The invention will now be described, by way of example only, with reference to the accompanying drawings, in which:
a is an idealised representation of a constellation diagram for 16 QAM;
b is a representation of a the constellation diagram for 16 QAM between a transmitter and receiver with a complex channel gain;
a is a schematic representation of an initial step of enumeration across possible symbols sent from transmit antennas 3 and 4 of a four transmit antenna, four receive antenna MIMO architecture;
b is a schematic representation of a step of enumeration, subsequent to that of
c is a schematic representation of a final step of enumeration across possible symbols sent from transmit antennas 1 and 2 of the four transmit antenna, four receive antenna MIMO architecture; and
Referring now to
The transmission device 102 comprises an encoder 105, an interleaver 106, a serial to parallel converter 108 and mappers 110a-d, each mapper 110a-d having a corresponding transmit antenna 112a-d.
The encoder 105 channel codes source data using, for example Parallel Concatenated Convolutional Codes (PCCC), Serial Convolutional Codes (SCC) or Low Density Parity Checks (LDPC). The channel coded source data is then interleaved by the interleaver and divided into m parallel, independent data steams at the serial to parallel converter 108, in this example four data steams. The four parallel, independent data streams are converted to complex symbols having a plurality of bits, typically, according to Gray coded constellation mapping, by the mappers 110a-d. Thus, this transmission strategy incorporates Bit Interleaved Coded Modulation (BICM). An individual complex symbol is transmitted, simultaneously, by each of the transmit antennas 112a-d.
The transmitted signals pass across independent complex Gaussian distributed channels, typically in a rich scattering environment containing multiple, randomly arranged scatterers that may be stationary or mobile, to the reception device 104.
The reception device 104 comprises n, in this instance four but it could be more, or less, than four, receive antennas 114a-d, channel state information (CSI) estimators 116a-d and a demapper 118. The reception device also includes a parallel to serial converter 120, a deinterleaver 122 and a decoder 123.
Each receive antenna receives all of the symbols simultaneously transmitted from the transmit antennas via a MIMO channel. Thus each of the receive antennas 114a-d receives a composite signal containing superposed weighted components of each of the transmitted symbols. The specific weighting of each of the symbols is given by a channel gain value for the channel between a given transmit antennas and a given receive antenna.
If the individual channels between each given transmit antenna and each receive antenna is different each receive antenna will receive a different composite signal. It is this spatial diversity upon receive that allows a symbol determination to be achieved.
In order to determine what symbols were transmitted across the channels prior art systems determine the probability of a given symbol being transmitted from a given transmit antenna by marginalising the other transmitted symbols.
Consider the case of a four transmit antenna, for four receive antenna MIMO system transmitting 16-QAM (Quadrature Amplitude Modulation) symbols, i.e. symbols from a set of 16 possible symbols. In order to marginalise three of the transmitted symbols it is necessary to cycle through the set of sixteen possible symbol values for each of the three transmitted symbols, as shown below. This requires 163 probability calculations to be executed in order to determine the marginal probability of a transmitted symbol, Cj being a specific value, Sp. This process must be repeated for the given symbol having each of the sixteen possible symbol values leading to a total computational load of 164 probability calculations.
In order to calculate the probability of symbol S, having been received it is necessary to marginalise out the probabilities of the contributions from the other three transmitted symbols. This is achieved by summing the probabilites of all possible combinations of the other three transmitted symbols whilst holding C1=S1:
This must now be repeated to calculate the marginal probabilities for C1=S2 to S16 in order that all symbol probabilities are calculated. The SISO operates at bit level LLR values and therefore conversion from symbol probabilities to bit level LLR values is required.
An example of a LLR calculation for a single bit is:
In the general case for symbols, the probability of a symbol transmitted from a given antenna, jth, being one of a set of transmitted symbols, C at the given transmit antenna, j, where 1≦j≦m and Sp ε{S1,S2, . . . , S2
The sum of conditional probabilities, conditioned on the transmitted symbols, summed over all possible transmitted symbol combinations from all other transmit antennas is given by:
The whole process must be repeated for C2, C3 and C4 thus leading to a very computationally intensive process for the determination of received symbols.
Once the codewords, C1, C2, C3, C4, have been determined they are compared to codewords in a codebook, typically a look up table, in order to determine what bit sequence each of them correspond to, and this bit sequence is output from the receive unit.
However, considering the case of 16 QAM, and idealised received codeword constellation diagram consisting of all possible 16 symbols (S1-S16) in 16 QAM is show in
In the case of a soft decision systems an incorrect codeword may still be determined based upon the basis of a higher calculated marginal probability however, the determined codewords are compared to allowable sequences of codewords prior to conversion to output bits. This comparison allows non-allowable codeword sequences to be reviewed and errors to be corrected before conversions to an output bit level data stream.
In the physical case, each receive antenna will have an independent distorted symbol constellation for symbols received from a given transmit antenna as the channel between transmit and receive antennas is independent, see for example
As the statistical processes, i.e. the additive Gaussian white noise, that cause the deviation of the received symbol away from its ideal constellation position are independent of each other the probabilities of a given signal being transmitted from a given transmit antenna, and received at the receive antennas can be multiplied in order to yield a joint probability of a given set of signals being transmitted and received across all receive antennas, as follows:
Using current techniques it is still necessary to enumerate through all possible 164 values of C for each receiver as any variation in C causes a change in the mean received symbols at each receive antenna.
Referring now to
Typically, signals transmitted from the transmission device 202 are transmitted across a scatter rich transmission environment 215, which introduces spatial diversity upon receive into the signal received at the reception device 204.
The reception device 204 comprises a four of receive antennas 214a-d, channel state information (CSI) estimators 216a-d, a combined joint detector-decoder 218 and a hard decision making device 220, a slicer.
The receive antennas 214a-d are arranged to receive the signals transmitted from the transmit antennas 212a-d. The signals are passed to the joint detector-decoder unit 218 where statistics, usually in the form of a log likelihood ratio (LLR), are calculated to produce a likelihood of a particular symbol being present at a given point in a data stream, as will be described hereinafter. The statistics are passed to the hard decision making device 220 where they are processed to make a hard decision as to which symbols are present within the data stream from a set of possible transmitted symbols.
The joint detector-decoder unit 218 comprises a QR decomposition unit 221, which receives inputs from the receive antennas 214a-d and also channel state information (CSI) 222 from the CSI estimators 216a-d, a symbol probability processor 224, a symbol to bit LLR converter 225, a parallel to serial converter 226, a deinterleaver 228 and a SISO decoder 230.
The operation of the QR decomposition unit 221 is described immediately hereinafter.
A MIMO data channel can be represented by:
for a four transmit antenna, four receive antenna system.
where:
For the general case Y1 is the receiving signal at receive antenna i where 1≦i≦n and n is the number of receive antennas.
C is constructed from a matrix of mMc bits, where m is the number of transmit antennas and Mc is the number of bits per symbol. For example, for 16 quadrature amplitude modulation (16-QAM) Mc=4.
The matrix C for the four transmitter 16-QAM case is given by C,
η is a column vector of complex additive white Gaussian noise (AWGN) samples taken from a Gaussian distribution with zero means and variance per dimension, σ2 and is a function that is representative of noise within the system, both general thermal noise and component noise.
The channel gain matrix, H, can be described by an orthogonal matrix, Q, and a matrix, R, having an upper triangular structure, subject to the channel gain matrix being a full rank matrix, therefore, there is sufficient diversity within the channels. Such a description of the channel gain matrix is called a QR decomposition of the channel gain matrix.
therefore Q−1Y=RC+Q−1η
Q
−1
Y={tilde over (Y)}=RC+{tilde over (η)}
It should be noted that the statistics of the noise vector, η, are invariant under the transformation of Q−1 due to their being circularly symmetric.
In the general case and accounting for any previous decision made relating to transmitted symbol values the marginalised, conditional symbol probabilities are given by:.
where Ec≦x≦m with the constraint Ec limiting the vector C to C=[C2+1−Ec, Cx+2−Ec, . . . , Cx]
The third term of the numerator
is not included in an initial decision for Ĉm, based upon
As {tilde over (Y)} is distributed by {tilde over (η)} in the same way as Y is by η. Y can be described as follows:
As can be seen from the above {tilde over (Y)}4 is dependent only upon the matrix element R44. Thus, using the above arrangement it is possible to determine the most probable symbol, Sp, by enumerating only through, in the case of 16 QAM, the sixteen possibilities for the value of C4. Whilst this is theoretically possible it would only be acceptable when the signal to noise ratio is very high. This is because if the mean value of a specific channel gain, in this case represented by R44, is small the effect of noise in disrupting the channel will be significant.
It is usual to enumerate through the possible symbols over two channels, for example {tilde over (Y)}3 and {tilde over (Y)}4 in order to ensure that there is sufficient diversity within the enumerated channels so as to reduce the possibility of all three channel gains enumerated being small enough to be affected by noise. This arrangement reduces the complexity of determining transmitted symbols as, in the example discussed above, C1 and C2 are not required to determine C3 and C4.
Referring now to
The conditional symbol probability including Gaussian noise, is given by:
when this calculation is dependent solely upon transmit and receive antennas 3 and 4.
Now C is limited to {tilde over (C)}=[C3,C4], as shown in
The symbol with the highest conditional probability is selected by the symbol probability processor 224 as an estimated transmitted symbol transmitted from transmit antenna 4 and is given by:
Ĉ
4
=argMaxP(C4=Sp)
Spε{C1C2. . . C2M.}
In effect the joint probability calculation is simplified to:
by the exclusion of C1 and C2 from consideration.
Once C4 is determined as Sn this value can be fixed for all subsequent calculations as this merely affects the mean value of subsequent calculations:
The effect of fixing C4=Sn is shown in
As can be seen this conditional symbol probability calculation takes into account the previous symbol estimate made for Ĉ4 and transmit and receive antennas 2 and 3 are considered for this calculation. The third term in the numerator cancels out the interference from transmit antenna 4, shown in
A soft decision is now made for the symbol transmitted from transmit antenna 3 based upon the conditional probability of the most likely symbol to have been transmitted, Ĉj where j=3, in a similar manner as that for the symbol transmitted from antenna 4 as described hereinbefore.
Referring now to
The vector {tilde over (C)}=[C1,C2] is used to represent these conditional probabilities. The third term in the numerator cancels out the interference effects from antennas 3 and 4, shown in
Again the transmitted symbols are estimated as being the symbol with the largest calculated marginal, conditional probability.
The estimated symbols probabilities are converted to conditional bit probabilities at the symbol to bit LLR convertor 225 through the following:
where for 16-QAM:
b3b2b1b0
P(C1)=P(0000)
P(C2)=P(0001)
P(C3)=P(0010)
P(C4)=P(0011)
P(C5)=P(0100)
P(C6)=P(0101)
P(C7)=P(0110)
P(C8)=P(0111)
P(C9)=P(1000)
P(C10)=P(1001)
P(C11)=P(1010)
P(C12)=P(1011)
P(C13)=P(1100)
P(C14)=P(1101)
P(C15)=P(1110)
P(C16)=P(1111)
P(b0=0)=P(C1)+P(C3)+P(C5)+P(C7)+P(C9)+P(C11)+P(C13)+P(C15)
P(b0=1)=P(C2)+P(C4)+P(C6)+P(C8)+P(C10)+P(C12)+P(C14)+P(C16)
P(b1=0)=P(C1)+P(C2)+P(C5)+P(C6)+P(C9)+P(C10)+P(C13)+P(C14)
P(b1=1)=P(C3)+P(C4)+P(C7)+P(C8)+P(C11)+P(C12)+P(C15)+P(C16)
P(b2=0)=P(C1)+P(C2)+P(C3)+P(C4)+P(C9)+P(C10)+P(C11)+P(C12)
P(b2=1)=P(C5)+P(C6)+P(C7)+P(C8)+P(C13)+P(C14)+P(C15)+P(C16)
P(b3=0)=P(C1)+P(C2)+P(C3)+P(C4)+P(C5)+P(C6)+P(C7)+P(C8)
P(b3=1)=P(C9)+P(C10)+P(C11)+P(C12)+P(C13)+P(C14)+P(C15)+P(C16)
Thus, bit level log likelihood ratios (LLR's) can be given by the natural logarithm:
The bit level LLR's are fed into the parallel serial converter 226 where they are converted into a single stream and are then passed to the deinterleaver 228 which removes the effect of the interleaver 206 at the transmitter.
The decoder 230 maps iteratively decodes the stream of bit level LLR's as a soft output by use of a soft input soft output (SISO) algorithm, such algorithms include Maximum-A-Posteriori (MAP) or Low Density Parity Check (LDPC) algorithms.
Optionally, information obtained from the decoder 230 at each iteration is fed back into the conditional probability calculations, typically this is symbol probability information. This information is treated as a-priori information which increases the accuracy of the information obtained according to:
After a number of iterations, as few as ten have been shown to yield improvements in performance over prior art systems, final, hard, definitive, bit decisions are based upon the soft output values from the decoder 230.
The method detailed hereinbefore estimates which symbol is most likely to have been transmitted using the Maximum-A-Posteriori (MAP) criteria in which:
Referring now to
The apparatus and method described hereinbefore reduce the computational complexity of symbol determination by trading diversity upon receive against computational complexity.
Using the MAP criterion to form decisions as in this approach gives a retained diversity order in symbol estimation that is given by the enumeration constraint Ec.
The constraint Ec establishes smaller areas for symbol enumeration instead of using the whole channel matrix. Larger areas lead to a larger list of possible symbol candidates. Computational complexity is maintained within areas of equal size as the matrix is traversed. Enumeration are still related to the modulation mode utilised and is given by:
Γ=(2m
The approach provides a flexible LLR computation, which is not restricted to the number of transmit antennas used in the MIMO architecture but upon a predefined subset of the transmit antennas at the receiver. The use of feedback within the computational scheme results in an improved computational scheme in which detection and decoding are not disjointed. This is of importance as any improvement in detection yields an improvement in decoding results and vice-versa.
Number | Date | Country | Kind |
---|---|---|---|
0307471.3 | Apr 2003 | GB | national |
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/GB04/01386 | 3/31/2004 | WO | 00 | 2/23/2007 |