GB2452616A - Adaptation of the Alamouti method for a MISO system to a non-stationary channel - Google Patents

Abstract

A method of adapting a space-time block code (Alamouti) scheme for a MISO system in an OFDM receiver to situations where the channels are non-stationary. Equalisation is provided to the received signal using diversity techniques. The equalisation means is adapted to use four channel gain values (h01, h11, h10, h11) from two transmitters and for two time slots. To provide the required outputs the complex conjugate (Conj.) of selected ones of these values are taken.

Description

OFDM RECEIVER

BACKGROUND OF THE INVENTION

This invention relates to OFDM (orthogonal frequency-division multiplexing) receivers.Various proposals have been made for the next-generation terrestrial Digital Video Broadcasting system (DVB-T2). One is that it should incorporate the option of multiple-input multiple-output (MIMO) operation.

In this configuration, two or more transmitters are used, together with a corresponding number of antennas at the receiver, to deliver a higher bit-rate than would be possible with conventional transmission. One suggested arrangement is co-sited transmissions on opposite polarisations and a corresponding dual-polarisation receiving antenna; another possibility is to have geographically separated transmissions with multiple directional receiving antennas (see European Patent Application 1821481, and BBC R&D White Paper WHP 144, referenced below).

Conversion of domestic reception set-ups to obtain full value from the MIMO transmissions would require at the very least an antenna upgrade, and possibly a new downlead. It is therefore likely that for a considerable transition period MIMO-enabled receivers would co-exist alongside single-antenna receivers receiving conventional or S ISO (single-input single-output) transmissions.

To cope with this transition period, it has been suggested that the new standard should offer the possibility of transmitting both MIMO and conventional parts within the same OFDM (orthogonal frequency- division multiplexing) multiplex. MIMO-enabled receivers would be able to decode all of the services, whilst legacy receivers would still be able to decode the services carried in the non-MIMO part; this may be as part of a MISO (multiple-input single output) transmission system. Achieving such backwards compatibility is however not a trivial operation.

Another proposal is that the OFDM receiver should take the form of a MISO receiver.

With either proposal there is a desire for effective MISO receivers as part of the DVB-T2 system.

Reference may be made to the following published documents by way of

background to the present invention:

1. Digital Video Broadcasting Project, DVB-T2 Call for Technologies, paper no SB 1644r1, 16 April 2007 (includes generic block diagrams of DVB-T transmitter and receiver).

2 J.D Mitchell, P.N. Moss and M.J. Thorp, A dual polarisation MIMO broadcast TV system", BBC R&D White Paper WHP 144, December 2006.

3. A. Dammann & S Kaiser, Performance of Low Complex Antenna Diversity Techniques for Mobile OFDM Systems, Proc. 3rd International Workshop on Multi-Carrier Spread-Spectrum, Oberpfaffenhofen, Germany, September 2001.

4. S. Kaiser, Spatial transmit diversity techniques for broadband OFDM systems, in Proceedings IEEE Global Telecommunications Conference (GLOBECOM 2000), November 2000, pp. 1824.1828.

5. S.M. Alamouti, "A Simple Transmit Diversity Technique for Wireless Communications", IEEE Journal on selected areas of communications, vol. 16 no. 8, October 1998.

6. European Patent Application 1821481 "OFDM -MIMO Radio Frequency Transmission System", BBC, Inventor Moss, P.N. (referred to above)

SUMMARY OF THE INVENTION

The invention in its various aspects is defined in the appended claims to which reference may now be made. Advantageous features of the invention are set forth in the appendant claims.

Preferred embodiments of the invention are described below with reference to the drawings. These embodiments take the form of an OFDM receiver for use in a MISO system, which comprises means for receiving a transmitted signal at an antenna, means for subjecting the received signal to a fast Fourier transform, means for separating pilots from the received signal, and means for providing equalisation to the received signal, the equalisation employing diversity techniques. The received cells each comprising one OFDM symbol on one carrier are received in pairs. The equalisation means is adapted to make use of four channel gain values and the two received cells from two transmitters, and to provide the required outputs by taking the complex conjugate of selected ones of these values, multiplying by selected ones of the channel gains, and normalising them with relation to the two channel gains The normalisation may be effected with relation to squares of the moduli of the gains on the respective channels.

The equalisation means preferably generates outputs sO and si in accordance with the following: rbO ConjuqateJO1Jtk1i CoJijuqatefrbj -hO C.o.nj tethO3.J-ihiO CQnjlIgeh11] Al rhO C�njuqatp11J_hoo Com]1Jgaterb1 hOO Conjugate(1101j4h10 Conuate[h11] where rbo and rbl are the pair of received cells, h1 is an estimate of the channel gain from each transmitter, where i is the transmitter index and j the cell index, and conjugate[X]' indicates the complex conjugate of X. Thus it is seen that the equalisation makes use of four channel gain values (hOi, hli, hlO, hil) and the two received cells (rbo, rbi) from two transmitters (0, 1), and provides the required outputs by taking the complex conjugate of selected ones of these values, multiplying by selected ones of the channel gains, and normalising them with relation to the two channel gains.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in more detail by way of example and with reference to the drawings, in which: Fig. I is an overall block diagram of a transmitter as described in our UK Patent Application 0710665.1; Fig. 2 shows a form of the Alamouti mapping block that may be used as block 20 in the transmitter of Fig. 1; Fig. 3 is an overall block diagram of a receiver for use with the transmitter ofFig.1; Fig. 4 shows a form of the equalisation block 124 in the receiver of Fig. 3 suitable for use with non-stationary channels in accordance with this invention; Figs. 5 to 12 illustrate various aspects of the performance of a system capable of operating with non-stationary channels, namely: Fig. 5 is a graph showing the penalty relative to the SNR sum due to phase changes between cells; Fig. 6 is a graph showing the penalty relative to the SNR sum due to amplitude changes between cells; Fig. 7 s a graph showing the gain change between adjacent carriers for a 0dB echo; Fig. 8 is a graph showing the penalty for an equal gain change in both paths, Fig. 9 is a graph illustrating the through-path error for a change in phase in the second path only; Fig 10 is a graph illustrating the through-path error for a gain change in the second path only; Fig. 11 is a graph illustrating the crosstalk for a simple Alamouti system with a change of phase in the first path only; and Fig. 12 is a graph illustrating the crosstalk for a gain change in the first path only.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE

INVENTION

Examples of the invention will now be described. These examples illustrate possible forms of coding with which the invention can be used, and receivers that can receive such coded signals. In these examples the signals include MISO (multiple-input single-output) signals.

Background

This invention is based on COFDM (coded orthogonal frequency-division multiplexing) or at least OFDM. It has a frame structure in which services are FEC-coded (forward error correction coded) individually and then multiplexed together. The multiplexing is applied in time such that a given service is carried on a number of successive OFDM symbols within each frame. A service can begin and end part-way through an OFDM symbol. The bits carried on a particular symbol are grouped together in groups corresponding to QAM (quadrature amplitude modulation) constellations; interleaving is then performed at the bit and constellation levels within the OFDM symbol. Bit interleaving is done on each service.

Reference should be made to our UK Patent Application 0710665.1 (Publication No. dated 2008 which describes a proposed system of MIMO transmission which includes receivers operating in MISO mode The following description assumes a knowledge of the contents of that application so as to avoid unnecessary repetition.

Briefly, our UK Patent Application 0710665.1 explains that the part of a service carried on a particular frequency (carrier) in a particular frame is referred to as a slot" Slots can begin and end part-way through a symbol.

Each receiver can obtain, for each OFDM cell' (that is, one symbol on one carrier), a separate estimate of the channel gain h from each transmitter, where is the receiver index and j the transmitter index. Taking all the receivers together, these form an N x N matrix, which has to be inverted in order to determine the N distinct constellation points transmitted by the N transmitters for that cell.

Separate estimates of channel gain can be obtained by inverting some of the pilots, in accordance with the above-mentioned European Patent Application (ref. 6). In the 2 x 2 MIMO case (two transmitters, two receivers) the pilots from one transmitter are normal; from the other transmitter half the pilots are normal and half are inverted. The receivers can use these pilots to obtain an estimate of both the sum and the difference of the channel gain for each cell, and from these it can calculate the individual gains by simple addition and subtraction.

Suppose now that for some of the symbols, or for some of the cells within a symbol, it is desired to operate in the MISO mode. One approach is to transmit the same constellation point, x, from both transmitters. The single receiver will therefore receive h00x from one transmitter and h01x from the other; the combined result will be (h00 + h01)x. (Here the first index is the receiver and the second is the transmitter. The first index will always be zero because there is only one receiver.) It can therefore estimate the required gain (h00 + h01) using only the pilots which were sent non-inverted from both transmitters. The other pilots yield (h00 -h01) which is of no use to the receiver, and from the point of view of the MISO receiver these pilots are a waste of power and bandwidth.

In this case it would be desirable to reduce the number of pilots in the MISO symbols, but pilots are not only used to equalise for the symbols in which they occur. Because of the temporal interpolation, they also contribute to the channel estimate on other symbols. It would be very difficult to design iriterpolators capable of dealing with an irregular pilot pattern, especially one whose exact nature depended on the configuration of the multiplex at any one time.

There is also the possibility that h00 = -h01 so that the two transmitters interfere destructively. This is quite probable if the transmitters are co-sited or transmit on a single-frequency network (SFN) The MISO receiver will be unable to recover the transmitted constellation point. If the relative delay between the transmitters is small, flat fading might occur such that the effect of switching on the second transmitter is to make reception worse.

Alamout, modulation technique The preferred form of modulation technique in accordance with our above UK Patent Application 0710665.1 is a MISO technique. One particularly preferred form of modulation technique is that described by S.M. Alamouti, in "A Simple Transmit Diversity Technique for Wireless Communications", IEEE Journal on selected areas of communications, vol. 16 no. 8, October 1998 (ref. 5 above) We propose that this technique is applied to the non-MIMO parts of the signal.

Alamouti proposes using two transmit antennas. For one cell, one transmitter antenna transmits s0 and the other s1, and on the next cell the first transmits _S1* and the second transmits s0, where the asterisk indicates complex conjugation. That is, on the second cell, a first one of the two transmitters transmits the complex conjugate of the cell previously transmitted on the second transmitter, while the second transmitter transmits the inverse of the complex conjugate of the cell previously transmitted on the first transmitter. At the receiver the signals are combined by generating both the sum and the difference of the corresponding received signals. The successive cells will normally be successive symbols on the same carrier but in principle may be the same symbol on different carriers.

Applying this and writing it mathematically, the receiver generates outputs sO and Si in accordance with the following: = hr0 + h01r1" h00I -i-1h011 Jhj -i-1h011 where rO and ri are the pair of received cells, hij is an estimate of the channel gain from each transmitter, where i is here the transmitter index and j the cell index within the pair, and the asterisk indicates complex conjugation.

In the case of Alamouti, constellations are paired up, typically taking two symbols on the same carrier together, and sent twice, once from each transmitter. The phases in which they are transmitted are desirably chosen such that if destructive interference occurs on one symbol, the interference will be constructive on the other symbol. Whatever the channel gains and phases, the two constellations can be recovered at the receiver. The resulting signal-to-noise ratio is as though the signals from the two transmitters combined by "power addition'.

In order to recover the two transmitted constellations, the receiver needs to know the complex channel gain from each transmitter individually for each cell.

Fortunately, enough normal and inverted pilots are already being transmitted to allow the receiver to estimate both gains. Although the overhead in lost data rate from the extra pilots has to be accepted, at least the extra pilots are now being put to good use even in the single-channel receiver.

In the standard Alamouti scheme the assumption is made that the channel gains h00 and h01 are the same on the two cells in which a pair of constellations is transmitted from one of the transmitters. In an OFDM implementation, the two cells in question will normally be successive symbols on a given carrier. This is appropriate since OFDM systems are normally dimensioned such that the channel changes more gradually from one symbol to the next than from one carrier to its neighbour.

However, if there is a significant amount of Doppler shift or spread, there is a possibility that the assumption above will break down and the Alamouti calculation at the receiver will not correctly recover the two transmitted constellations. The result is cross-talk between the two constellations carried in the pair of cells, combined with mis-equalisation of the wanted constellation. It is possible to perform a more complicated calculation given that all four h's are known (h and h01 for the two symbols).

Our above UK Patent Application 0710665.1 describes with reference to Figs. 2 and 3 thereof how cells can be paired up for use of the Alamouti technique. The cells (carriers) for each successive pairs of symbols can be arranged to relate to the same service.

An alternative approach is to arrange the Alamouti pairs on adjacent carriers on the same symbol. This is illustrated in Fig. 3(a) of our above-mentioned UK Patent Application. Normally this would be a poor choice, since OFDM systems are generally dimensioned such that channel variation from one carrier to the next is greater than for one symbol to the next on the same carrier.

This is because OFDM can tolerate a relatively large delay spread as a fraction of the active symbol period (e.g. one quarter or more depending on the guard interval), but a much smaller Doppler spread as a function of symbol rate (e.g. about 5-10%). However, the parameters being considered for DVB-T2 include very long symbols with very small fractional guard intervals. In this case, the variation from one carrier to the next would be relatively small. In this case the symbol interleaving needs to be designed so as to keep the Alamouti pairs together. Fig. 3(b) of our earlier UK Patent Application shows the time/frequency grid after such "pair-wise" symbol interleaving. It will be noted that the cells for a given service still occur in neighbouring pairs. One advantage of this is that the symbol interleaver could be different on different symbols.

Exemplaiy implementation -transmitter An exemplary implementation is described in our above UK Patent Application with reference to Fig. 5 thereof, which is included as Fig. 1 of the present application. A block diagram of the transmitter (i.e. modulator) 10 is shown. At the input are the bit-streams corresponding to each of the services in the multiplex. Some services 12, shown at the top, may be conveyed by MIMO transmission, whilst others 14, shown at the bottom, are for non-MIMO delivery.

The MIMO services are partitioned into two streams as shown at 15, one stream to be carried on each of two transmitters. The detail of the second stream is not shown separately. Channel encoding and interleaving 16 is applied to each stream individually, and the encoded bits are then mapped onto constellations 18. For the non-MIMO (e.g. MISO) services, there is no partitioning, and the channel coding and interleaving 16, and constellation mapping 18, are applied as for the MIMO services.

The resulting non-MIMO constellations are then processed in order to provide two different constellation values for each cell, that is one for each transmitter. Two different options for this processing have been described, namely using Alamouti or phase mapping techniques. The chosen technique is indicated in Fig. 1 by the block 20 marked Alamouti mapping' to which the present invention relates One such block is provided for each non-MIMO service.

The resulting MIMO and processed non-MIMO/MISO constellations are then multiplexed together along with pilot values and ancillary information, using time and frequency-division multiplexing 22, as in a conventional OFDM transmitter. A pilot generator 24 generates inverted pilots where necessary on one of the transmitters, as well as any ancillary signalling. The multiplexed constellations and pilots from the multiplexer 22 are mapped onto OFDM carriers as in a conventional OFOM modulator, and the following stages of inverse FET 26, guard interval insertion 28, filtering 30, digital-to-analogue (DAC) conversion 34 and RF upconversion 36 are all performed as normal. The output is then sent to the respective transmitting antenna 38 Alamouti mapping Where, as shown, the Alamouti option is to be used, the block 20 in Fig. 1 is constituted by the circuit 40 illustrated in Fig. 2. Referring to Fig. 2, incoming constellations at input 42 are grouped into pairs as shown at 44. On the first symbol, two switches 46a and 46b are in the position shown, so that the two constellations are passed unmodified to outputs 54 and the time-and-frequency-division multiplexing blocks 22 of the two transmitters Txl and Tx2. On the second symbol, the switches 46a and 46b are placed in the other position so that the constellations are conjugated in circuit 48, one (only) is inverted in circuit 50, and both are routed to the transmitter that did not carry them on the first symbol.

A delay 52 of one symbol is included so that the same cells are camed on successive symbols.

The "form pairs" block 44 will normally contain internal buffering and only produces an output when required. It will be appreciated that this circuit delivers two constellations at a time at the output, but half as often as they arrive at the input, so that the net input and output rates are the same.

This assumes that the Alamouti implementation uses pairs of cells taken from a given carrier on successive symbols. If adjacent carriers on a given symbol are used instead, the symbol delays are replaced by delays corresponding to one carrier.

Exemplary implementation -receiver Fig 3 shows an overall block diagram of a single-input receiver 100. The stages of antenna 102, RF front end 104, A-to-D (analogue-to-digital) conversion 106, channel filtering 108, time synchronisation 110, FFT (fast Fourier transform) 112, and AFC (automatic frequency control) 114 are as in a conventional DVB receiver There is only a single receiver stage.

The received cells are then partitioned at 116 into pilots and data.

Furthermore the pilot cells are partitioned into the normal pilots and those pilots that are inverted on one of the transmitters. Interpolation is performed in frequency and time at 118 using any appropriate design of two-dimensional interpolation, so as to obtain an estimate of both h00+ h01 and h00-h01 that is the sum and difference of the channel gains for a pair of cells. These estimates are fed to an adder 120 and a subtractor 122 in order to derive estimates of the two channel responses h00 and h01 individually.

The two estimates are then fed together with the data cells to an equalisation block 124. The details of this block depend on which MISO method was employed at the transmitter and are described below. The output of the equalisation block consists of equalised constellations.

The subsequent demultiplex block 126 extracts the constellations belonging to the selected stream and passes these on to the channel decoding and de-iriterleaving processes 128, which are conventional; the exact details depend on the particular transmission standard being used.

Our above UK Patent Application 0710665.1 shows in Fig. 9 an equaliser that can be used in the equalisation block 124 in the case where the Alamouti technique is employed. It can be shown that Alamouti (ref. 5) has a number of advantages for use in DVB-T2, including improving reception in the overlap region of an SFN (single-frequency network).

The present invention One problem is that Alamouti, as normally presented, assumes that the channel response is essentially the same on the two OFDM cells forming a pair.

This is implicit in the above. It is generally supposed that the technique will be less than optimal if there is significant channel variation, and the parameters of the proposed transmission system would tend to be designed in order to ensure that the variation is small.

We have appreciated that an OFDM receiver will have available to it an estimate of all four potentially distinct complex channel gains, and that therefore it should in principle be possible to solve the resulting equations even if the channel changes arbitrarily between the two cells.

The original Alamouti scheme can be stated thus. On the first transmitter is transmitted (taOO r sO taOl) I.-Conjugate[slJ) (1) and on the second jtalO1 si I,tall) (conjugate[so]) (2) where, again, the first index is the transmitter index, and the second is the cell index. The received signal on each cell is the sum of the signals transmitted for that cell, multiplied by the corresponding complex channel gain h. (rhO -1h00 taOO + hlO talO + naO ! rbl) -hOl taOl + hil tall + nal) (3) The indices for the h's are the same as for the ta's. (That is, the indices for the h's in this Section of this specification have a different meaning from that used in the Section above headed "Background".) Here, hlO means the channel gain for the signal received from transmitter 1 during cell 0. Substituting for the ta's: (rbO (naO+hOOSO+hlOsl I rhi J -na1 + h11Con]ugatesO -hO1Conjugates1J (4) In the zero-forcing equaliser, the noise terms are ignored (set to zero) and the two equations solved for the two unknowns, sO and 51, in terms of the received values rb0 and rbl - This gives: rbfl Cunjuqate]kO1-f.h1O Conjugate frblj sO -hUV ConjwaterhOt1+ jkjJ CQnjIqaite[hii] -rbO Conjugate P111_hoe Conigate Irb11 ]kOIJ Conjugate(kOlJ4hlU Cn)ugateh11] (5) This equation (or these equations) now enables the construction of an equaliser for use in a receiver which will take account of time variations between cells in the channel characteristics. They use four channel gain values (hOl, hil, hiO, hil) for signals received from two transmitters (0, 1) in respect of two cells a (rb0, rbl) and two received values for the two received signals on the two cells, and provides the required outputs by taking the complex conjugate of selected ones of these values and normalising them with relation to the two channel gains by using products of the gains on the respective channels (the denominator in equation (5)) Implementation for non-st ationary channels The equations to be implemented by the receiver are presented in equation (5), above. The numerators require two complex multiplications each; the denominator is the same for both calculations and requires a further two complex multiplications. Each calculation involves one complex division. There are therefore six complex multiplications and two complex divisions to be performed for each pair of cells, i.e. three multiplies and one divide per cell.

The complex multiplications require four real multiplies each, whilst the complex division is a complex multiplication, two real multiplications and two real divisions. In total this comes to 3 x 4 + 4 + 2 = 18 real multiplications and two real divisions.

Using the terminology of equations (1) to (5), for the simple Alamouti decoder, the equations are: sO -1 (conjuqate[hoI rhO + hi ConjugaterhiJ sI -(AbsjhOOI2 +ithslhloJ2) !iConjugateh1JrbO_hOconjugater}j1J This is two complex multiplications plus one division by a real number per cell, plus four real multiplies to calculate the common denominator, i.e. two per cell. In total this gives 2 x 4 + 2 = 10 real multiplications and two real divisions per cell.

This can be compared to the non-Alamouti case familiar from conventional COFDM, in which each cell requires one complex division, resulting in 6 real multiplications and two real divisions. The comparison is therefore four extra real multiplications per cell for simple Alamouti compared to normal OFDM, and a further eight real multiplications for the full ZF (zero forcing) Alamouti equaliser. The number of real divisions, the most costly operation, is the same in each case. The extra eight multiplications per cell do not represent a serious increase in complexity when the demodulation and decoding process as a whole is considered, especially considering the performance benefit.

I

The calculations in this section are for the worst case. Further optimisations may well be possible.

Fig 4 shows a hardware implementation of the full-Alamouti equations implementing equation (5). This figure represents the circuitry that goes in place of the "equalisation" block 124 in Fig. 3. The blocks marked "conj" compute the complex conjugate of the input, also indicated by an asterisk (e g hOl*). The four h's come from the interpolation in frequency and time of normal and inverted pilots and the rb0 and rbl come from the partitioning block. The arrangement of multipliers (X), dividers (-), adders (+), subtractor (-), and conjugators (Conj.) is clearly set out in Fig. 4, and the person skilled in the art will not require a detailed textual description of their connections. In each divider the input which is the divisor is indicated by a small circle; the other input is the dividend. In the subtractor the input which is the inverting input is indicated by a small circle, the other input is the non-inverting input.

Thus it has been shown that the original constellations can be recovered from a signal transmitted using the Alamouti method, even if the channel changes between the two cells forming a pair. The expressions that have been derived implement a zero-forcing (ZF) equaliser. This is not necessarily the optimum in mean-squared-error (MSE) terms, but it gives no crosstalk between the two constellations in a pair.

It will be appreciated by those skilled in the art that the detailed implementation of the equaliser may take other equivalent f orms to that specifically shown in Fig. 4.

Non-stationary channel system performance Although the original constellations can be recovered without crosstalk, there is a penalty arising from the changing channel: the signal-to-noise ratios on the constellations are not as good as Alamouti achieves in the stationary case.

Considering again equation (5) above, we can now substitute for the received cells rbO and rbl from (3): (naO+hOO O) ConugatehO1J+k1O (sO Con]uqateIh11J+Cc,njugate(naj) sO -hOO ConjugatehO1J+h1O Conjugate thill -hOO s1ConjugatehO1J+(naOsh1o si) Conjugateh11J_hoo Conjugatena1J hOO ConjugatehO1j+h1O Conjugateh11J (6)

S

We can check that substituting zero for the noise terms naO and nal gives sO lush (7) as expected.

The error in the estimate is given by naO Conjugate (hOlJ +hlO Conjugate[nalJ sO sO -hOOCon)uqate(hOlJ+hloConjugatelhllJ -t.si) -naOConjugate(hllJ-hflOConjugate(nalJ hOD ConjugatehO1J+h1O Conjugateh11J (8) It will be noted that there are no crosstalk terms, i.e. the error in sO is not a function of si or vice versa. It is not a function of sO either. This is a result of using the zero-forcing equaliser. An MSE (mean squared error) equaliser would reduce the noise terms at the expense of introducing crosstalk and data-dependent error terms.

How the channel changes from one cell to the next will now be discussed.

The magnitudes of the channel gains in the first cell are defined as aO and ci, where: 1h0012= 02 and hi 012= 12 (9) Complex factors f by which each channel gain changes between the two cells are defined by: hOl = 30 hOO, (10) hll=131h10 (11) The SNR (signal to noise ratio) can now be calculated. For convenience we will consider only the first of the two transmitted constellations, sO. Because of the symmetry, the same result would be achieved if we took the second constellation.

The noise power is the expected value of the squared magnitude of the error: peO =E { J sb-so 2} (12) Substituting from (8), (10) and (11), sb -sO h1Ona1Conjugateh1O Conjugate(nalj + hOOh1O$OConjugatenaO Conjugatelnall naOnalConjugatejhoo) ConjugatefhlOj Conjugate($OJ hOO naO$OConjugatehOOJ ConjugatelnsOl Conjugate$Ol (13) It will be noted that only the ri's are random variables, and furthermore the noise terms are independent so that the expectation of the cross-terms is zero This leaves only the first and last terms when we take the expectation E { sb -sO 121 E (h10na1Conjugateh10J Conjugatena1J) + E (hOO na0 $0 Conjugateh0OJ Conjugate[naOJ Conjugate$OJ) (14) Letting the power of the noise term be pn, and substituting from (9) whence -" + cr02 $0 Conjugatej$0J) pe -(a02 $0 + cr12 $1) (cr02 Conjugate[$0J + cr12 Conjugate$1J) (15) If we suppose that the constellations sO and si have unit power, the signal-to-noise ratio is 1/pe0: -(cr02 $0 + cr12 $1) (cr02 Conjugate$0J + a12 Conjugate$1) -pn (a12 + cr02 $0 Conjugate[$0J) (16) In the stationary case, both s are equal to 1, so that a02 cr12 SNR (stationary) = + P" (17) But the transmitted constellations had unit power, and inspection of equation (4) reveals that hOOsO and hi isO were received; the received powers due to sO are therefore 1h0012 and hi 112 respectively on the two cells, and pn is the received noise power. Now, 1h0012= 002 from (9), and 1h1112= a12 l1I2 from (9) and (11). Recalling that 31=1, the two terms in (17) are therefore the two signal-to-noise ratios for sO. In other words, the (power) SNR is the sum of the two SNRs, provided that the channel responses do not change between the two cells making up a pair. This is the known Alamouti result: the SNR is the same as for maximum ratio combining (MRC).

If the channels do change we expect the result to be less good than for the stationary case, since the Alamouti scheme was optimised for the latter situation. Since Alamouti in a stationary channel is as good as MRC, we can get an idea of how much the performance is degraded by comparing the equalised SNR with the SNR that would be achieved for MRC, i.e. the sum of the two power SNRs. First, the SNR sum in the general case where 131 has both non-zero phase and non-unit amplitude is: a02 + a12 IthsI$112 Received SIIR. sum = Pfl (18) The SNR degradation is the SNR from equation (16) divided by the SNR sum from (18). It can be shown that: (a02$O + cr12 $1) (a02 Conjugate($OJ + cr12 Conjugate$1J) SNRdegradation (a12 + a02$O Conjuqate($O) (cr02 + a12 $1Conjugate$1J) (19) First it will be noted that the degradation is not a function of the noise level itself. We are therefore concerned only with the relationship between the SNRs and not their absolute values.

Let us define the (voltage) ratio of the two received signals (and therefore also the two SNRs) as r, so that alr aO.

Let us further define the 13s in polar form: 30=b0.e° and I31=b1.e Simplifying, we find b02 +.b12r2 + 2bOb1rCos['O -yl] StIR, degradation = (b02+r) (1+bl2r) (20) where we can also note that the degradation is a function only of the phase difference (yO -yl) between the p3's, not the absolute phase.

Let us assume that the channel from the first transmitter does not change significantly in amplitude, so that bO=1 This leaves us with bl, r, and (yO -yl).

The following description refers to the graphs of Figs. 5 to 12 to describe the system performance. In these graphs we assume that the amplitude of the second channel does not change (bl=1), and allow the phase to change. The ratio r of the two SNRs on the first cell will be varied as a parameter. The results are shown in Fig. 5.

This shows the penalty relative to the SNR sum due to phase change between cells. The path from the first transmitter (Txl) does not change at all between the two cells. The path from the second transmitter (Tx2) changes only in phase, by y, shown on the horizontal axis; its amplitude remains constant.

The Ly axis is labelled in fractions of a whole turn. On the first cell, the signal received from Tx2 is higher than that from Txl by a (voltage) factor of r. The vertical axis shows the SNR penalty resulting from the changing channel. The penalty is expressed relative to what would be obtained if the received power SNRs simply added as they do in the simple Alamouti case.

The graph is equally applicable if the phase of the path from Txl does change, but in this case the horizontal axis Liy represents the difference between the phase changes from the two transmitters (the difference between the phase differences).

If y=0, there is no penalty. This is not surprising if neither channel changes at all. there is no penalty because this is the simple Alamouti case.

However, the penalty remains at zero even if both channels change phase by the same (arbitrary) angle. This is easily understood, since all the receiver needs to do is to rotate the second cell back by y, whereupon the situation will be identical to the simple Alamouti case.

In all other cases there is some penalty. The penalty is worst when equal signal strengths are received from the two transmitters (r=0, top curve in Fig. 5).

Now, variation in phase will arise in one of two different ways depending on how the Alamouti pairs are chosen. If the two cells in question are assigned to the same carrier in successive symbols, the phase variation will be a result of Doppler. Conversely, if the cells are taken from a pair of neighbouring carriers in one symbol, then phase variation will be a result of delay.

Roughly speaking, the change in phase y in whole turns will be related to the Doppler as a fraction of the symbol rate, or the delay as a fraction of the active symbol period, respectively. This is because a frequency offset equal to the symbol rate would cause a rotation of one whole turn per symbol, and similarly a delay equal to the active symbol period corresponds to one rotation per carrier.

Note that these quantities should only be regarded as "related". Delays and Doppler do not really exist in isolation, because the receivers' time synchronisation or AFC respectively would correct for each. Rather, they exist as the result of multipath, i.e. the channel contains multiple echoes with different values of delay or different Doppler shifts. The individual paths exhibit the rotations across frequency or through time described above. However, the channel that we need to consider for the purposes of interpreting the graph is the combination of all the paths. Unfortunately, although the paths themselves combine linearly, their phases do not. Worse than this, the phase in the combined channel is likely to vary somewhat faster than the phases of the individual paths.

In the extreme case of a 0dB echo, the phase is discontinuous: it jumps by 180° at each null.

The nulled carriers are of course useless anyway, but the pairing intrinsic to Alamouti will mean that the bad cell effectively "contaminates" its partner.

With this warning in mind, consider a delay spread of Tu/4, the limit for ISI-free (inter-symbol interference-free) reception ri a one-quarter guard interval, the longest fractional guard interval being considered. The corresponding Doppler would be one quarter of the symbol rate, probably beyond what the system could tolerate for any reasonable echo level. The worst-case penalty, when the two signals are of equal strength, is 3dB. the SNR is exactly half what it would have been had the two signal powers combined. Put another way, the SNR is the same as it would be for one of the transmitters alone. Switching on the second transmitter has not done any harm.

The cases where the signals are of different strengths are more benign in terms of the penalty, so we can conclude that the effect of phase changes up to one quarter of a turn is not too serious.

The penalty increases monotonically as the phase change increases, and for equal powers it tends to infinity as the phase change approaches 180°. In effect, a change of 180° exactly uundoes the phase reversals deliberately introduced in the Alamouti process, and the resulting equations become linearly dependent.

Note that although only positive dB values have been plotted for r in Fig. 5, the curves for negative values are the same as the corresponding positive values. This is because a negative dB ratio can be recast as a positive ratio by swapping the labelling of the two transmitters and negating the phase change, and the graphs are symmetrical with regard to phase.

We will now allow the amplitude of the path from one transmitter only, say Tx2, to change on the second cell, whilst keeping the phase constant (or changing by the same amount for both transmitters). We will again assume that the path from the first transmitter does not change in amplitude.

The result is shown in Fig. 6. The horizontal axis shows bi, the amount by which the channel gain from Tx2 changes between the two cells, in dB. Again, a range of values of r are plotted; this time both negative and positive dB ratios have been included, because here it matters whether it is the stronger or weaker signal which changes its gain. There is a symmetry here too, but it is more complicated as will be appreciated from the figure.

I

A penalty of 3dB in the worst case occurs when the weaker signal gets stronger by about 15dB (or symmetrically if the stronger signal gets weaker by the same amount). Consideration needs to be given to what kind of amplitude change would be expected in real-life channels. Clearly a single path will correspond to a flat channel and there will be no amplitude variation. As before, the problems will arise when there are multiple paths Again, the 0dB echo case is the most extreme: at the nulls the channel response is zero so the change in gain between a nulled carrier and any other carrier will be infinite when expressed in dB.

Fig. 7 shows the gain change between frequencies one carrier-spacing apart for 0dB echoes of a range of delays. The horizontal scale is frequency, normalised such that the nulls occur at a spacing of 1 unit. For the echo at one quarter of the active symbol period, a significant proportion (about 14%) of the carriers exceed the 15dB change and so could suffer a 3dB penalty. In practice the situation could be worse if the delay is exactly one quarter, because one in four of the carriers might fall in the hole. In real life, the delay is unlikely to hit this value so precisely, allowing the carriers to explore the full range of the horizontal axis.

For the Tu/8 case the figure is around 10% of carriers changing by 15dB, and the proportion reduces as the delay decreases. When we remember that these are the carriers which are degraded relative to a single transmitter, and that the other carriers will see their SNR improved relative to the single-transmitter case, it seems likely that the performance would be broadly acceptable. It may be wise not to rely on Alamouti in the % guard interval configuration, but for shorter guard-interval fractions the gains should outweigh the losses.

Again, these are for the 0dB echo case whereas channels with weaker echoes will in general be more benign.

The situation where there is an equal amplitude change from both transmitters will now be considered. It will be recalled that, if the phases of both paths change by the same angle, this can be exactly undone in the receiver and there is no penalty compared to the stationary case. It might be thought that the same is true if both paths change amplitude by the same amount. This has been investigated by setting bO=bl and plotting the penalty against bO for a range of values of r, as in the previous sections.

Fig 8 shows such a graph It is seen that in fact there is a penalty, even though the receiver could undo the scale change and combine the cells using the simple Alamouti method. A better result might be obtained by umatching the transmitted powers to the channel gains, and transmitting more power on the cell with the greater gain, were that possible.

The normal Alamouti process, assuming a stationary channel, is described by: (sO 1 fCofljugatehOJ rbO +h1Conjugaterh1J i1 = (Abs[h00J2 +Ahs[h10J2) (conjugate[hl]rbo_hoconjugate[rblJ (21) What happens if this is applied in a varying channel will now be considered. Firstly we need to decide what value to use for the h's, since we have four distinct values and the formula assumes only two. We will assume here that the values for the first cell of the pair, hOO and hlO, are used for hO and hi respectively. It would probably be better to use a value interpolated between the two cells in some way, but this is sufficient for the present discussion.

Substituting from (4) for the rb's, we find, for s'O: naO Conjugate IhOOl hOO sOConjugatehooJ hlO slConjugate(hOOJ SlllpleAlamoutioutputo + + -AbslhOOJ2 * AbsfhlOJ2 AbsfhOOJZ AbslhlOl2 AbslhOOI2 + Abs(h10J2 hlO BlConjugatejholj hiC sOConjugateh11J h1OConJugatena1j + 6 AbsIhOOIZ $ AbslhlOl2 s(hOOJZ + AbsthlOJ2 AbsjhOOJ2 * AhB(hlOjZ The six terms represent three effects: the wanted straight-through path for sO, a noise term, and a crosstalk term from Si. Separating these out, we get for the straight-through term (i.e. the coefficient of sO): * bOO ConjugateLhOOJ + hlO Conjugateb11j slmpleAlamoutiThl,ougheajno = ____________________________________ -Jths(h00J2 + Pbs[h10J2 (22) This would ideally equal 1, since the output should be the original constellation point. We can measure the error by subtracting 1: * hlO (-Conjugatelhloj + Conjugate[hi1J) SmpleA1aJnoutjErrorO = _____________________________________ AbsLhOOjZ+AbsthlOJ2 (23) This confirms that there will be no error if the channel is stationary, since hlO=hii in this case.

For the crosstalk term (the coefficient of Si).

hlO (ConjugatehOO] -ConjugatehO1i) simpleAlamoutiCrosstalkOl = Ahs[h0012 +AbsIhlOJ2 (24) Again, the crosstalk will fall to zero if the gains hOO and hOl are equal.

The through-path error will now be considered. Making the various substitutions for r and the 13's from the above: r2 (-1+Conjugate[J31J) Sinip1eLlainoutiError0 1+r2 (25) Fig. 9 shows the error for the case where the phase of the second path changes, as described above. Immediately we can see that this approach is disastrous. The error is already at the 20dB level, approaching the failure point for 64QAM, at about 1.5% of the active symbol period or symbol rate as appropriate.

Fig. 10 shows the result for a gain change in the second path. Again, we have 20dB of error at about 1dB of amplitude change. Note that the through-path error doesn't depend on the change in the path from Txl, because of the pattern in which the constellations are carried on the cells and our decision to take our values for hO and hi from the first cell.

Considering crosstalk, and making the same substitutions for the crosstalk term, we find: r2Abst-1 +13012 Crosstalkpower = (1+rZ)2 (26) Note that this expression is for the squared magnitude of the crosstalk, not the complex voltage gain as for equation 25. This time the crosstalk depends on the change in the path from Txl, and not that from Tx2. The result for changes of phase and amplitude in the first path are shown in Fig. 11 and Fig. 12 respectively. The onset of crosstalk is slightly less severe than for through-path error, but we can tolerate only about 2.5% or 1.5dB respectively at the 20dB level.

The performance of the overall system may be degraded by naturally occurring channel variation, as will now be discussed.

It is most likely that DVB-T2 would apply Alamouti to pairs of cells adjacent in frequency on a given OFDM symbol. It appears that such a system may be able to tolerate echoes up to one-quarter of an active symbol period without the degradation being too great, although there is concern as to whether it could tolerate a 0dB echo. It might be better to use some of the larger suggested FFT sizes and consequently longer symbols in order to reduce the fractional delays. Echoes up to 1/8 of the active symbol should be tolerable even at the 0dB level.

Alamouti pairs could also be assigned to successive symbols on the same carrier, in which case the fractions of an active symbol period should be replaced by fractions of OFDM symbol rate. This would be less risky if larger guard interval fractions are used, but fits less well into the current DVB-T2 baseline

specification.

It will be appreciated that many modifications may be made to the specific arrangements described and illustrated, and in particular that equivalent or alternative implementations of the Alamouti equalisation circuits from those shown may be employed.

Claims (4)

I CLAIMS

1 An OFDM receiver for use as a MISO receiver, comprising means for receiving a transmitted signal at an antenna; means for subjecting the received signal to a fast Fourier transform; means for separating pilots from the received signal; and means for providing equalisation to the received signal, the equalisation employing diversity techniques; wherein the received cells each comprising one OFDM symbol on one carrier are received in pairs, and the equalisation means is adapted to make use of four channel gain values and the two received cells from two transmitters, and to provide the required outputs by taking the complex conjugate of selected ones of these values, multiplying by selected ones of the channel gains, and normalising them with relation to the two channel gains.

2 An OFDM receiver according to claim 1, in which the normalisation is effected with relation to squares of the moduli of the gains on the respective channels.

3. An OFDM receiver according to claim 1, in which the equalisation means generates outputs sO and si in accordance with the following: rbO ConjigateI]iflhI-ik1O ConpigaterbiJ -hOO ConjlLgateIhOtIthlU Ciiijuq.teh11.] -rbO Cja.gatGt]k11I-kOU Con)'iIgat(rb1I hOO Conjugat(hU1J+h1t Conjugath (hil] where rb0 and rbl are the pair of received cells, h is an estimate of the channel gain from each transmitter, where i is the transmitter index and j the cell index, and conjugate[X]' indicates the complex conjugate of X

4. An OFDM receiver for use as a MISO receiver substantially as herein described with reference to and as shown in Fig. 3 taken with Fig. 4 of the drawings.