4x4 MIMO the peak data rate is simply four time that, or 403Mbps. (Of course, a more robust FEC coding, lowers the bitrate to 336Mbps at 64QAM 5/6, or 302Mbps at 64QAM 3/4.)

Note that the above accounts for every resource block, which has to carry overhead signaling, reference signals, etc. Practically, looking at resource elements in a resource block for one (1ms) subframe, some resource elements are reserved (for instance with control frame indicator CFI=2).


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Figure 9.12: Some LTE resource elements are reserved for control channel and reference signals only a subset are used for user data, thus lowering actual throughput.

Out of the 12x14 RE, 36 are used for control (PDCCH) and reference signals, so only 132 can carry data. (See figure 9.12). So 20% of the physical layer data rate is reserved. So the maximum physical layer data rate is 80.64Mbps (or 322.56Mbps in 4x4 MIMO).

Commonly cited numbers are 75Mbps uplink, and 300Mbps downlink for LTE, this because layer 2 has additional transport block size (TBS) restrictions and frame overhead – typically around 9-10%, leading to 75Mbps and 300Mbps rates (for 4x4 MIMO in 20MHz).


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Figure 9.13: A comparison table between various OFDM standards is a good starting point for comparison between standards; it allows to clearly outline advantages of certain standards.

9.4.3 Other Wireless Standards

Many other wireless standards exist and are continually in development for a wide range of applications. Figure 9.14 shows a summary of the most popular ones with their typical throughput, range, and domain of applications.

Such table is difficult to keep up-to-date as standards work focuses on new needs and new opportunities; and incorporate the latest technology innovations into them as needed. Some of them become extremely successful and nearly omnipresent, while others miss their window of opportunity and nearly die on the vine. They range over a wide industry interest from wireless cellular and LAN’s to smart grids, RFID tagging, entertainment and consumer electronics, and much more.


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Figure 9.14: A comparison table between many wireless standards shows their approximate throughput, range, and applications.

9.5 Homework

  1. Derive equation (9.2) using the definition of Fourier transform in 9.1.2.
  2. An 802.11a system uses Nc = 48 subcarriers for data and 4 more for pilot.
    1. What is the nearest power of two N = 2p ?
    2. 802.11a uses 20 MHz channels, what is Δf between subcarriers in such a channel?
    3. What is each user information bitrate? (Assume a BPSK modulation, i.e. only one bit transmitted per symbol)
    4. Compare to the spectral efficiency of WCDMA where 3.84 Mc/s are transmitted in 5 MHz. (Again assume 1 chip is 1 symbol for that comparison)

      Other non standard solutions are becoming popular, such as one by Flarion (now owned by Qualcomm). The proposal was the basis of work to another IEEE group to be created: 802.20. The proposal initially used 113 subcarriers, 17 of which are used for pilots. (The next four questions refer to this solution)

    5. What is the nearest power of two N = 2p ?
    6. This uses 1.25 MHz channels (convenient for current CDMA providers). What is Δf between subcarriers in such a channel?
    7. What is each user information bit rate? (Assume a BPSK modulation, i.e. only one bit transmitted per symbol)
    8. Compare to the spectral efficiency of 802.11a above.
  3. Beside spectral efficiency, what advantages and disadvantages can you think of between the solutions presented in the previous problem? (Hint: think of fading characteristcs and 9.1.5).
  4. The following 14-bit sequence 00001111001101 is to be encoded on an OFDM system. Represent each bit by a BPSK symbol, 1. Ignore any pilot signal, i.e. every subcarrier is for data transmission.
    1. Implement a system within 1 MHz of spectrum bandwidth. Specify how many subcarriers are used and their frequency separation.
    2. Compute complex coefficients for each subcarrier by FFT. (Zero out the Nz trailing ports). Use matlab for instance, and compute the FFT.
    3. Show the approximate spectral shape, i.e. the modulus of the sum of all subcarrier with their associated coefficient. (Use matlab, or any other graphic software, or approximate by hand drawing; in any case, show details of your method).
    4. Truncate the result to the first 14 bits, again fill in the remaining bits by zero, compute the IFFT and explain how to retrieve data from the original bit stream.
  5. We consider a Wi-Fi 802.11g system where approximately 64 subcarriers are used in a 20 MHz channel.
    1. Assuming that symbol periods must be greater than 10 times delay spread (Ts > 10στ), what is the maximum delay spread in which this system performs well.

      (For simplicity, ignore guard bands, cyclic prefix, etc, and assume that the entire symbol duration is for user data).

    2. What happens if the delay spread is much greater?
    3. Searching for typical delay spreads in various sources, is Wi-Fi subcarrier spacing adequate for most indoor environments?
    4. We now consider a WiMAX 802.16d system with 256 subcarriers over a 3.5 MHz channel. Searching again for typical delay spreads in various sources, in what environment would this system be appropriate? (indoors? in rural areas? in major cities?)
    5. 802.16e now standardizes 512 subcarriers for 3.5 MHz channels. In what environment might this be an improvement?
    6. Explain why WiMAX is better suited for providing wireless access throughout a city than Wi-Fi access points.
  6. A city is interested in a system providing coverage for its citizens city-wide.
    1. Suggest a few state-of-the-art wireless systems for the city’s consideration and justify your choices.
    2. Make a table showing advantages of these technologies for a carrier to provide extensive wireless coverage for a city. (Include at least considerations around: spectrum, cell sizes (consider power allowed, propagation, and delay spread), indoor service availability, mobility (Doppler, handoff).
    3. The city is also interested in having its police, fire department and other first response emergency services communicate on that system. Are there any additional important arguments to consider for this type of use? Would they preclude any of your above systems — why?