The signal processing complexity has been significantly increased by the extension of the IEEE 802.11 standard to MIMO communication. Thus, the design of PHY layer ASICs compliant to the IEEE 802.11n standard is a non-trivial task. In order to provide insight into the signal processing steps required to implement a standard compliant transceiver, we introduced a generic transmitter in Section 2.1.1. Based on this generic transmitter, we explained all signal processing tasks required to generate a standard compliant transmit signal.
In the next subsection, we elaborated the frame formats and the IFS specified in the standard. Based on the frame format, we have seen that the header information has to be processed prior the subsequent part of the frame. Hence, a large delay in the processing of the header increases the buffer requirements in the PHY layer ASIC. We further explained that the IFS imposes stringent latency constraints to the transmitter and the receiver.
Based on the knowledge about the transmit signal and the stringent latency constraints, we presented a transmitter architecture in the first part of Section 2.2.2. We showed how the latency
ing module, residual CFO estimation and compensation have been discussed. For the subsequent RxSTProcessing module, the main signal processing task was defined and a strategy to reduce the receiver latency based on preprocessing was presented. Finally, the RxChannelCoding module, reversing the channel encoding performed at the transmitter was shortly discussed.
The implementation results in terms of area and error rate performance of the entire PHY layer ASIC have been presented in Section 2.2.3. Even with a low complexity MIMO detector the RxSTProcessing module proved to be the largest circuit component. While many publications discussing MIMO detectors focus on the actual detection circuit, we showed that a large portion of the computational complexity of a MIMO detector is in its preprocessing circuit.
Further, we showed in Section 2.3 that many typical preprocessing algorithms for MIMO de- tectors are based on matrix decomposition algorithms. Subsequently, we suggested a pipelined architecture for such linear algebra algorithms, being used to process a large number of channel matrices. This pipelined architecture was well suited to be integrated in PHY layer ASICs employing low latency FFT modules.
Eventually, we proposed for the pipelined architecture an implementation method. The proposed method allowed sweeping the number of clock-cycles used per module. This was enabled by implementing a parametizable design as well as a scheduler for the operations required to complete the task of each module. In a next step, we showed that the proposed implementation method enables a large Pareto-optimal front of achievable synthesis results near the AT-efficiency of the implementation with the best AT-efficiency. Therefore, the proposed design method allows to achieve an implementation that meets the important metrics for preprocessing circuits – throughput, initial latency, and block latency – with minimal area overhead.
3.1
Algorithmic Considerations for MMSE MIMO Detection and
Soft-Output Computation
The focus of this thesis is on fitting all the proposed implementations into the IEEE 802.11n compliant ASIC implementation, presented in Section 2.2. Therefore, we consider a MIMO- OFDM system, such as specified in IEEE 802.11n, with Ntxtransmit and Nrxreceive antennas,
where Nrxis larger or equal to Ntxand both are smaller than or equal to four. The bit-stream to be
transmitted is mapped to Ntx-dimensional transmit symbol vectors s ∈ ONtx, where O corresponds
to the underlying constellation points, corresponding either to BPSK, QPSK, 16-QAM or 64- QAM. The energy of the transmit symbol vector s is normalized, such that EhssHi = 1
NtxINtx,
where INtx is a Ntx × Ntx-dimensional identity matrix. Therefore, the input-output relation
per OFDM tone of the associated complex-valued base-band system for this MIMO-OFDM communication system is given by
y= Hs + n, (3.1)
where H is the Nrx× Ntx-dimensional complex-valued channel matrix, y corresponds to the
Nrx-dimensional received signal vector, and n is a zero-mean i.i.d. complex-valued Gaussian
noise vector of dimension Nrxwith variance σ2nper dimension. For this base-band system the
SNR is given as
SNR= Es/σ2n, (3.2)
A linear MIMO detector for a MIMO-OFDM communication system, such as the PHY layer ASIC presented in Section 2.2, computes a linear filter matrix W once per frame for each utilized OFDM tone. Based on this linear filter matrix W and the received symbol vector y, the linear detector computes for each OFDM tone an estimate ˜s of the transmitted symbol vector s according to the following equation
˜s= Wy, (3.3)
where for zero forcing (ZF) detection the filter matrix W is given by
W= H−1≈ (HHH)−1HH, (3.4)
and for the better performing linear MMSE detector the filter matrix W is given by
W= (HHH+ Ntxσ2nI)−1HH (3.5)
and corresponds to the regularized Moore-Penrose pseudo inverse of the channel matrix H.
Based on the output of the linear filter given in (3.3), two basic options exists to compute the output of the MIMO detector. If only hard-output MIMO detection is required for the system performance, then the resulting estimated vector ˜s is quantized to the nearest constellation point and the corresponding bits are output from the linear MMSE detector.
In coded systems, however, the error rate performance of the overall receiver can be improved over hard-output MIMO detection by computing the reliability of the computed estimates given by the log-likelihood ratio (LLR) for each bit. The LLR corresponds to the probability that the corresponding transmitted bit is one, divided by the probability that the bit corresponds to zero. For the lth bit in the kth spatial stream, this is given by
L(bl,k|˜sk)= log
P(bl,k = 1|˜sk)
P(bl,k = 0|˜sk)
!
. (3.6)
A low-complexity approximation of the LLR for that specific bit can be obtained from the output of the MMSE equalizer ˜s and the per-stream post-equalization signal to interference and noise ratio (SINR) ηkaccording to
L(bl,k|˜s) ≈ ηk· (min ˜a∈A0 l |˜s − ˜a|2− min ˜a∈A1 l |˜s − ˜a|2), (3.7)
where A0l and A1l denote the sets of constellation points for which the lth bit is zero or one, respectively. Hence, the approximation of the LLR corresponds to the difference of the distance of the non quantized output of the MMSE estimator to the nearest constellation point, encoding for that specific bit a one and the distance to the nearest constellation point encoding for the same