Performance Assessment of MIMO-BICM Demodulators based on System Capacity

In MIMO-BICM systems, the optimum demodulator is the soft-output maximum a posteriori (MAP) demodulator, which provides the channel decoder with log-likelihood ratios (LLRs) for the code bits.

Due to its high computational complexity, numerous alternative demodulators have been proposed in the literature. Applying the max-log approximation [7] to the MAP demodulator reduces complexity without significant performance loss and leads to a search for data vectors minimizing a Euclidean norm.

Exact implementations of the max-log MAP detector based on sphere decoding have been presented in [8]- [10]; sphere decoder variants in which the Euclidean norm is replaced with the ℓ ∞ norm have been proposed in [11], [12]. However, the complexity of sphere decoding grows exponentially with the number of transmit antennas [9]. An alternative demodulator that yields approximations to the true LLRs is based on semidefinite relaxation (SDR) and has polynomial worst-case complexity [13], [14].

Several demodulation schemes use a list of candidate data vectors to obtain approximate LLRs. The size of the candidate list offers a trade-off between performance and complexity. The candidate list can be generated using i) tree search techniques as with the list sphere decoder (LSD) [15], ii) lattice reduction (LR) techniques [16]- [20], or iii) bit flipping techniques, i.e., flipping some of the bits in the label of a data vector obtained by hard detection, e.g. [21].

MIMO demodulators with still smaller complexity consist of a linear equalizer followed by per-layer scalar soft demodulators. This approach has been studied using zero-forcing (ZF) equalization [22], [23] and minimum mean-square error (MMSE) equalization [24], [25]. The soft interference canceler (SoftIC) proposed in [26] iteratively performs parallel MIMO interference cancelation by subtracting an interference estimate which is computed using soft symbols from the preceding iteration.

Hard-output MIMO demodulators are alternatives to soft demodulators that provide tentative decisions for the code bits but no associated reliability information. Among the best-known schemes here are maximum likelihood (ML), ZF, and MMSE demodulation [27] and successive interference cancelation (SIC) [28]- [30].

In the context of MIMO-BICM, the performance of the MIMO demodulators listed above has mostly been assessed in terms of coded bit error rate (BER) using a specific channel code. These BER results depend strongly on the channel code and hence render an impartial demodulator comparison difficult. Equivalent “modulation” channel . . . . .

A block diagram of our MIMO-BICM model is shown in Fig. 1. The information bits b[q] are encoded using an error-correcting code and is then passed through a bitwise interleaver Π. The interleaved code bits are demultiplexed into M T antenna streams (“layers”). In each layer k = 1, . . . , M T , groups of Q code bits

where H[n] is the M R × M T channel matrix, and v[n] (v 1 [n] . . . v MR [n]) T is a noise vector with independent identically distributed (i.i.d.) circularly symmetric complex Gaussian elements with zero mean and variance σ2 v . In most of what follows, we will omit the time index n for convenience. At the receiver, the optimum demodulator uses the received vector y and the channel matrix H to calculate LLRs Λ l for all code bits c l , l = 1, . . . , R 0 , carried by x. In practice, the use of suboptimal demodulators or of a channel estimate Ĥ will result in approximate LLRs Λl . The LLRs are passed through the deinterleaver Π -1 and then on to the channel decoder that delivers the detected bits b[q].

Assuming i.i.d. uniform code bits (as guaranteed, e.g., by an ideal interleaver), the optimum soft MAP demodulator calculates the exact LLR for c l based on (y, H) according to [7]

Here, p(c l |y, H) is the probability mass function (pmf) of the code bits conditioned on y and H, X 1 l and X 0 l denote the complementary sets of transmit vectors for which c l = 1 and c l = 0, respectively (note that

), i.e., exponential in the number of transmit antennas. For this reason, several suboptimal demodulators have been proposed which promise near-optimal performance while requiring a lower computational complexity. The aim of this work is to provide a fair performance comparison of these demodulators.

In order for the information rates discussed below to have interpretations as ergodic capacities, we consider a fast fading scenario where the channel H[n] is a stationary, finite-memory process. We recall that the ergodic capacity with Gaussian inputs is given by [32]

(here, I denotes the identity matrix). The non-ergodic regime (slow fading) is discussed in Section III-D.

In a code

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